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| <?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1d1 20130915//EN" "JATS-archivearticle1.dtd"><article article-type="research-article" dtd-version="1.1d1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="hwp">eLife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">00960</article-id><article-id pub-id-type="doi">10.7554/eLife.00960</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research article</subject></subj-group><subj-group subj-group-type="heading"><subject>Ecology</subject></subj-group><subj-group subj-group-type="heading"><subject>Genomics and evolutionary biology</subject></subj-group></article-categories><title-group><article-title>Spatial self-organization favors heterotypic cooperation over cheating</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes" id="author-2296"><name><surname>Momeni</surname><given-names>Babak</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="corresp" rid="cor1">*</xref><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-3"/><xref ref-type="other" rid="par-4"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-5570"><name><surname>Waite</surname><given-names>Adam James</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="other" rid="par-2"/><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-2203"><name><surname>Shou</surname><given-names>Wenying</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="corresp" rid="cor2">*</xref><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-2"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><institution content-type="dept">Division of Basic Sciences</institution>, <institution>Fred Hutchinson Cancer Research Center</institution>, <addr-line><named-content content-type="city">Seattle</named-content></addr-line>, <country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Tautz</surname><given-names>Diethard</given-names></name><role>Reviewing editor</role><aff><institution>Max Planck Institute for Evolutionary Biology</institution>, <country>Germany</country></aff></contrib></contrib-group><author-notes><corresp id="cor1"><label>*</label>For correspondence: <email>bmomeni@fhcrc.org</email> (BM);</corresp><corresp id="cor2"><label>*</label>For correspondence: <email>wenying.shou@gmail.com</email> (WS)</corresp></author-notes><pub-date date-type="pub" publication-format="electronic"><day>12</day><month>11</month><year>2013</year></pub-date><pub-date pub-type="collection"><year>2013</year></pub-date><volume>2</volume><elocation-id>e00960</elocation-id><history><date date-type="received"><day>17</day><month>05</month><year>2013</year></date><date date-type="accepted"><day>04</day><month>10</month><year>2013</year></date></history><permissions><copyright-statement>© 2013, Momeni et al</copyright-statement><copyright-year>2013</copyright-year><copyright-holder>Momeni et al</copyright-holder><license xlink:href="http://creativecommons.org/licenses/by/3.0/"><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife00960.pdf"/><related-article ext-link-type="doi" id="ra1" related-article-type="article-reference" xlink:href="10.7554/eLife.00230"/><abstract><object-id pub-id-type="doi">10.7554/eLife.00960.001</object-id><p>Heterotypic cooperation—two populations exchanging distinct benefits that are costly to produce—is widespread. Cheaters, exploiting benefits while evading contribution, can undermine cooperation. Two mechanisms can stabilize heterotypic cooperation. In ‘partner choice’, cooperators recognize and choose cooperating over cheating partners; in ‘partner fidelity feedback’, fitness-feedback from repeated interactions ensures that aiding your partner helps yourself. How might a spatial environment, which facilitates repeated interactions, promote fitness-feedback? We examined this process through mathematical models and engineered <italic>Saccharomyces cerevisiae</italic> strains incapable of recognition. Here, cooperators and their heterotypic cooperative partners (partners) exchanged distinct essential metabolites. Cheaters exploited partner-produced metabolites without reciprocating, and were competitively superior to cooperators. Despite initially random spatial distributions, cooperators gained more partner neighbors than cheaters did. The less a cheater contributed, the more it was excluded and disfavored. This self-organization, driven by asymmetric fitness effects of cooperators and cheaters on partners during cell growth into open space, achieves assortment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.001">http://dx.doi.org/10.7554/eLife.00960.001</ext-link></p></abstract><abstract abstract-type="executive-summary"><object-id pub-id-type="doi">10.7554/eLife.00960.002</object-id><title>eLife digest</title><p>Cooperation between individuals of the same species, and also between different species, is known to be important in evolution. Large fish, for example, rely on small cleaner fish to remove parasites, while the small fish benefit from the nutrients in these parasites. However, cooperation can be undermined by other individuals or species who “cheat” by taking advantage of those who cooperate, without providing any benefits in return. For example, some cleaner fish cheat by biting off healthy tissue from their host, in addition to parasites.</p><p>Genetically-related individuals who cooperate by sharing identical benefits can combat cheaters by giving preferential treatment to their relatives (a process known as kin discrimination) or by staying close to the relatives to form clusters (kin fidelity). However, two genetically-unrelated populations that mutually cooperate by sharing different benefits cannot employ these methods to overcome cheaters. Instead they rely on either partner choice or partner fidelity feedback.</p><p>Partner choice – the approach adopted by cleaner fish and their hosts – relies on one population recognizing a signal from the other population and responding accordingly: for example, large fish observe cleaner fish and approach those that cooperate with their current host and avoid those that cheat. Partner fidelity feedback, on the other hand, relies on repeated interactions between the two populations providing an advantage in terms of evolutionary fitness to both: for example, organelles called mitochondria and chloroplasts live inside cells, helping the cells to harvest energy and providing energy for themselves and the host cells in the process. In some cases – such as the cooperation between figs and fig wasps, or between certain plants and the bacteria that fix nitrogen in their roots – researchers cannot agree if the populations are relying on partner choice or partner fidelity feedback.</p><p>Now Momeni et al. have used a combination of experiments on yeast and mathematical modeling to explore partner fidelity feedback in greater detail. They started by using genetic engineering techniques to produce two species of yeast that mutually cooperate, each providing a metabolite that is essential to the other, but are not able to recognize each other: this means that these populations cannot rely on partner choice to combat cheaters. Momeni et al. then observed how these two species interacted with each other and a third species of yeast that cheated by consuming one of the metabolites without releasing any metabolite of its own<bold>.</bold></p><p>Momeni et al. found that as long as there was space for the yeast cells to grow into, the two species that cooperated self-organized into mixed clusters, with the cheating species being excluded from these clusters. The self-organization was driven by a positive feedback loop involving the two species that cooperated, with each species helping to increase the fitness of the other. The results of Momeni et al. demonstrate that it is possible for two genetically unrelated populations to cooperate and combat cheaters without the use of partner choice.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.002">http://dx.doi.org/10.7554/eLife.00960.002</ext-link></p></abstract><kwd-group kwd-group-type="author-keywords"><title>Author keywords</title><kwd>cooperation</kwd><kwd>self-organization</kwd><kwd>pattern formation</kwd><kwd>community ecology</kwd><kwd>mutualism</kwd><kwd>spatial structure</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd><italic>S. cerevisiae</italic></kwd></kwd-group><funding-group><award-group id="par-1"><funding-source><institution-wrap><institution>National Institute of Health</institution></institution-wrap></funding-source><award-id>1 DP2 OD006498-01</award-id><principal-award-recipient><name><surname>Momeni</surname><given-names>Babak</given-names></name><name><surname>Shou</surname><given-names>Wenying</given-names></name></principal-award-recipient></award-group><award-group id="par-2"><funding-source><institution-wrap><institution>W M Keck Foundation</institution></institution-wrap></funding-source><principal-award-recipient><name><surname>Waite</surname><given-names>Adam James</given-names></name><name><surname>Shou</surname><given-names>Wenying</given-names></name></principal-award-recipient></award-group><award-group id="par-3"><funding-source><institution-wrap><institution>Gordon and Betty Moore Foundation</institution></institution-wrap></funding-source><award-id>GBMF 2550.01</award-id><principal-award-recipient><name><surname>Momeni</surname><given-names>Babak</given-names></name></principal-award-recipient></award-group><award-group id="par-4"><funding-source><institution-wrap><institution>Life Sciences Research Foundation</institution></institution-wrap></funding-source><principal-award-recipient><name><surname>Momeni</surname><given-names>Babak</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta><meta-name>elife-xml-version</meta-name><meta-value>2</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Two cooperative populations of yeast cells that cannot distinguish between cooperative partners and cheating intruders can still self-organize into clusters that exclude cheaters.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Cooperation, providing a benefit available to others at a cost to self, has been postulated to drive major transitions in evolution (<xref ref-type="bibr" rid="bib27">Maynard Smith and Szathmary, 1998</xref>). Cooperation may take place between similar individuals contributing and sharing identical benefits (homotypic cooperation) or between two populations exchanging distinct benefits such as in some forms of mutualism (heterotypic cooperation). Both homotypic and heterotypic cooperation are vulnerable to cheaters (<xref ref-type="bibr" rid="bib43">Turner and Chao, 1999</xref>; <xref ref-type="bibr" rid="bib40">Strassmann et al., 2000</xref>; <xref ref-type="bibr" rid="bib4">Bronstein, 2001</xref>; <xref ref-type="bibr" rid="bib35">Rainey and Rainey, 2003</xref>; <xref ref-type="bibr" rid="bib42">Travisano and Velicer, 2004</xref>). Cheaters exploit cooperative benefits without contributing their fair share and are therefore competitively superior to their cooperating counterparts. How might cooperation avoid being taken over by cheaters? The answer lies in ‘positive assortment’ (<xref ref-type="bibr" rid="bib14">Fletcher and Doebeli, 2009</xref>), in which benefit-supplying individuals interact more with other benefit-supplying individuals than with cheaters.</p><p>In homotypic cooperation that involves genetic relatives, positive assortment can be realized through ‘kin discrimination’, which is based on the active recognition and preferential treatment of more closely related individuals over distantly related ones (<xref ref-type="bibr" rid="bib36">Sachs et al., 2004</xref>). Positive assortment can also be realized through ‘kin fidelity’ (<xref ref-type="bibr" rid="bib36">Sachs et al., 2004</xref>). For example, restricted migration in a spatial environment causes homotypic cooperators and cheaters to cluster with their respective progeny. This clustering allows cooperators to preferentially interact with each other (<xref ref-type="fig" rid="fig1">Figure 1A</xref>, top). Both mechanisms of positive assortment can favor cooperation (<xref ref-type="bibr" rid="bib18">Hamilton, 1964a</xref>; <xref ref-type="bibr" rid="bib18a">Hamilton, 1964b</xref>; <xref ref-type="bibr" rid="bib28">Maynard Smith, 1964</xref>; <xref ref-type="bibr" rid="bib8">Chao and Levin, 1981</xref>; <xref ref-type="bibr" rid="bib33">Nowak and May, 1992</xref>; <xref ref-type="bibr" rid="bib13">Fletcher and Doebeli, 2006</xref>; <xref ref-type="bibr" rid="bib22">Kerr et al., 2006</xref>; <xref ref-type="bibr" rid="bib26">MacLean and Gudelj, 2006</xref>; <xref ref-type="bibr" rid="bib48">West et al., 2006</xref>; <xref ref-type="bibr" rid="bib25">Lion and Baalen, 2008</xref>; <xref ref-type="bibr" rid="bib52">Wild et al., 2009</xref>; <xref ref-type="bibr" rid="bib47">West and Gardner, 2010</xref>). A spatial environment may also impede homotypic cooperation by intensifying competition among cooperators (<xref ref-type="bibr" rid="bib41">Taylor, 1992</xref>; <xref ref-type="bibr" rid="bib53">Wilson et al., 1992</xref>; <xref ref-type="bibr" rid="bib50">West et al., 2002</xref>) and in certain cases, by potentially encouraging cheating strategies (<xref ref-type="bibr" rid="bib20">Hauert and Doebeli, 2004</xref>).<fig-group><fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.003</object-id><label>Figure 1.</label><caption><title>A spatial environment favors heterotypic cooperation over cheating.</title><p>(<bold>A</bold>) Top: clustering with self-type can favor homotypic cooperators (yellow) over cheaters (black). Bottom: clustering with self-type should not favor heterotypic cooperation since cooperator clusters (red) and competitively superior cheater clusters (blue) should have equivalent access to the heterotypic cooperative partner (green). (<bold>B</bold>) We engineered three yeast strains: a red-fluorescent <inline-formula><mml:math id="inf343"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> strain requiring lysine and releasing adenine; a green-fluorescent <inline-formula><mml:math id="inf344"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> strain requiring adenine and releasing lysine; and a cyan-fluorescent <inline-formula><mml:math id="inf345"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> strain requiring lysine and not releasing adenine. The three strains purely competed (‘Comp’) or additionally cooperated and cheated (‘Co&Ch’), depending on whether the medium contained or lacked adenine (‘Ade’) and lysine (‘Lys’), respectively. (<bold>C</bold>) In competitive communities, <inline-formula><mml:math id="inf1"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf2"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> dropped below the initial value of 1 (dotted line) during community growth due to the fitness advantage of <inline-formula><mml:math id="inf3"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf4"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. In contrast, <inline-formula><mml:math id="inf5"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf6"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> rose above 1 when the strains engaged in cooperation and cheating. Population ratios in experiments were measured using flow cytometry. All communities started from an initial density of 3000 total cells/mm<sup>2</sup> with the three strains at a 1:1:1 ratio on top of an agarose column (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>) and were analyzed after approximately six to eight generations (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref>). p Values are from the Wilcoxon signed rank test, comparing the median with 1.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.003">http://dx.doi.org/10.7554/eLife.00960.003</ext-link></p></caption><graphic xlink:href="elife00960f001"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.004</object-id><label>Figure 1—figure supplement 1.</label><caption><title>Community setup.</title><p>(<bold>A</bold>) Unless otherwise stated (see <bold>B</bold>), experiments and simulations were initiated by randomly distributing the three cell populations on top of a filter placed above an agarose column of equal size. The agarose column was 6 mm in diameter and 11 mm in height. (<bold>B</bold>) Alternatively, a 2 mm-diameter spot of cell mixture was deposited at the center of a membrane filter on top of an agarose pad (24 mm × 24 mm × 4 mm). In this configuration, the initial inoculum spot had ∼8 × 10<sup>4</sup> total cells/mm<sup>2</sup>. Unless otherwise stated, all communities were initiated from equal proportions of <inline-formula><mml:math id="inf430"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf431"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf346"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> populations.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.004">http://dx.doi.org/10.7554/eLife.00960.004</ext-link></p></caption><graphic xlink:href="elife00960fs001"/></fig><fig id="fig1s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.005</object-id><label>Figure 1—figure supplement 2.</label><caption><title>In experimental spatial communities, cooperators <inline-formula><mml:math id="inf347"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> are favored over cheaters <inline-formula><mml:math id="inf348"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>.</title><p>(<bold>A</bold>–<bold>D</bold>) In the communities of heterotypic cooperation and cheating (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>), the <inline-formula><mml:math id="inf349"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf350"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio increased over time before leveling off. The initial surface cell density was 3000 cells/mm<sup>2</sup> in (<bold>A</bold> and <bold>B)</bold> and 10<sup>4</sup> cells/mm<sup>2</sup> in (<bold>C</bold> and <bold>D)</bold>. The ratios did not change considerably in late stages of community growth (approximately six to eight generations in <bold>B</bold> and <bold>D</bold>) and were therefore used for reporting results (e.g., in <xref ref-type="fig" rid="fig1">Figure 1C</xref>). Since sampling was destructive, all data points were from independent communities grown to various times and generations. The consistency in the data trend highlights small variations among independent spatial communities. The leveling off of the <inline-formula><mml:math id="inf351"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf352"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio in later generations likely reflects the fact that by that time, not much open space is available for self-organization (<xref ref-type="fig" rid="fig7">Figure 7</xref>). As a reference, 10<sup>4</sup>/mm<sup>2</sup> is two generations away from confluence. (<bold>E</bold> and <bold>F</bold>) Unlike in (<bold>A</bold>–<bold>D</bold>) where the growth area was limited to the original inoculation domain (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>), the <inline-formula><mml:math id="inf353"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf354"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio continued to increase during later generations when the growth medium extended beyond the original inoculation domain (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>). The initial decrease in <inline-formula><mml:math id="inf357"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf358"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> suggests that <inline-formula><mml:math id="inf359"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was more starvation-tolerant and therefore fitter than <inline-formula><mml:math id="inf360"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in this lysine-limited environment before sufficient cell growth and spatial organization occurred. Exp: experiment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.005">http://dx.doi.org/10.7554/eLife.00960.005</ext-link></p></caption><graphic xlink:href="elife00960fs002"/></fig></fig-group></p><p>Heterotypic cooperation can occur between populations that are genetically related but phenotypically differentiated, such as between different cell types in a multicellular organism. Alternatively, heterotypic cooperation can involve two genetically unrelated populations (e.g., species) exchanging distinct benefits that are costly to produce. For example, legume plants supply organic carbon and other essential nutrients to rhizobia, and rhizobia reciprocate with fixed nitrogen (<xref ref-type="bibr" rid="bib44">Udvardi and Poole, 2013</xref>). Positive assortment in heterotypic cooperation can be achieved through ‘partner choice’ and ‘partner fidelity feedback’ (<xref ref-type="bibr" rid="bib6">Bull and Rice, 1991</xref>; <xref ref-type="bibr" rid="bib36">Sachs et al., 2004</xref>; <xref ref-type="bibr" rid="bib15">Foster and Wenseleers, 2006</xref>; <xref ref-type="bibr" rid="bib51">Weyl et al., 2010</xref>). In partner choice, active mechanisms (disruptable through for example mutational or pharmacological means) enable an individual to differentially reward cooperative instead of non-cooperative partners based on a signal. Thus, discrimination mediated by partner choice can occur in advance of exploitation (<xref ref-type="bibr" rid="bib6">Bull and Rice, 1991</xref>). For instance, in the mutualism between client fish and cleaner fish in which cleaner fish obtain food from removing client parasites, client fish recognize and avoid cheating cleaners that also bite healthy tissues (<xref ref-type="bibr" rid="bib5">Bshary, 2002</xref>). In partner fidelity feedback, fitness-feedback from repeated interactions ensures that aiding the partner helps self. Examples of partner fidelity feedback can be found in mutualism between hosts and their vertically transmitted symbionts, for example, between eukaryotes and their endosymbioic mitochondria and chloroplasts (<xref ref-type="bibr" rid="bib37">Sachs et al., 2011</xref>).</p><p>Natural heterotypic cooperative systems often benefit from a combination of partner choice and partner fidelity feedback. Often, for a particular system, it is challenging to determine which mechanism is mainly responsible for fending off cheaters. For instance, the mutualism between fig and fig wasp and between legume and rhizobia have been thought to employ partner choice by some investigators (<xref ref-type="bibr" rid="bib23">Kiers et al., 2003</xref>; <xref ref-type="bibr" rid="bib36">Sachs et al., 2004</xref>; <xref ref-type="bibr" rid="bib15">Foster and Wenseleers, 2006</xref>; <xref ref-type="bibr" rid="bib21">Jandér and Herre, 2010</xref>) and partner fidelity feedback by others (<xref ref-type="bibr" rid="bib51">Weyl et al., 2010</xref>).</p><p>In this study, using engineered yeast strains and mathematical models devoid of possibilities for partner choice, we examined how through partner fidelity feedback heterotypic cooperation between microbes may be protected against cheaters. Spatial environment, which facilitates repeated interactions between neighboring individuals, has been shown to promote heterotypic cooperation (<xref ref-type="bibr" rid="bib3">Boucher et al., 1982</xref>; <xref ref-type="bibr" rid="bib11">Doebeli and Knowlton, 1998</xref>; <xref ref-type="bibr" rid="bib54">Yamamura et al., 2004</xref>; <xref ref-type="bibr" rid="bib49">West et al., 2007</xref>; <xref ref-type="bibr" rid="bib19">Harcombe, 2010</xref>; <xref ref-type="bibr" rid="bib29">Mitri et al., 2011</xref>). However, the mechanism for how partner fidelity feedback unfolds in a spatial environment is not well understood. Specifically, how might spatial correlation in the tendency to contribute arise between genetically unrelated heterotypic cooperators when such correlation was initially absent (<xref ref-type="bibr" rid="bib16">Frank, 1994</xref>)? If population viscosity was the sole driving force, then clusters of cooperators and clusters of competitively superior cheaters would be expected to have equivalent access to clusters of heterotypic cooperative partners. This would seem to favor cheaters (<xref ref-type="fig" rid="fig1">Figure 1A</xref>, bottom). Instead, we show that in a spatial environment, asymmetric fitness effects of cooperators and cheaters on partners during cell growth into open space drives assortment. This emergence of non-random patterns from initially random spatial distributions, known as self-organization, automatically grants cooperators instead of cheaters more access to heterotypic cooperative partners, disfavoring cheaters. Thus, partner fidelity feedback through self-organization excludes cheaters without evolving recognition mechanisms.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>Environment-dependent engineered heterotypic cooperation and cheating</title><p>To examine how partner fidelity feedback unfolds in a spatial environment, we started with an engineered experimental system incapable of partner recognition (<xref ref-type="bibr" rid="bib38">Shou et al., 2007</xref>; <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). This system consisted of three reproductively isolated <italic>Saccharomyces cerevisiae</italic> strains: a green-fluorescent strain requiring adenine and releasing lysine (<inline-formula><mml:math id="inf7"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>), a red-fluorescent strain requiring lysine and releasing adenine (<inline-formula><mml:math id="inf8"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>), and a cyan-fluorescent strain requiring lysine and not releasing adenine (<inline-formula><mml:math id="inf9"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>). Release of lysine or adenine was caused by metabolite overproduction due to a mutation that made the first enzyme of the biosynthetic pathway (Lys21 and Ade4, respectively) insensitive to end-product inhibition (<xref ref-type="bibr" rid="bib2">Armitt and Woods, 1970</xref>; <xref ref-type="bibr" rid="bib12">Feller et al., 1999</xref>). <inline-formula><mml:math id="inf10"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> still produced adenine for itself at the wild-type level, but without the overproduction mutation, the adenine produced by <inline-formula><mml:math id="inf11"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was not sufficient to support the growth of <inline-formula><mml:math id="inf12"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (Figure supplement 6 in <xref ref-type="bibr" rid="bib38">Shou et al., 2007</xref>).</p><p>These strains engaged in different types of interactions depending on the environment. In minimal medium supplemented with abundant adenine and lysine, they competed for nutrients required by all three strains (e.g., glucose and nitrogen) and limited space (<xref ref-type="fig" rid="fig1">Figure 1B</xref>, ‘Comp’). In minimal medium without supplements, in addition to competition, <inline-formula><mml:math id="inf13"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf14"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> exchanged essential metabolites lysine and adenine (<xref ref-type="bibr" rid="bib38">Shou et al., 2007</xref>), while <inline-formula><mml:math id="inf15"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> consumed lysine without releasing adenine. Not overproducing adenine, <inline-formula><mml:math id="inf16"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> showed a ∼2% growth rate advantage over <inline-formula><mml:math id="inf17"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> when lysine was abundant (competition assay in Figure 1 of <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). In the absence of lysine, there was no significant difference in the death rates of <inline-formula><mml:math id="inf18"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf19"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (Figure S1 in <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). Finally, in media lacking lysine and adenine, binary cocultures of <inline-formula><mml:math id="inf20"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf21"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> could grow from low to high cell densities (Figure 1 in <xref ref-type="bibr" rid="bib38">Shou et al., 2007</xref>), whereas cocultures of <inline-formula><mml:math id="inf22"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf23"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> failed to grow (Figure supplement 6 in <xref ref-type="bibr" rid="bib38">Shou et al., 2007</xref>). These results collectively suggest that <inline-formula><mml:math id="inf24"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> acts as a cheater variant of <inline-formula><mml:math id="inf25"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). In other words, in the absence of supplements, cooperator <inline-formula><mml:math id="inf26"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and the competitively superior cheater <inline-formula><mml:math id="inf27"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> competed for the lysine supplied by the heterotypic cooperative partner (partner) <inline-formula><mml:math id="inf28"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig1">Figure 1B</xref>, ‘Co&Ch’). Cooperator <inline-formula><mml:math id="inf29"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> ‘reciprocated’ by releasing adenine, which is essential for partner <inline-formula><mml:math id="inf30"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, but cheater <inline-formula><mml:math id="inf31"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> did not release adenine.</p></sec><sec id="s2-2"><title>A spatial environment can stabilize heterotypic cooperation against cheaters</title><p>We first verified that a spatial environment could stabilize heterotypic cooperation against a competitively superior cheater in our system. We initiated experimental communities from randomly distributed equal proportions of the three cell populations on agarose pads (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>). During pure competition in the presence of supplemented adenine and lysine, the <inline-formula><mml:math id="inf32"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf33"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio dropped below the original value of 1 after approximately six to eight generations (<xref ref-type="fig" rid="fig1">Figure 1C</xref>), consistent with the known 2% growth advantage of <inline-formula><mml:math id="inf34"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf35"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). In contrast, during cooperation and cheating in the absence of adenine and lysine supplements, cooperating <inline-formula><mml:math id="inf36"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was favored over cheating <inline-formula><mml:math id="inf37"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig1">Figure 1C</xref>, time course in <xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref>).</p><p>If the spatial aspect of the environment is disrupted, either by periodically mixing a community or by growing it as a well-mixed liquid coculture, partner fidelity feedback should not operate and cheaters are expected to be favored over cooperators. However, the ratio of cooperators <inline-formula><mml:math id="inf38"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> to cheaters <inline-formula><mml:math id="inf39"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> in periodically mixed replicate communities varied dramatically (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). This was because the lysine-limited environment strongly selected for adaptive mutants in <inline-formula><mml:math id="inf40"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf41"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). Thus, <inline-formula><mml:math id="inf42"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf43"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> engaged in an ‘adaptive race’ (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>) akin to clonal interference: if <inline-formula><mml:math id="inf44"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> had the best mutation to grow under lysine limitation, then the coculture was quickly destroyed by cheaters; if <inline-formula><mml:math id="inf45"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> had the best adaptive mutation, then the coculture quickly purged cheaters. As a result, <inline-formula><mml:math id="inf46"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> outcompeted <inline-formula><mml:math id="inf47"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="inf48"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> outcompeted <inline-formula><mml:math id="inf49"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> depending on which population had a better mutation, not because of social interactions. This kind of phenomenon has also been observed for non-engineered cooperating and cheating microbes (<xref ref-type="bibr" rid="bib32">Morgan et al., 2012</xref>). We chose two evolving cocultures in which the <inline-formula><mml:math id="inf50"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> populations were increasing in frequency, When we grew these two cocultures in well-mixed and in periodically perturbed spatial environments, <inline-formula><mml:math id="inf51"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was favored (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>; ‘Materials and methods’). However, in a spatial environment, <inline-formula><mml:math id="inf52"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was favored (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>), consistent with previous experiments on a different microbial system (<xref ref-type="bibr" rid="bib19">Harcombe, 2010</xref>). Our experiments involved non-clonal and non-isogenic populations. In nature, cheaters can be of different species (such as the non-pollinating wasps of fig) and therefore not isogenic with their cooperating counterpart. Additionally, upon environmental stresses, originally isogenic cooperators and cheaters can quickly acquire different mutations and become nonisogenic (<xref ref-type="bibr" rid="bib32">Morgan et al., 2012</xref>; <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). Regardless, we resorted to mathematical models to eliminate the confounding influence of adaptive mutations.</p><p>We extended a three-dimensional individual-based model of community growth (previously described as the ‘diffusion model’ in <xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>) to include cooperators, cheaters, and heterotypic partners. The main assumptions of this model were: (1) that the growth of individual cells depended on consumption of the limiting metabolite, and the consumption rate in turn depended on the local concentration of the limiting metabolite according to Michaelis–Menten kinetics; (2) that spatial distribution of metabolites was governed by release, diffusion, and consumption; and (3) that cells rearranged when necessary to accommodate new cells as per experimental observations (‘Materials and methods’). Parameters of this model (such as the rates of growth, death, and metabolite consumption and release) were experimentally determined (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>), mostly through characterizing properties of monocultures (<xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). <inline-formula><mml:math id="inf53"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was assumed to have a constant intrinsic fitness advantage over <inline-formula><mml:math id="inf54"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> at all lysine concentrations, as modeled by a higher maximum uptake rate (<inline-formula><mml:math id="inf55"><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> in ‘The diffusion model’ in ‘Materials and methods’). In the absence of adaptations, simulation results confirmed that a spatial environment favored cooperators over cheaters and that disrupting the spatial aspect of the environment gave cheaters an advantage over cooperators (<xref ref-type="fig" rid="fig2">Figure 2</xref>).<fig-group><fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.006</object-id><label>Figure 2.</label><caption><title>In simulated communities, a spatial environment is required to promote heterotypic cooperation.</title><p>The <inline-formula><mml:math id="inf56"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf57"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios of simulated (‘Sim’) spatial cooperating and cheating communities were grown either unperturbed (purple circles) or periodically mixed (orange squares). To simulate periodic mixing, the arrangement of cells was completely randomized every 12 hr. In each mixing event, the concentration of adenine and lysine throughout the community was assigned to be the average value over the entire community. Error bars show the standard deviation of ratios in six independent communities. The solid black line shows the ratio in a simulated well-mixed liquid coculture using the same parameters as simulated communities on agarose (<xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). The fitness advantage of cheater over cooperator was either 2% (top panel) or 8% (bottom panel).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.006">http://dx.doi.org/10.7554/eLife.00960.006</ext-link></p><p><supplementary-material id="SD1-data"><object-id pub-id-type="doi">10.7554/eLife.00960.007</object-id><label>Figure 2—source data 1.</label><caption><title>Parameter values used in the diffusion model simulations.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.007">http://dx.doi.org/10.7554/eLife.00960.007</ext-link></p></caption><media mime-subtype="xls" mimetype="application" xlink:href="elife00960s001.xls"/></supplementary-material></p></caption><graphic xlink:href="elife00960f002"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.008</object-id><label>Figure 2—figure supplement 1.</label><caption><title>Stochastic cheater outcomes in periodically mixed communities of ancestral cooperators, cheaters, and partners.</title><p>The <inline-formula><mml:math id="inf361"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf362"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios diverged in six replicate experimental communities periodically mixed during growth. Cell migration during mixing allowed the mutant type most adapted to the low-lysine environment to sweep through the entire community. The most adaptive mutation could occur in either <inline-formula><mml:math id="inf341"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="inf342"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, which led to stochastic outcomes similar to those observed in well-mixed liquid cocultures (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). We started these communities from a spot at a density of ∼8 × 10<sup>4</sup> total cells/mm<sup>2</sup> (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>) and physically mixed them daily (approximately every two generations) using a glass rod. The cells attached to the glass rod (estimated to be ∼10% of the community population) were suspended in water and analyzed using flow cytometry. Exp: experiment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.008">http://dx.doi.org/10.7554/eLife.00960.008</ext-link></p></caption><graphic xlink:href="elife00960fs003"/></fig><fig id="fig2s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.009</object-id><label>Figure 2—figure supplement 2.</label><caption><title>A spatial environment is required to favor heterotypic cooperation over cheating.</title><p>(<bold>A</bold>) To preadapt cooperators and cheaters in the lysine-limited coculture environment so that no new mutations of large fitness benefits could quickly arise, we started eight well-mixed replicates (marked by different symbols) consisting of <italic>rsp5</italic> <inline-formula><mml:math id="inf365"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <italic>rsp5</italic> <inline-formula><mml:math id="inf366"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and the ancestral <inline-formula><mml:math id="inf367"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>(‘Materials and methods’). The <italic>rsp5</italic> mutation was previously found to be highly adaptive for the lysine-requiring cells in a lysine-limited environment (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). The initial stochastic phase was indicative of additional rounds of adaptive races (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>) between <italic>rsp5</italic> <inline-formula><mml:math id="inf368"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>and <italic>rsp5</italic> <inline-formula><mml:math id="inf369"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. After 250 hr, the <inline-formula><mml:math id="inf370"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf371"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios showed steady trends, suggesting no additional rapid adaptive races. Two of these cultures (brown) that had <inline-formula><mml:math id="inf372"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf373"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios close to 1:1 were revived from frozen stocks. (<bold>B</bold>) In the two revived cocultures where the evolved populations were denoted with a “ <bold>ʹ</bold> ”, <inline-formula><mml:math id="inf374"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf375"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> continued to decline steadily. The broken axis indicates the period of time elapsed during which a small revived inoculum (30 μl frozen stock into 200 μl minimal medium and then expanded to 2 ml minimal medium) grew to detectable densities. (<bold>C</bold>) When preadapted communities were grown unperturbed on agarose pads, cooperators were favored as communities grew (purple circles). In contrast, cheaters were favored when the spatial aspect of the environment was either disrupted (daily mixing after day 5, orange squares) or absent (well-mixed liquid cocultures, black diamonds). We started all spatial communities at ∼8 × 10<sup>4</sup> total cells/mm<sup>2</sup> in a ∼2 mm-diameter spot (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>) and liquid communities at 5 × 10<sup>5</sup> total cells/ml in 3 ml SD. Exp: experiment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.009">http://dx.doi.org/10.7554/eLife.00960.009</ext-link></p></caption><graphic xlink:href="elife00960fs004"/></fig></fig-group></p><p>During spatial growth of the yeast community, ancestral <inline-formula><mml:math id="inf58"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf59"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> should also engage in an adaptive race to adapt to the lysine-limited environment. However, unlike in the liquid environment, mutants in <inline-formula><mml:math id="inf60"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf61"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> were spatially restricted to the neighborhood of their origins, and thus these mutants could not sweep through the entire community. Consequently, population dynamics from different replicates were highly reproducible (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2</xref>). Thus, we used ancestral <inline-formula><mml:math id="inf62"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf63"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> for all other experiments.</p></sec><sec id="s2-3"><title>Differential spatial association with partner favors heterotypic cooperation over cheating</title><p>How might a spatial environment promote heterotypic cooperation? The relative positioning of cells in a community, the ‘spatial pattern’ of a community, can develop differently based on the fitness effects of cell–cell interactions (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Due to the inability of confocal or two-photon microscopy to yield three-dimensional patterns of cells in yeast communities, we only had access to the top-views (xy) and vertical cross-sections (z), with the latter being obtained through cryosectioning (<xref ref-type="bibr" rid="bib31">Momeni and Shou, 2012</xref>). In vertical cross-sections, we have previously shown that in the absence of adenine and lysine supplements, <inline-formula><mml:math id="inf64"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf65"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> as a strongly cooperative pair (i.e., there is a large fitness gain from interacting with the other population) are expected to spatially mix (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). In contrast, <inline-formula><mml:math id="inf66"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf67"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, a competing pair, should form segregated columns, with each column consisting primarily of a single cell type (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Finally, for the commensal pair <inline-formula><mml:math id="inf68"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf69"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> in which each <inline-formula><mml:math id="inf70"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cell can support the local growth of multiple <inline-formula><mml:math id="inf71"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cells, <inline-formula><mml:math id="inf72"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> is expected to grow over <inline-formula><mml:math id="inf73"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). However, it is unclear what patterns would form when the three strains grow together in a community and how the patterns might impact cooperators and cheaters differently.</p><p>To examine how cooperation and cheating might affect community patterns, we compared communities grown in a spatial environment under conditions of competition (‘Comp’) or cooperation and cheating (‘Co&Ch’) (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Specifically, equal proportions of <inline-formula><mml:math id="inf74"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf75"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf76"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cells were randomly distributed on top of an agarose surface and allowed to grow. Top-views of experimental (‘Exp’) communities grown in the presence of adenine and lysine supplements revealed that <inline-formula><mml:math id="inf77"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf78"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf79"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, when engaged in pure competition, were evenly distributed in the horizontal xy plane (<xref ref-type="fig" rid="fig3">Figure 3A</xref>, top panel). This pattern was caused by the initial cells growing into microcolonies which, after running into each other, were forced to grow upward (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1A</xref>) (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Indeed, vertical cross-sections exhibited patterns consistent with our expectations that competitive populations should form segregated columns (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>) (<xref ref-type="fig" rid="fig3">Figure 3A</xref>, bottom panel).<fig-group><fig id="fig3" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.010</object-id><label>Figure 3.</label><caption><title>Growing cells self-organize to exclude cheaters from heterotypic cooperators.</title><p>(<bold>A</bold> and <bold>B</bold>) Experimentally, as the initially randomly distributed cells grew, different patterns emerged depending on whether the medium contained or lacked adenine and lysine supplements and consequently whether the dominant cell-cell interaction was respectively competition (‘Comp’) or cooperation and cheating (‘Co&Ch’). Top-views: ‘xy’; vertical sections: ‘z’. (<bold>C</bold>) Compared to <inline-formula><mml:math id="inf80"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf81"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> had a higher level of association with <inline-formula><mml:math id="inf82"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> during cooperation and cheating (<inline-formula><mml:math id="inf83"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>> 1) but not during competition. In (<bold>C</bold>), the communities were analyzed after approximately six to eight generations. (<bold>D</bold>, <bold>E</bold> and <bold>F</bold>) We observed similar results in the simulated communities. In simulated top-views, higher color intensity indicates a greater number of cells of the corresponding fluorescent color stacked at that position. In simulated vertical cross-sections, low and high color intensity represent dead and live cells, respectively. Scale bar: 100 μm. In <bold>C</bold> and <bold>F</bold>, grey: competition; magenta: cooperation and cheating. p Values are from the Mann–Whitney <italic>U</italic>-test. All communities started from an initial density of 3000 total cells/mm<sup>2</sup> (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.010">http://dx.doi.org/10.7554/eLife.00960.010</ext-link></p></caption><graphic xlink:href="elife00960f003"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.011</object-id><label>Figure 3—figure supplement 1.</label><caption><title>Cooperation-cheating and pure competition led to distinct community patterns in top-views.</title><p>(<bold>A</bold>) On media supplemented with adenine and lysine, <inline-formula><mml:math id="inf376"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf377"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf378"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> competed for shared resources. Individual cells initially grew into microcolonies (hour 5) and expanded until they reached other microcolonies (hours 9–13). Subsequent growth was mainly in the vertical direction due to physical constraints (hour 46), and top-view patterns remained static (hours 46–120). (<bold>B</bold>) On media not supplemented with adenine or lysine, <inline-formula><mml:math id="inf379"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf380"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> were the heterotypic cooperative pair and <inline-formula><mml:math id="inf381"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was the cheater. After small microcolonies formed (hour 81), the positive feedback between <inline-formula><mml:math id="inf382"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf383"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> led to the formation of pods consisting of mixed heterotypic cooperators (red and green) surrounded by isolated patches of cheaters (blue) (hours 101–171). All parameters in simulations are similar to those in <xref ref-type="fig" rid="fig3">Figure 3</xref>. ‘Sim w/delay’ incorporated a 60 hr delay in the death of <inline-formula><mml:math id="inf384"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and in the consequent release of lysine according to experimental observations (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). This simulation generated results qualitatively similar to simulations without incorporating the delay (‘Sim’). For generality, we opted to use simulations without such a delay throughout the paper. Scale bar: 100 μm. Co&Ch: cooperating and cheating; Comp: competing; Exp: experiment; Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.011">http://dx.doi.org/10.7554/eLife.00960.011</ext-link></p></caption><graphic xlink:href="elife00960fs005"/></fig><fig id="fig3s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.012</object-id><label>Figure 3—figure supplement 2.</label><caption><title>The partner association indexes in simulated communities showed more association between <inline-formula><mml:math id="inf385"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf386"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> than between <inline-formula><mml:math id="inf387"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf388"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> during cooperation and cheating but not during competition.</title><p>(<bold>A</bold>) Quantifying the partner association index in top-views (‘xy’) and vertical cross-sections (‘z’) of simulated communities shows trends similar to the experimental results in <xref ref-type="fig" rid="fig3">Figure 3C</xref>. (<bold>B</bold>) When quantified using a three-dimensional neighborhood, the partner association indexes showed similar results as in (<bold>A</bold>). The partner association indexes are less variable when averaged across each three-dimensional community using a three-dimensional neighborhood instead of across each two-dimensional slice of a community using a two-dimensional neighborhood (compare <bold>B</bold> with <bold>A</bold>). Co&Ch: cooperating and cheating; Comp: competing; Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.012">http://dx.doi.org/10.7554/eLife.00960.012</ext-link></p></caption><graphic xlink:href="elife00960fs006"/></fig></fig-group></p><p>In the absence of adenine and lysine supplements, the three populations engaged in heterotypic cooperation and cheating in addition to competition for shared resources. Top-views of these experimental communities showed patterns distinct from those of purely competitive communities. Regions dominated by a mixture of the cooperating pair <inline-formula><mml:math id="inf84"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf85"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> appeared isolated from regions dominated by the cheater <inline-formula><mml:math id="inf86"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig3">Figure 3B</xref>, top panel and <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1B</xref>). Vertical cross-sections of these communities revealed that cooperating <inline-formula><mml:math id="inf87"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf88"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> intermixed and formed tall ‘pods’. In contrast, cheating <inline-formula><mml:math id="inf89"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was relegated to the periphery of these pods and grew relatively poorly (<xref ref-type="fig" rid="fig3">Figure 3B</xref>, bottom panel).</p><p>To quantify differential partner association, the result of partner fidelity feedback, we define ‘partner association index’ <inline-formula><mml:math id="inf90"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>: for those <inline-formula><mml:math id="inf91"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf92"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cells bordering at least one other cell type (‘Materials and methods’), <inline-formula><mml:math id="inf93"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> is the ratio of the average number of <inline-formula><mml:math id="inf94"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in the immediate neighborhood of <inline-formula><mml:math id="inf95"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> to the average number of <inline-formula><mml:math id="inf96"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in the immediate neighborhood of <inline-formula><mml:math id="inf97"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. A partner association index <inline-formula><mml:math id="inf98"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>> 1 indicates more <inline-formula><mml:math id="inf99"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> neighbors surrounding <inline-formula><mml:math id="inf100"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> than surrounding <inline-formula><mml:math id="inf101"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. Using a two-dimensional neighborhood to quantify <inline-formula><mml:math id="inf102"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> in top-views and vertical cross-sections, we found that <inline-formula><mml:math id="inf103"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> significantly exceeded 1 during cooperation and cheating but not during competition (<xref ref-type="fig" rid="fig3">Figure 3C</xref>). This self-organization—the formation of non-random patterns from initially randomly distributed individuals purely driven by internal local interactions (<xref ref-type="bibr" rid="bib7">Camazine et al., 2003</xref>; <xref ref-type="bibr" rid="bib39">Solé and Bascompte, 2006</xref>)—automatically makes <inline-formula><mml:math id="inf104"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> partner more accessible to cooperating <inline-formula><mml:math id="inf105"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> than to cheating <inline-formula><mml:math id="inf106"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>.</p><p>Similar to the experiments, top-views and vertical cross-sections in the communities simulated through the diffusion model (‘Sim’) also showed that cooperating <inline-formula><mml:math id="inf107"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf108"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> preferentially associated with each other and formed tall pods, while cheating <inline-formula><mml:math id="inf109"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was isolated (<xref ref-type="fig" rid="fig3">Figure 3E</xref>). Such self-organization was absent in pure competition (<xref ref-type="fig" rid="fig3">Figure 3D</xref>). We quantified the partner association index of simulated communities using a three-dimensional neighborhood averaged across the entire community (<inline-formula><mml:math id="inf110"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>), which turned out to be much less variable than analyzing two-dimensional slices (<xref ref-type="fig" rid="fig3s2">Figure 3—figure supplement 2</xref>). During cooperation and cheating, <inline-formula><mml:math id="inf111"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> increased from an initial value of 1 to a steady level greater than 1 (<xref ref-type="fig" rid="fig3">Figure 3F</xref>, top). This greater-than-1 <inline-formula><mml:math id="inf112"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> favored cooperating <inline-formula><mml:math id="inf113"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over cheating <inline-formula><mml:math id="inf114"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, as the ratio <inline-formula><mml:math id="inf115"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf116"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> continued to increase even after <inline-formula><mml:math id="inf117"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> had leveled off (<xref ref-type="fig" rid="fig3">Figure 3F</xref>, bottom). In contrast, during pure competition, <inline-formula><mml:math id="inf118"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was close to 1 and <inline-formula><mml:math id="inf119"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was favored over <inline-formula><mml:math id="inf120"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig3">Figure 3F</xref>).</p></sec><sec id="s2-4"><title>Self-organization can in theory discriminate among cooperators of varying quality</title><p>In addition to generating information difficult to obtain from experimental communities (such as the detailed time course of <inline-formula><mml:math id="inf121"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> described above), simulations enabled us to explore a broader class of cooperator–cheater communities. Simulations showed that self-organization also allowed discrimination among cooperators of varying quality (<xref ref-type="fig" rid="fig4">Figure 4</xref>). Specifically, we initiated diffusion-model simulations using three populations: <inline-formula><mml:math id="inf122"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf123"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf124"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. The adenine release rate of <inline-formula><mml:math id="inf125"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was a fraction <bold>d</bold> (< 1) of that of <inline-formula><mml:math id="inf126"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and like <inline-formula><mml:math id="inf127"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf128"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> had a constant growth rate advantage over <inline-formula><mml:math id="inf129"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> at all lysine concentrations. When grown in the absence of supplements, <inline-formula><mml:math id="inf130"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> were isolated and outcompeted by <inline-formula><mml:math id="inf131"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. This effect was quantitative, as a lower <bold>d</bold> value resulted in a larger <inline-formula><mml:math id="inf132"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> (i.e., the less <inline-formula><mml:math id="inf133"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> released, the more it was excluded; <xref ref-type="fig" rid="fig4">Figure 4A,B</xref>), and a greater advantage of <inline-formula><mml:math id="inf134"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf135"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig4">Figure 4C,D</xref>). In contrast, <inline-formula><mml:math id="inf136"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> was not highly sensitive to the intrinsic growth rate advantage of <inline-formula><mml:math id="inf137"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf138"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>). <inline-formula><mml:math id="inf139"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was still strongly disfavored even when it had relatively large (50%) intrinsic growth rate advantage over <inline-formula><mml:math id="inf140"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>). Taken together, self-organization favors cooperators that supply the most benefits.<fig-group><fig id="fig4" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.013</object-id><label>Figure 4.</label><caption><title>Self-organization leads the most giving cooperator to associate most with the heterotypic cooperative partner, allowing discrimination of cooperators of varying quality.</title><p>In diffusion model simulations, <inline-formula><mml:math id="inf141"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> produced adenine at a rate <bold>d-</bold>fold (0 ≤ <bold>d</bold> < 1) of the release rate of <inline-formula><mml:math id="inf142"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="inf143"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> had a 5% fitness advantage over <inline-formula><mml:math id="inf144"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> at all lysine concentrations. <inline-formula><mml:math id="inf145"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> that released less (smaller values of <bold>d</bold>) were isolated more in spatial patterns (<bold>A</bold>, steady-state values summarized in <bold>B</bold>) and disfavored more as the community grew (<bold>C</bold> and <bold>D</bold>). In (<bold>D</bold>), the fitness advantage of <inline-formula><mml:math id="inf146"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf147"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was calculated from the rate of changes in the ratio <inline-formula><mml:math id="inf148"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf149"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> between generations 2 and 6 in (<bold>C</bold>). In (<bold>B</bold>) and (<bold>D</bold>), data from six replicates were plotted. The communities were initiated at 3000 total cells/mm<sup>2</sup>. Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.013">http://dx.doi.org/10.7554/eLife.00960.013</ext-link></p></caption><graphic xlink:href="elife00960f004"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.014</object-id><label>Figure 4—figure supplement 1.</label><caption><title>Spatial self-organization allowed <inline-formula><mml:math id="inf389"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> to increase in frequency even when <inline-formula><mml:math id="inf390"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was much fitter.</title><p>In diffusion model simulations, the percent growth rate advantage of <inline-formula><mml:math id="inf391"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf392"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, marked in the insets, was assumed to be fixed at all concentrations of lysine. Here, <bold>d</bold> = 0. The partner association index (<inline-formula><mml:math id="inf393"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>) did not show strong dependence on the intrinsic advantage of <inline-formula><mml:math id="inf394"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf395"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<bold>A</bold> and <bold>B</bold>). The overall advantage of <inline-formula><mml:math id="inf396"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf397"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in the self-organized communities was reduced when the intrinsic growth rate advantage of <inline-formula><mml:math id="inf398"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf399"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> increased (<bold>C</bold>). However, <inline-formula><mml:math id="inf400"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> were still disfavored compared to <inline-formula><mml:math id="inf401"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and a larger intrinsic advantage of <inline-formula><mml:math id="inf402"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf403"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> did not translate proportionally into better overall survival of <inline-formula><mml:math id="inf404"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in the community (<bold>D</bold>). The partner association indexes in (<bold>B</bold>) corresponded to communities after seven generations of growth. The <inline-formula><mml:math id="inf405"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> advantage over <inline-formula><mml:math id="inf406"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in (<bold>D</bold>) was calculated from changes in the ratio <inline-formula><mml:math id="inf407"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf408"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="bold">d</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> between generations 2 and 6 in (<bold>C</bold>). The communities were initiated at 3000 total cells/mm<sup>2</sup>. Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.014">http://dx.doi.org/10.7554/eLife.00960.014</ext-link></p></caption><graphic xlink:href="elife00960fs007"/></fig><fig id="fig4s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.015</object-id><label>Figure 4—figure supplement 2.</label><caption><title>Cheaters with a much higher affinity for cooperative benefits than cooperators can destroy heterotypic cooperation even in a spatial environment.</title><p>The evolved cheater <inline-formula><mml:math id="inf409"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>–<italic>LYP1</italic> (with a mutation in <italic>LYP1</italic> (see CT10 in Table 1 of <xref ref-type="bibr" rid="bib46">Waite and Shou., 2012</xref>) is much more efficient in taking up lysine at low lysine concentrations than the ancestral cooperator <inline-formula><mml:math id="inf410"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>). Thus, the evolved cheater consumed lysine and grew while keeping the lysine concentration at very low levels where the ancestral <inline-formula><mml:math id="inf411"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> could hardly grow. In a spatial environment with no supplements, starting from equal proportions of <inline-formula><mml:math id="inf412"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf413"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf414"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>–<italic>LYP1</italic>, cheaters were favored (purple circles). When supplied with abundant adenine and lysine (gray triangles), the high affinity of <inline-formula><mml:math id="inf415"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>–<italic>LYP1</italic> for low concentrations of lysine was no longer advantageous; the <inline-formula><mml:math id="inf416"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf417"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>–<italic>LYP1</italic> ratio slowly changed in favor of cheaters in this case, similar to the ‘Comp’ case in <xref ref-type="fig" rid="fig1">Figure 1C</xref>. Exp: experiment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.015">http://dx.doi.org/10.7554/eLife.00960.015</ext-link></p></caption><graphic xlink:href="elife00960fs008"/></fig><fig id="fig4s3" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.016</object-id><label>Figure 4—figure supplement 3.</label><caption><title>In obligatory byproduct mutualism (benefit production incurs no cost and non-producers have no fitness advantage over producers), high levels of non-producers can still destroy byproduct mutualism in a spatial environment.</title><p>In simulations, we examined the growth of communities of <inline-formula><mml:math id="inf418"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf419"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf420"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> at different initial ratios in well-mixed (<bold>A</bold> and <bold>B</bold>) and spatial (<bold>C</bold> and <bold>D</bold>) environments lacking supplements. The initial population size of <inline-formula><mml:math id="inf421"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was always one third of the initial total population size, which was kept constant. <inline-formula><mml:math id="inf422"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf423"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> varied among 1:10, 1:1, and 10:1 (dashed, solid, and dotted lines, respectively). Even though non-producer <inline-formula><mml:math id="inf424"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was assumed to have no fitness advantage over producer <inline-formula><mml:math id="inf425"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, high levels of non-producers still destroyed mutualism (<inline-formula><mml:math id="inf426"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf427"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> = 1:10) in liquid (<bold>B</bold>) and spatial (<bold>D</bold>) environments (cross indicates the extinction of the community). Error bars in (<bold>D</bold>) are standard deviations calculated using six independent replicates. Note that non-producers are disfavored in spatial, but not well-mixed, environment. Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.016">http://dx.doi.org/10.7554/eLife.00960.016</ext-link></p></caption><graphic xlink:href="elife00960fs009"/></fig></fig-group></p></sec><sec id="s2-5"><title>Heterogeneity in the initial spatial distribution of cells facilitates but is not required for self-organization</title><p>One might hypothesize that among the initially randomly distributed cell populations, the occasional fortuitous proximity of a cooperator cell to a partner cell is necessary for self-organization. To examine this hypothesis, we simulated communities starting from a periodic and symmetric initial distribution of cells (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). In the absence of initial spatial asymmetry, other stochastic effects such as the initial metabolite-storage state of the cell, cell rearrangement, and death events broke the symmetry and self-organization still emerged (<xref ref-type="fig" rid="fig5">Figure 5B</xref>). Even though the final partner association index from random initial distribution was greater than that from periodic distribution, the latter was still significantly greater than 1 (<xref ref-type="fig" rid="fig5">Figure 5C</xref>). Consequently, cooperators still outperformed cheaters in periodic initial distribution, even though the degree of outperformance was greater in random initial distribution (<xref ref-type="fig" rid="fig5">Figure 5D</xref>). These simulation results suggest that the heterogeneity in the initial spatial distribution of cells promoted but was not required for self-organization.<fig id="fig5" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.017</object-id><label>Figure 5.</label><caption><title>Heterogeneity in the initial spatial distribution of cells facilitates but is not required for cheater isolation.</title><p>Starting from a symmetric and periodic distribution in which all cooperators <inline-formula><mml:math id="inf150"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and cheaters <inline-formula><mml:math id="inf151"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> had an equal access to the partner <inline-formula><mml:math id="inf152"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (<bold>A</bold>), heterotypic cooperators self-organized (<bold>B</bold> and <bold>C</bold>) and were favored (<bold>D</bold>). (<bold>B</bold>–<bold>D</bold>) corresponded to generation 6. Break of symmetry from the initial symmetric spatial distribution can be due to stochastic effects such as differences in the initial amounts of metabolites cells possessed, death of cells, or the random direction of cell division. Compared to a random initial distribution, communities with a periodic initial distribution showed smaller mean <inline-formula><mml:math id="inf153"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>; nonetheless, <inline-formula><mml:math id="inf154"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> significantly exceeded 1 (Wilcoxon signed rank test). In these simulations, the growth rate advantage of <inline-formula><mml:math id="inf155"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf156"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was assumed to be 10% at all concentrations of lysine. The communities were initiated at 4400 total cells/mm<sup>2</sup>. Scale bar: 100 μm. In simulated top-views, higher color intensity indicates a greater number of cells of the corresponding color stacked at that position. Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.017">http://dx.doi.org/10.7554/eLife.00960.017</ext-link></p></caption><graphic xlink:href="elife00960f005"/></fig></p></sec><sec id="s2-6"><title>Asymmetric fitness effects of cooperators and cheaters on partners drives self-organization</title><p>What drives differential partner association during self-organization? Since self-organization was only observed during cooperation and cheating but not during competition, the very acts of cooperation and cheating are required. When the fitness effects of interactions are the major driving force of patterning, interacting populations are expected to intermix if both supply spatially localized large fitness benefit to the other (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). In contrast, lack of benefit to either population causes population segregation (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Thus, we reason that the asymmetry between cooperators and cheaters in their capacity to reciprocate partner’s benefits drives self-organization.</p><p>To examine how this asymmetry leads to self-organization, we simulated a community in which a center stripe of partners was initially bordered by a stripe of cooperators on one side and cheaters on the other (<xref ref-type="fig" rid="fig6">Figure 6</xref>). This simulation configuration allowed us to examine the process of self-organization from the simplest form of initial symmetry. Near the cooperator side, partners intermixed with cooperators due to the spatially localized large benefits to both (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>; red and green in <xref ref-type="fig" rid="fig6">Figure 6</xref>). In contrast, near the cheater side, the lack of benefits to partners caused minimal intermixing between cheaters and partners (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>; blue and green in <xref ref-type="fig" rid="fig6">Figure 6</xref>). This isolation of cheaters allowed cooperators to increase in frequency despite the intrinsic fitness advantage of cheaters over cooperators.<fig-group><fig id="fig6" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.018</object-id><label>Figure 6.</label><caption><title>Asymmetric fitness effects of cooperators and cheaters on partners drive self-organization.</title><p>Time progression of self-organization in a simulated community as observed in top-views (top) and vertical cross-sections (bottom). Heterotypic cooperative partners (green) supply large benefits to both cooperators (red) and cheaters (blue). Since the benefit is spatially localized, only cooperators and cheaters that are close to partners will grow. Given that cells dividing toward partners will on average have more access to benefits than those dividing away from partners, both cooperators and cheaters pile over partners. Cooperators reciprocate by supplying a large, but different, localized benefit to the partner, while cheaters do not. Thus, partners grow and pile over cooperators but not cheaters. Consequently, further growth of cooperators is facilitated, while cheaters become isolated and disfavored. In this simulation, cheaters have an 8% fitness advantage over cooperators. To mimic the top-view from microscopy, the top-view in this simulation represents the top-most layer of cells instead of the total intensity integrated over z at each pixel.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.018">http://dx.doi.org/10.7554/eLife.00960.018</ext-link></p></caption><graphic xlink:href="elife00960f006"/></fig><fig id="fig6s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.019</object-id><label>Figure 6—figure supplement 1.</label><caption><title>Localization of cooperative benefits is required for self-organization.</title><p>The partner association indexes and the <inline-formula><mml:math id="inf428"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf429"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios of simulated cooperating and cheating spatial communities were compared at different levels of localization of benefits. ‘Co&Ch’ communities had parameters similar to those in <xref ref-type="fig" rid="fig3s2">Figure 3—figure supplement 2B</xref> (purple circles) and therefore had normal levels of spatial localization of benefits. In ‘Exc. release’ communities (brown squares), cooperators and partners released excessive amounts of adenine and lysine, respectively (200-fold higher compared to the original communities). Since the neighboring cells could not consume the released metabolites fast enough, the benefits no longer remained localized to the vicinity of the releasing cell. In ‘Inst. distr.’ cases (black diamonds), the diffusion coefficient in the community was assumed to be very large, such that any released metabolite was instantly distributed among all cells. When benefits were delocalized either because of excessive metabolite release or rapid distribution of metabolite throughout the community, self-organization was diminished (<bold>A</bold>) and cooperators were disfavored compared to cheaters (<bold>B</bold>). In all cases, cheaters had an 8% intrinsic fitness advantage over cooperators, and communities were not disturbed (i.e., cells were not repositioned). Error bars show the standard deviation of ratios in six independent communities. Sim: simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.019">http://dx.doi.org/10.7554/eLife.00960.019</ext-link></p></caption><graphic xlink:href="elife00960fs010"/></fig></fig-group></p></sec><sec id="s2-7"><title>Cell growth into open space is required for self-organization</title><p>If the cell densities in the initial inoculum were so high that all cell types were forced to be each other’s immediate neighbor, then the degree of self-organization might be limited. To test whether access to open space is required for self-organization, we initiated communities at high initial cell densities such that two cell layers covered the inoculation spot. We then allowed communities to grow unperturbed in a spatial environment (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>). Compared to the center, the expanding front where open space offered opportunities for self-organization showed a significantly higher partner association index (<xref ref-type="fig" rid="fig7">Figure 7</xref>, <xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>). In the community center, cooperators were not favored over cheaters. In contrast, <inline-formula><mml:math id="inf157"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf158"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> increased progressively above the initial value of 1 as the community grew into open space away from the inoculum (<xref ref-type="fig" rid="fig7">Figure 7</xref>). Thus, similar to what has been observed for homotypic cooperation (<xref ref-type="bibr" rid="bib10">Datta et al., 2013</xref>; <xref ref-type="bibr" rid="bib45">Van Dyken et al., 2013</xref>), growth into open space during range expansion also favors heterotypic cooperation over cheating.<fig-group><fig id="fig7" position="float"><object-id pub-id-type="doi">10.7554/eLife.00960.020</object-id><label>Figure 7.</label><caption><title>Cell growth into open space is required for self-organization and cheater isolation.</title><p>In an unperturbed spatial environment, a community starting from a high-density (∼10<sup>5</sup> total cells/mm<sup>2</sup>) confluent inoculum expanded to new territories (purple). Compared to ‘Center’, self-organization was significantly more in ‘Expanding front’. Consequently, the initially 1:1 <inline-formula><mml:math id="inf159"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf160"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio changed in favor of cooperators as the community expanded outward but not in ‘Center’. Sections were collected from three independent communities. Using the Mann–Whitney <italic>U</italic>-test, the association indexes of the ‘Center’ and of the ‘Expanding front’ were significantly different (p = 4 × 10<sup>−4</sup>). Exp: experiment.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.020">http://dx.doi.org/10.7554/eLife.00960.020</ext-link></p></caption><graphic xlink:href="elife00960f007"/></fig><fig id="fig7s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00960.021</object-id><label>Figure 7—figure supplement 1.</label><caption><title>Vertical cross-sections of communities started from a high-density inoculum.</title><p>A schematic diagram (<bold>A</bold>) shows positions (gray solid lines) of cross-sections (<bold>B</bold>–<bold>E</bold>) taken from a community initiated from a high-density inoculum (dashed circle). Vertical cross-sections in (<bold>B</bold>) and (<bold>C</bold>) were 100 μm and 180 μm from the edge of the community, respectively. (<bold>D</bold>) and (<bold>E</bold>) show respectively the center portion and the expanding front portion of a vertical cross-section through the initial inoculum region. Cheater patches became smaller or disappeared as the community front expanded out. Scale bar: 200 μm.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.021">http://dx.doi.org/10.7554/eLife.00960.021</ext-link></p></caption><graphic xlink:href="elife00960fs011"/></fig></fig-group></p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>Using an engineered yeast community and a mathematical model devoid of partner recognition, we examined how partner-fidelity feedback unfolds in a spatial environment at the individual cell level. In our system, partner cells released essential metabolites for cooperators and cheaters, and cooperators reciprocated with a different essential metabolite while cheaters did not. We found that despite an initially random or periodic spatial distribution, cells ‘self-organized’ into a non-random and non-symmetric pattern: cooperators had more partner neighbors than cheaters did. The level of differential partner association, as quantified by the partner association index, is correlated with how much cooperators outperform cheaters despite the intrinsic fitness advantage of cheaters over cooperators.</p><p>What is required for self-organization? Self-organization is driven by the asymmetry between cooperators and cheaters in the amount of spatially localized benefits they supply to the heterotypic partner during cell growth into open space. Our previous work has shown that if two distinct populations receive spatially localized large fitness benefits from each other, then the two populations are expected to intermix (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). In contrast, when the fitness benefit to at least one population is small, then cell types are not expected to intermix (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Consequently, partners intermix with cooperators but not cheaters (<xref ref-type="fig" rid="fig3 fig4 fig5 fig6 fig7">Figures 3–7</xref>). This difference in the tendency to intermix causes differential partner association, which facilitates the growth of cooperators and isolates and disfavors cheaters. Indeed in simulations, if intermixing was prevented through delocalizing benefits (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>; <xref ref-type="bibr" rid="bib1">Allen et al., 2013</xref>), or if intermixing was imposed on all cells through high initial cell densities, self-organization and cooperator advantage over cheaters diminished (<xref ref-type="fig" rid="fig6s1">Figure 6—figure supplement 1</xref>, <xref ref-type="fig" rid="fig7">Figure 7</xref>). Similar trends are observed in recent works which mathematically examined diffusion of public good in homotypic cooperation (<xref ref-type="bibr" rid="bib1">Allen et al., 2013</xref>; <xref ref-type="bibr" rid="bib2a">Borenstein et al., 2013</xref>).</p><p>Simulations showed that spatial self-organization could discriminate among cooperators that supply different levels of benefits (<xref ref-type="fig" rid="fig4">Figure 4</xref>). When cooperative benefits were limiting, the most ‘helpful’ cooperator ended up with the highest number of partners and was most favored. In our mathematical model, we could be sure that this was not due to partner recognition. Thus, in theory, self-organization through partner fidelity feedback is capable of achieving finer levels of discrimination without requiring sophisticated cognition and memory. Without knowing the molecular mechanisms of interactions, one could easily confuse partner fidelity feedback with partner recognition, because both are capable of discriminating partners of varying cooperative qualities. Our work suggests that any argument on partner recognition in a system that is intrinsically spatial (such as legume and rhizobia and fig and colonizing fig wasp) will require identifying variants that fail to distinguish cooperators from cheaters. Otherwise, interpreting cheater discrimination as ‘partner choice’ can be misleading.</p><p>Spatial self-organization can fend off cheaters with large fitness advantages over cooperators (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). However, if (non-isogenic) cheaters are much better than cooperators at taking up low concentrations of benefits, then cheaters will destroy heterotypic cooperation even in a spatial environment (experimental results in <xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>). In byproduct mutualism (benefit production incurs no cost and thus non-producers have no fitness advantage over producers), non-producers are excluded and disfavored in a spatial environment (<xref ref-type="fig" rid="fig4s3">Figure 4—figure supplement 3</xref>). Furthermore, high levels of non-producers can still destroy byproduct mutualism in a spatial environment (simulation results in <xref ref-type="fig" rid="fig4s3">Figure 4—figure supplement 3</xref>). This is because non-producers compete with producers for benefits from the partner. If the initial level of non-producers is too high, producers receive few benefits and suffer, which in turn negatively impacts the partner.</p><p>Conceptually, spatial self-organization favoring heterotypic cooperation can be considered as an example of niche construction or environmental feedback (<xref ref-type="bibr" rid="bib24">Lehmann, 2007</xref>; <xref ref-type="bibr" rid="bib34">Pepper, 2007</xref>). Cooperators construct favorable niches and cheaters construct unfavorable niches for partners. Through differential partner association, partners construct better niches for cooperators than for cheaters. Niche construction not only affects the growth of current cells, but also that of the future progeny. This reciprocal niche construction favors heterotypic cooperation over cheating.</p><p>In summary, spatial self-organization is the mechanism for partner fidelity feedback. Not requiring the evolution of partner recognition (<xref ref-type="bibr" rid="bib42">Travisano and Velicer, 2004</xref>; <xref ref-type="bibr" rid="bib15">Foster and Wenseleers, 2006</xref>), spatial self-organization offers a simple and fundamental mechanism solely driven by acts of strong cooperation and cheating during cell growth into open space. Even in natural heterotypic cooperative systems with long evolutionary histories, self-organization may act either alone or in synergy with potential recognition mechanisms (<xref ref-type="bibr" rid="bib51">Weyl et al., 2010</xref>) to exclude cheaters.</p></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Engineered yeast strains</title><p><inline-formula><mml:math id="inf161"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf162"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf163"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> were respectively WS950 (<italic>MATa ste3::kanMX4 lys2Δ0 ade4::ADE4(PUR6) ADHp-DsRed.T4</italic>), WS954 (<italic>MATa ste3::kanMX4 ade8Δ0 lys21::LYS21(fbr) ADHp-venus-YFP</italic>), and WS962 (<italic>MATa ste3::kanMX4 lys2Δ0 ADHp-CFP</italic>).</p></sec><sec id="s4-2"><title>Community growth and measurements</title><p>To grow yeast communities, agarose columns were prepared by pouring 2× concentrated SD minimal medium (<xref ref-type="bibr" rid="bib17">Guthrie and Fink, 1991</xref>) with 2% low melting temperature agarose either into flat-bottom 96-well plates (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>) or into rectangular petri dishes (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>). Agarose in the rectangular petri dishes was subsequently cut into 24 mm × 24 mm × 4 mm pads. For competition experiments, 2× SD was supplemented with lysine and adenine (650 μM and 430 μM final concentrations, respectively). The communities on agarose were inoculated either from a uniform distribution of all cells (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref> at 3000 or 10,000 total cells/mm<sup>2</sup>) or a high-density inoculum of ∼2 mm diameter (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref> at ∼8 × 10<sup>4</sup> total cells/mm<sup>2</sup>), as specified. We grew well-mixed liquid cocultures in 3 ml of 1× SD without supplementing adenine or lysine, with initially 5 × 10<sup>5</sup> total cells/ml. In all cases, cultures were initiated from equal proportions of <inline-formula><mml:math id="inf164"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf165"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf166"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> populations. Flow cytometry was used to measure population sizes of different types in a community (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Fluorescent imaging equipment and procedures are described in <xref ref-type="bibr" rid="bib30">Momeni et al. (2013)</xref>. Cryosectioning to obtain vertical cross-sections of yeast communities followed <xref ref-type="bibr" rid="bib30">Momeni and Shou (2012)</xref>.</p></sec><sec id="s4-3"><title>Quantification of partner association</title><p>We quantified the relative association of cooperators and cheaters with the heterotypic partner by dividing the average number of immediate <inline-formula><mml:math id="inf167"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> neighbors per focal <inline-formula><mml:math id="inf168"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cell by the average number of immediate <inline-formula><mml:math id="inf169"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> neighbors per focal <inline-formula><mml:math id="inf170"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cell when a focal cell neighbored at least one different population (<inline-formula><mml:math id="inf171"><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>, partner association index). We chose to count the immediate <inline-formula><mml:math id="inf172"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> neighbors because nearest neighbors presumably had the greatest impact on the growth of the focal cell due to spatially localized benefits. We chose to analyze focal cells neighboring at least one different population because cells surrounded by their own types do not contribute as much to population growth as cells surrounded by partners.</p><p>In simulations, a three-dimensional neighborhood around each cell was used to quantify the association index (<inline-formula><mml:math id="inf173"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>C</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mi>D</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>), whereas in experiments, a two-dimensional neighborhood was used in two-dimensional top-views or cross-sections of the community. Based on fluorescence intensities in the DsRed, YFP, and CFP channels, cell types were assigned to each pixel in fluorescent images. Pixels having fluorescence intensities less than 30% above the background in all fluorescence channels were defined as ‘no signal’. Otherwise, fluorescence intensities in each channel were normalized to their respective image-wide 90th percentile values and pixel identity was assigned to be the same as the fluorescence channel with the highest normalized intensity. For cross-sections taken from the center of communities in <xref ref-type="fig" rid="fig7">Figure 7</xref>, the top crown of cross-sections appeared very bright, whereas the middle and lower regions appeared dim (<xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>). This large dynamic range caused artifacts in cell identification. The intensity thresholds in these sections were therefore manually adjusted to increase the accuracy of cell identification. Eliminating manual adjustments did not alter the conclusions.</p></sec><sec id="s4-4"><title>The diffusion model</title><p>To simulate the growth of three-dimensional yeast communities, we used the agent-based diffusion model (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). In this model, metabolites are released by cooperators and partners, diffuse throughout the community and agarose, and are consumed by cells that need the metabolite. Most parameters were measured experimentally (<xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). We provide a summary of the most relevant features of the model below, without repeating the implementation details that can be found in <xref ref-type="bibr" rid="bib30">Momeni et al. (2013)</xref>.</p><p>Cells take up their required metabolites depending on the local concentration of the metabolite according to the Michaelis–Menten equation:<disp-formula id="equ1"><mml:math id="m1"><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>where, <italic>i</italic> = <inline-formula><mml:math id="inf174"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf175"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, or <inline-formula><mml:math id="inf176"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> corresponding to each cell type, <italic>S</italic><sub><italic>i</italic></sub> is the concentration of the required metabolite for each cell type (<italic>S</italic><sub><italic>i</italic></sub> = <italic>S</italic><sub><italic>L</italic></sub>, lysine concentration for <inline-formula><mml:math id="inf177"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf178"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <italic>S</italic><sub><italic>i</italic></sub> = <italic>S</italic><sub><italic>A</italic></sub>, adenine concentration for <inline-formula><mml:math id="inf179"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>), <italic>v</italic><sub><bold><italic>m,i</italic></bold></sub> is the maximum uptake rate when metabolites are abundant, and <italic>K</italic><sub><italic>i</italic></sub> is assumed to be equal to the Monod constant (the concentration of limiting nutrient at which half maximal growth rate is achieved) for each cell type. <inline-formula><mml:math id="inf180"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf181"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cells require <inline-formula><mml:math id="inf182"><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> fmole of lysine and <inline-formula><mml:math id="inf183"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cells require <inline-formula><mml:math id="inf184"><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> fmole of adenine to produce a new daughter cell.</p><p>The distribution of metabolites is modeled using the diffusion equation, with uptake and release as sinks and sources. Using simplified notations of <inline-formula><mml:math id="inf185"><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf186"><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula> at time <italic>t</italic>, the metabolite distributions after a time step <italic>t</italic><sub><italic>u</italic></sub> are calculated as<disp-formula id="equ2"><mml:math id="m2"><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mo>∇</mml:mo><mml:mo>⋅</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>∇</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:msub><mml:mi>n</mml:mi><mml:mi>R</mml:mi></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula> and<disp-formula id="equ3"><mml:math id="m3"><mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mo>∇</mml:mo><mml:mo>⋅</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>∇</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi>M</mml:mi><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:msubsup><mml:mi>n</mml:mi><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p><p>Here, <italic>n</italic><sub><italic>R</italic></sub>, <italic>n</italic><sub><italic>C</italic></sub>, and <italic>n</italic><sub><italic>G</italic></sub> are, respectively, the densities of live <inline-formula><mml:math id="inf187"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf188"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf189"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cells in a focal community grid. <inline-formula><mml:math id="inf190"><mml:mrow><mml:mo>∇</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>z</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math></inline-formula> is the vector differential operator. <inline-formula><mml:math id="inf191"><mml:mrow><mml:msubsup><mml:mi>n</mml:mi><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is the density of <inline-formula><mml:math id="inf192"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cells that die (which is distributed as binomial (<italic>n</italic><sub><italic>G</italic></sub><italic>, p</italic>) where <italic>p = t</italic><sub><italic>u</italic></sub><italic>·d</italic><sub><italic>G</italic></sub>, with <italic>d</italic><sub><italic>G</italic></sub> being the death rate of <inline-formula><mml:math id="inf193"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> ) and release lysine in the time step <italic>t</italic><sub><italic>u</italic></sub>. <italic>D</italic> is a spatially varying function representing the diffusion coefficient in the environment (the value of <italic>D</italic> was 360 μm<sup>2</sup>/s inside agarose, 20 μm<sup>2</sup>/s inside yeast communities, and 0 μm<sup>2</sup>/s in the surrounding air, according to experimental measurements). Considering <italic>D</italic> as a spatially varying function simplifies the numerical calculations by automatically incorporating the boundary conditions at the community–air interface. <inline-formula><mml:math id="inf194"><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>, the maximum uptake rate of the limiting nutrient per cell, relates to the maximum growth rate <inline-formula><mml:math id="inf195"><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> through <inline-formula><mml:math id="inf196"><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>ln</mml:mi><mml:mo></mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="inf197"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the amount of limiting nutrient required to produce a new cell (<inline-formula><mml:math id="inf198"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf199"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>). <inline-formula><mml:math id="inf200"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> has a fixed intrinsic fitness advantage over <inline-formula><mml:math id="inf201"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> at all lysine concentrations. This advantage was modeled as a higher uptake rate for the limiting nutrient. For example, a 2% fitness advantage of cheaters means <inline-formula><mml:math id="inf202"><mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow><mml:mn>1.02</mml:mn><mml:mtext> </mml:mtext><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> or equivalently <inline-formula><mml:math id="inf203"><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo></mml:mrow><mml:mn>1.02</mml:mn><mml:mtext> </mml:mtext><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. <italic>β</italic><sub><italic>L</italic></sub> is the amount of lysine released upon the death of a <inline-formula><mml:math id="inf204"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cell, and <italic>γ</italic><sub><italic>A</italic></sub> is the release rate of adenine per <inline-formula><mml:math id="inf205"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cell. <inline-formula><mml:math id="inf206"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cheaters do not release any adenine. For other types of cheaters that release adenine with a lower rate compared to cooperators (e.g., in <xref ref-type="fig" rid="fig4">Figure 4</xref>), a corresponding release term is included in the equation.</p><p>To solve this diffusion equation, we follow the above finite difference time-domain equations over time. The diffusion equation is solved over two separate spatial domains (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>), one containing the agarose (with a 60 μm grid size), and the other containing the community and the air above it (with a 15 μm grid size). These grid sizes accommodated different diffusion coefficients in agarose and in community and represented the average distance nutrient molecules diffuse in 3.5 s. When we used the same diffusion coefficient (360 μm<sup>2</sup>/s and one grid size of 50 μm) for agarose and community, similar results were obtained. No-flow (<inline-formula><mml:math id="inf207"><mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mtext>0</mml:mtext></mml:mrow></mml:mrow></mml:math></inline-formula>) boundary conditions are applied to the top and bottom surfaces of the simulation domain and periodic boundary conditions are applied to the four vertical sides of the domain.</p><p>To incorporate the effects of competition for other shared resources, the growth of all cells also depended on, in addition to adenine or lysine, a shared resource (for instance, glucose) that was initially supplied in the medium (<xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). In such simulations, diffusion and uptake of glucose were also simulated in a way similar to the above equations. Each cell divided only after acquiring enough glucose, in addition to adenine or lysine. Once a cell had accumulated one metabolite sufficient for one cell division, it stopped consuming that metabolite and continued to acquire the second metabolite until a sufficient amount had been acquired to trigger the birth of a daughter cell.</p><p>In simulations, <inline-formula><mml:math id="inf208"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf209"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf210"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> cells are initially randomly distributed on the surface of solid medium. The cells start from random initial storage of their required metabolites. In each <italic>t</italic><sub><italic>u</italic></sub> time step, each live cell takes up its required metabolites according to the Michaelis–Menten equation shown above. Each cell type is assumed to require its limiting metabolite and a shared metabolite (<inline-formula><mml:math id="inf211"><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> lysine for <inline-formula><mml:math id="inf212"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf213"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf214"><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> adenine for <inline-formula><mml:math id="inf215"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf216"><mml:mrow><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>G</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> for the shared glucose for all cell types, all listed in <xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>) to divide. The state of cells is examined at every <italic>τ</italic> time interval (<italic>τ</italic> = 6 min, which contains several diffusion <italic>t</italic><sub><italic>u</italic></sub> time steps, but is still much shorter than the minimum cell doubling time of ∼2 hr). The cells that have acquired the required amount of limiting metabolites divide.</p><p>Cell divisions in a three-dimensional community often required cell rearrangement. Assumptions concerning cell rearrangement were derived from experimental observations (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Time-lapse images of the growth of a single fluorescent cell into a microcolony showed that the center of the microcolony became brighter due to multiple cell layers when the microcolony grew to larger than a five-cell radius (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Thus, we assumed that each cell initially budded in the horizontal plane and pushed others in its immediate neighborhood to the side along the shortest path to empty space. Once a cell was completely surrounded on each side by roughly five cells, it either budded directly upward with a probability of 70% or randomly budded to one of the sides at the same level, pushing up the displaced cell and all the cells above. The probability of 0.7 (instead of 1) of dividing directly upward is estimated from experimental observations: when individual green-fluorescent cells were surrounded by many equally fit competing red-fluorescent cells, vertical cross-sections showed that as z increased, the progeny of the green-fluorescent cell ‘diffused’ laterally (instead of remaining a vertical line) (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1F</xref> in <xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). Since we cannot experimentally track all possible outcomes of cell rearrangement, this assumption is a simplification of reality. This simplification could have contributed to the discrepancy between experimental and simulation patterns, although our conclusions from experiments and simulations are similar.</p><p>The cells also die stochastically corresponding to their fixed death rates (<italic>d</italic><sub><italic>R</italic></sub>, <italic>d</italic><sub><italic>G</italic></sub>, or <italic>d</italic><sub><italic>C</italic></sub> as listed in <xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>). After each cell state update (<italic>τ</italic>), the diffusion coefficient is updated: the diffusion coefficient in each community diffusion grid (15 μm × 15 μm × 15 μm, maximally containing 3 × 3 × 3 = 27 cells of size 5 μm × 5 μm × 5 μm) is assumed to be proportional to the occupancy of that grid, changing from 0 to 20 μm<sup>2</sup>/s. In this three-dimensional agent-based model of community growth, the initial conditions of cells, cell death, random direction of growth, and cell rearrangement are the only sources of stochasticity; metabolite uptake and diffusion of metabolites in the environment are modeled as deterministic phenomena.</p><p>Most of the parameters used for the simulations (<xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>) are measured experimentally. More details of the implementation and assumptions can be found in <xref ref-type="bibr" rid="bib30">Momeni et al. (2013)</xref>. An example of the implementation of this model as a MATLAB code is included in additional files (<xref ref-type="supplementary-material" rid="SD2-data">Source code 1</xref>).</p></sec><sec id="s4-5"><title>Yeast strains adapted to low-nutrient conditions</title><p>When the ancestral <inline-formula><mml:math id="inf217"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf218"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf219"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> were periodically mixed on an agarose pad lacking adenine and lysine, the final <inline-formula><mml:math id="inf220"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf221"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios were stochastic, either in favor of cheaters or cooperators (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). This is consistent with previous experiments in liquid cocultures (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>) that also yielded stochastic cheater outcomes due to an adaptive race between <inline-formula><mml:math id="inf222"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf223"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. During the adaptive race, both <inline-formula><mml:math id="inf224"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf225"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> sampled from the same set of mutations that enhanced cell fitness in the lysine-limited cooperative environment. The population with the fittest mutant rapidly dominated the coculture (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>; <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>).</p><p>To mitigate the confounding effect of adaptive race, we used <inline-formula><mml:math id="inf226"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf227"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> populations preadapted to the cooperative environment. First, <inline-formula><mml:math id="inf228"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> containing a mutation in <italic>RSP5</italic> (CT8, see Table 1 in <xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>), known to significantly improve the fitness of lysine-requiring cells under lysine-limitation (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>), was crossed to the ancestral <inline-formula><mml:math id="inf229"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> to produce a diploid (WS1421). Sporulation of the diploid yielded a cyan-fluorescent cooperator (WS1447) and a red-fluorescent cheater (WS1448), both harboring the <italic>rsp5</italic> mutation. The temperature sensitivity of this <italic>rsp5</italic> allele allowed its easy selection at 37°C. To avoid confusion, we indicate these cooperators and cheaters as <italic>rsp5</italic> <inline-formula><mml:math id="inf230"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <italic>rsp5</italic> <inline-formula><mml:math id="inf231"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, respectively. Several well-mixed cocultures consisting of <italic>rsp5</italic> <inline-formula><mml:math id="inf232"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <italic>rsp5</italic> <inline-formula><mml:math id="inf233"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and the ancestral partner <inline-formula><mml:math id="inf234"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (WS954) were initiated at a ratio of 1:1:1. The initial stochastic phase in population dynamics was indicative of additional rounds of adaptive races (<xref ref-type="bibr" rid="bib46">Waite and Shou, 2012</xref>) between <italic>rsp5</italic> <inline-formula><mml:math id="inf235"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <italic>rsp5</italic> <inline-formula><mml:math id="inf236"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2A</xref>). After 250 hr, the <inline-formula><mml:math id="inf237"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf238"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios showed steady trends, suggesting the absence of further rapid adaptive races (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2A</xref>). After ∼500 hr, two of the lines (brown) that displayed a steady change of the <italic>rsp5</italic> <inline-formula><mml:math id="inf239"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<italic>rsp5</italic> <inline-formula><mml:math id="inf240"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio in favor of cheaters and a final ratio close to 1:1 were frozen down. After reviving these preadapted cocultures (hereafter marked as “ <bold>’</bold> ”), <inline-formula><mml:math id="inf241"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf242"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> continued to decline steadily (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2B</xref>). Propagating well-mixed liquid cocultures from these lines for an additional 400 hr, we observed that the <inline-formula><mml:math id="inf243"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>:<inline-formula><mml:math id="inf244"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio exhibited a steady decline (<xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2C</xref>, ‘In liquid, well-mixed’), suggesting a cheater <inline-formula><mml:math id="inf245"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> fitness advantage of around 8% (7.5 ± 0.8% SD) over <inline-formula><mml:math id="inf246"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. It should be noted that since <inline-formula><mml:math id="inf247"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf248"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> are not isogenic, the fitness advantage of <inline-formula><mml:math id="inf249"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf250"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> is likely not solely due to the lack of adenine overproduction by <inline-formula><mml:math id="inf251"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. Nevertheless, this case models an advantage for the cheating type over the cooperating type, similar to what might be observed in nature if cheaters and cooperators are of different species (<xref ref-type="bibr" rid="bib9">Côté and Cheney, 2005</xref>; <xref ref-type="bibr" rid="bib21">Jandér and Herre, 2010</xref>).</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We would like to thank Chi-Chun Chen, David Skelding, Robin Green, Alexander Pozhitkov, Ben Kerr, Harmit Malik, Katie Peichel, Suzannah Rutherford, Kevin Foster, and Jim Bull for their suggestions. We thank Aric Capel for constructing the WS1447 and WS1448 yeast strains. We thank the reviewing editor and anonymous reviewers for their constructive feedback and suggestions.</p></ack><sec sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="conflict" id="conf1"><p>The authors declare that no competing interests exist.</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>BM, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con2"><p>AJW, Conception and design, Acquisition of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con3"><p>WS, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn></fn-group></sec><sec sec-type="supplementary-material"><title>Additional files</title><supplementary-material id="SD2-data"><object-id pub-id-type="doi">10.7554/eLife.00960.022</object-id><label>Source code 1.</label><caption><title>A MATLAB code for simulating the progression of patterns in a community of <inline-formula><mml:math id="inf432"><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf433"><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf434"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</title><p>The code is based on the diffusion model (‘Materials and methods’) and includes initially supplied glucose in the medium as a shared resource consumed by all populations (parameters in <xref ref-type="supplementary-material" rid="SD1-data">Figure 2—source data 1</xref>).</p></caption><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00960.022">http://dx.doi.org/10.7554/eLife.00960.022</ext-link></p><media mime-subtype="m" mimetype="application" xlink:href="elife00960s002.m"/></supplementary-material></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Allen</surname><given-names>B</given-names></name><name><surname>Gore</surname><given-names>J</given-names></name><name><surname>Nowak</surname><given-names>MA</given-names></name></person-group><year>2013</year><article-title>Spatial dilemmas of diffusible public goods</article-title><source>eLife</source><comment>(in press)</comment></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Armitt</surname><given-names>S</given-names></name><name><surname>Woods</surname><given-names>RA</given-names></name></person-group><year>1970</year><article-title>Purine-excreting mutants of <italic>Saccharomyces cerevisiae</italic>. 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Planck Institute for Evolutionary Biology</institution>, <country>Germany</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see <ext-link ext-link-type="uri" xlink:href="http://elife.elifesciences.org/review-process">review process</ext-link>). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.</p></boxed-text><p>Thank you for sending your work entitled “Spatial Self-organization Favors Heterotypic Cooperation over Cheating” for consideration at <italic>eLife</italic>. Your article has been evaluated by a Senior editor and 3 reviewers, one of whom is a member of our Board of Reviewing Editors.</p><p>The Reviewing editor and the other reviewers discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.</p><p>The study is based on a previously developed system of two yeast strains that can enter cooperative interactions. The authors have already published an <italic>eLife</italic> paper (<ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.7554/eLife.00230">http://dx.doi.org/10.7554/eLife.00230</ext-link>) describing a spatial patterning model in conjunction with a series of experiments that aimed to study inter-population cooperation. The present paper deals with the question of how cooperating patterns could emerge in the presence of a cheater. They use a similar technological approach as in their first paper and show that self-organization occurs among the cooperators, to the exclusion of the cheater. They validate their findings through modeling.</p><p>While the referees consider the topic of potential interest for <italic>eLife</italic>, there are two major concerns that need to be clarified before a final decision can be taken. One of these requires additional experiments and the conceptual scope of this paper will depend on the outcome of these experiments. Thus it is currently not possible to state that the paper can be accepted once the experiments are done, but the authors are welcome to resubmit the revised version for new assessment.</p><p>The first concern relates to the use of the term “heterotypic cooperation” rather than “mutualism”, which is not simply a semantic question, but has direct relevance for the conceptual framing and the experimental approach to be taken. Due to the current interest in social interactions in microbes, this is a crucial issue for the paper. To qualify for cooperation, you need to show that:</p><p>(i) In isolation, cooperators grow faster than cheaters. Here, one probably has to show that R outcompetes C in the presence of G. This crucial point does not seem to be addressed, so the system could simply be a case of negative frequency dependent selection. Even in this case, one could have a case of cooperation, but it still remains to be shown that pure cooperator populations maximize fitness (see e.g., MacLean et al, PLoS Biology, <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1371/journal.pbio.1000486">http://dx.doi.org/10.1371/journal.pbio.1000486</ext-link>; please check also definitions of ““cooperator” in Nowack, Science 314, 1560 and Doebeli & Hauert, Ecology Letters 8, 748).</p><p>(ii) In any mixture, defectors outcompete co-operators. Probably this is what you refer to when you write that “C had a growth advantage over R”, but this crucial point remains unclear. Instead, you turn off the interaction by providing lysine and adenine in the medium, but this is not the same.</p><p>With respect to mutualism, referee 2 sees a need to revisit and properly discuss previous concepts. Currently you posit partner choice/recognition as a possible mechanism favouring mutualism and contrast a spatial environment as an alternative explanation. You state however that the “mechanism is unclear” and that there is a “paradox” in terms of the effect of space. In fact this is an example of “partner fidelity feedback”, a mechanism that is well known in the mutualism literature, so there is no paradox. The essence of partner fidelity feedback is that increasing the fitness of a mutualistic partner itself leads to increased fitness for the other partner. The results can thus be easily explained within this framework: cooperators increase the local fitness of their mutualist partners, thus receiving more cooperation themselves. Empty space is required for cooperators and their partners to grow into in order to self-organise.</p><p>To clarify these issues, it will be necessary to repeat the experiments (in both supplemented and un-supplemented media) with monocultures of both the cooperator and cheater strains, showing that growth rate is higher for the cheaters when supplemented, but lower when un-supplemented. Ideally you should be able to show that cheaters should also outcompete cooperators. However, it is acknowledged that this relies on an unstructured environment, so you would need to add a non-spatial treatment. If this is feasible it would be great, but other approaches to solve this issue might also be acceptable.</p><p>The second concern is about the details of the modeling. The reason for performing simulations are obscure. Do you indeed imply that simulation results “ensure that no biological mechanism beyond cell growth [...] where required for spatial self organisation”? It seems that modeling efforts would only help to arrive at such statements, but would not be sufficient to “ensure” this. Even more problematic is the fact that the model description is far from sufficient to repeat the simulations. In the equation, D is treated as a spatially varying function, but then referred to as a constant. With two different constant values, there are two different equations, but the position of D in a later equation suggests an unnecessary complication. The text suggests that this equation is solved numerically, but no details are given except the boundary conditions. Instead, you give many simulation results as figures, but it is completely unclear how randomness emerges in the deterministic equations. Is this based on some stochastic initial condition (although you speak of densities)? Or do you use a stochastic algorithm to numerically solve a deterministic equation? In the supplement, you list many parameters (enough to fit all kinds of things), but there is no information on how exactly these enter. The only equation in the paper seems to be almost decoration.</p><p>The figures combining simulations and experiments are impressive, but it remains unclear how the various parameters of the model where chosen to generate this similarity (which appears to be difficult to quantify). Moreover, a closer inspection of cluster size and form does suggest that there is some qualitative difference between simulations and experiments. Note that it would not be enough to only clarify the source of parameters – so far the model is not described in a way that one could repeat this study. Please describe it in a way that anyone who reads the paper should be able to come up with his or her own numerical code that leads to the same results.</p><p>Finally, the current version of the manuscript is unnecessarily condensed, i.e., Results and Discussion are combined and much important information is relegated to the supplementary material. Given that there are no space constraints, an extended version of the manuscript should be envisaged, including all figures that document results and use supplementary files primarily for additional documentation that would in it self not be required for understanding the work.</p><p>[Editors’ note: before acceptance, the following revisions were also requested.]</p><p>Thank you for resubmitting your work entitled “Spatial Self-organization Favors Heterotypic Cooperation over Cheating” for further consideration at <italic>eLife</italic>. Your revised article has been favorably evaluated by a Senior editor and a member of the Board of Reviewing Editors. The manuscript has been improved but there are remaining issues that need to be addressed before acceptance, as outlined below.</p><p>The comments of referees 2 and 3 are included below. In addition, there was a consultation session with the referees that came to the following conclusion:</p><p>The presentation at the places referee 3 has pointed to is a big issue. Taking the perspective of someone reading the paper for the first time, they would quite likely be left confused on many points. A significant improvement in presentation, and addressing the use of non-isogenic lines are the main things the authors need to address.</p><p><italic>Reviewer #2:</italic></p><p>I have major reservations about the experiments presented in <xref ref-type="fig" rid="fig2">Figure 2</xref> of the revised manuscript, which I feel must be addressed before I can suggest acceptance of the manuscript.</p><p>In attempting to demonstrate that a cooperative dilemma occurs the authors pre-adapted both cooperators and cheaters to a lysine-limited environment in order to attempt to remove the confounding effect of adaptation to this environment. While I appreciate that the “adaptive race” could be a large confounding effect, I feel the potential biases introduced are not acceptable. As the strains have been pre-adapted they are likely to no longer be isogenic. As such, all fitness effects observed thereafter could be owing to differing mutations between cooperators and cheaters that have different effects depending on the environment. While much early research on social behaviour in microbes used similarly non-isogenic lines, this has resulted in reduced impact of this work in molecular microbiology. The gold standard now is clearly to use isogenic lines, and I do not feel that I can recommend publication of results using non-isogenic lines in a journal with the aspirations of <italic>eLife</italic>.</p><p>The obvious solution to this problem for me would be to remove the experiments presented in <xref ref-type="fig" rid="fig2">Figure 2</xref> from the paper and simply point to the evidence from Shou et al. 2007 and Waite & Shou 2012 supporting the existence of a cooperative dilemma. Alternatively, if the authors could analyse co-cultures on a short enough timescale so that the adaptive race is not a problem this would be preferable, but I don’t know whether this is possible. Regardless I don’t think inclusion of experiments with non-isogenic lines is acceptable for a journal of <italic>eLife’s</italic> standing.</p><p><italic>Reviewer #3:</italic></p><p>After reading the manuscript carefully, I still do have several concerns. Most importantly, the results are presented in a way that is confusing and most probably not beneficial to the community. For example:</p><p>- I have checked with several colleagues and the terms “homotypic cooperation” and “heterotypic cooperation” are not at all familiar terms. From the authors reply, I have not understood why they phrase their work in their own terms.</p><p>- “Kin selection can achieve positive assortment” makes no sense.</p><p>- “Can increase in frequency if it leads to more offspring that are genetically related to the original co-operator” seems to hold for anything that evolves - this statement seems to be empty unless you indicate that the “more offspring” is not produced by the focal individual.</p><p>- “Spatial environment, which allows repeated interactions” is a weird formulation. Usually, these two are treated separately, as repeated interactions allow for sophisticated behaviour conditioned on the past, whereas spatial structure per se does not.</p><p>- “Can act as a cheater of the system” is a weird formulation. C cheats G by not providing A, but does it cheat R?</p><p>- “break of symmetry from the initial symmetric distribution can be due to stochastic effects such as differences in the initial state of cells” - this seems to be self-contradictory.</p><p>- “cells attached to the glass rod” - are you sure all cells equally attach? Is this some biased sample?</p><p>I am still not convinced that <xref ref-type="fig" rid="fig3">Figure 3</xref> shows a good agreement between experiment and simulations beyond “red-green domains grow, whereas blue regions remain constrained”. Simulations suggest a more complex micro-structure, which is absent ion the experiment. <xref ref-type="fig" rid="fig3">Figure 3 C and F</xref> suggests a much stronger association in the Co&Ch treatment than the experiment. I was also wondering why the authors look at frequencies of the two strains throughout – are absolute population sizes not relevant for the interaction? Why?</p><p>In the new, slightly improved model section, the notation should be streamlined and made readable. E.g. K always has two indices, but MM is always the same. This is unusual and not necessary. The nabla operator is not defined and nothing is mentioned on its (probably) discrete spatial version. The metabolite model is basically a time discrete version of a stochastic partial differential equation, is there a reason to use a first order algorithm? Why use two separate grid sizes?</p><p>All this suggests a high level of sophistication in terms of numerically formulating the model, but it is not clear that the model results are robust. The dynamics of yeast cells is of course individual based, but some formulations suggest that many choices in this model have been made that are not explicitly described in the text. Thus, the model cannot be understood in detail without looking into the source code, which must be commented in a way that it could be read more easily.</p><p>While I find the experimental system and the experimental results interesting, it seems that they follow in a straightforward way from the interactions in the system. Partners and co-operators can coexist and grow to high densities, whereas partners and cheaters cannot, which isolates cheaters.</p><p>In summary, while this paper has improved in the revision and while I find the basic results of interest, it is not written in a way that makes it easily accessible. I feel that these results could be presented in a much nicer, less confusing way.</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.00960.024</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p><italic>“In isolation, cooperators grow faster than cheaters.</italic>”</p><p>Do you wonder whether pure cooperators do better than pure cheaters in the presence of the partner? If so, then our answer is yes, pure cooperators indeed do better than pure cheaters. In the absence of adenine and lysine supplements, a coculture of <inline-formula><mml:math id="inf252"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf253"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> can grow to high density, but a coculture of <inline-formula><mml:math id="inf254"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf255"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> fails to grow (<xref ref-type="fig" rid="fig8">Author response image 1</xref>, adapted from Shou et al. 2007). We have made this point more explicitly in the main text.</p><fig id="fig8" position="float"><label>Author response image 1.</label><caption><title>Adapted from <xref ref-type="fig" rid="fig1 fig6">Figures 1 and 6</xref> in (Shou et al. 2007): When partner <inline-formula><mml:math id="inf256"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was paired with the cooperator <inline-formula><mml:math id="inf257"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, the coculture grew from low to high densities. No persistent growth was observed when partner <inline-formula><mml:math id="inf258"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was paired with the cheater <inline-formula><mml:math id="inf259"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</title></caption><graphic xlink:href="elife00960f008"/></fig><p><italic>“Here, one probably has to show that R outcompetes C in the presence of G.</italic>”</p><p>Do you mean <inline-formula><mml:math id="inf260"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> outcompetes <inline-formula><mml:math id="inf261"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in the presence of <inline-formula><mml:math id="inf262"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> ? Performing this experiment in a well-mixed environment is not straightforward. The lysine-limited coculture environment strongly selects for adaptive mutants in <inline-formula><mml:math id="inf263"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf264"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>. Thus, <inline-formula><mml:math id="inf265"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf266"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> engage in an “adaptive race” (Waite & Shou 2012): if <inline-formula><mml:math id="inf267"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> gets the best mutation to grow under lysine limitation, then the coculture is quickly destroyed by cheaters; if <inline-formula><mml:math id="inf268"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> gets the best adaptive mutation, then the coculture quickly purges cheaters. In this case, <inline-formula><mml:math id="inf269"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> outcompetes <inline-formula><mml:math id="inf270"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="inf271"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> outcompetes <inline-formula><mml:math id="inf272"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> depending on which population gets a better mutation, not because of the social interactions. This kind of phenomenon has also been observed for non-engineered cooperating and cheating microbes (Morgan et al. 2012).</p><p>In our original manuscript as well as other published work, we have used two approaches to confirm the fitness advantage of <inline-formula><mml:math id="inf273"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf274"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> while being mindful of the complication introduced by the adaptive race. First, we measured fitness differences between <inline-formula><mml:math id="inf275"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf276"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> under conditions where adaptive race is minimized. In the presence of abundant lysine to minimize selective pressure, <inline-formula><mml:math id="inf277"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> has a 2% fitness advantage over <inline-formula><mml:math id="inf278"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in both well-mixed environment (see <xref ref-type="fig" rid="fig1">Figure 1B</xref> in (Waite & Shou 2012)) and spatial environment (<xref ref-type="fig" rid="fig1">Figure 1C</xref> in the original and revised manuscript). In the absence of lysine so that any adaptive mutants, even if preexisting, could not grow and increase in abundance, <inline-formula><mml:math id="inf279"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> showed no disadvantage compared to cheaters (Waite & Shou 2012). Thus, <inline-formula><mml:math id="inf280"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> has an overall advantage over <inline-formula><mml:math id="inf281"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>.</p><p>Second, we took advantage of an <italic>rsp5</italic> mutation previously found to be highly adaptive for the lysine-requiring cells in a lysine-limited environment (Waite & Shou 2012). When we grew replicate cocultures of <italic>rsp5</italic> <inline-formula><mml:math id="inf282"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <italic>rsp5</italic> <inline-formula><mml:math id="inf283"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf284"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in well-mixed liquid environment, we again observed stochastic outcomes with some cocultures dominated by cooperators and other succumbing to cheaters (Figure 1–figure supplement 4 in the original manuscript, now <xref ref-type="fig" rid="fig2">Figure 2 A and B</xref> in the revised manuscript). This is indicative of additional rounds of adaptive races between <italic>rsp5</italic> <inline-formula><mml:math id="inf285"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <italic>rsp5</italic> <inline-formula><mml:math id="inf286"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> toward better adaptation to the lysine-limited coculture environment. We revived from frozen stocks two of these cocultures that exhibited declining <inline-formula><mml:math id="inf287"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf288"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (purple). <inline-formula><mml:math id="inf289"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf290"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> in these revived cocultures continued to decline steadily, suggesting that evolved <inline-formula><mml:math id="inf291"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> continued to be more fit than evolved <inline-formula><mml:math id="inf292"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> by ∼8% (<xref ref-type="fig" rid="fig9">Author response image 2B</xref>). Even though the additional fitness advantage of <inline-formula><mml:math id="inf293"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf294"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> may not be solely due to adenine overproduction, previous work has used mutations unrelated to social interactions to augment the “cost of cooperation” (Chuang et al. 2010; Gore et al. 2009). We have used these pre-adapted cocultures to show that in a well-mixed liquid environment and in a periodically mixed spatial environment in which spatial self-organization was disrupted, the ratio of cooperator <inline-formula><mml:math id="inf295"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> to cheater <inline-formula><mml:math id="inf296"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> consistently declined (now <xref ref-type="fig" rid="fig2">Figure 2C</xref> of the revised manuscript). If we did not perturb the spatial environment, cooperators were favored over cheaters (<xref ref-type="fig" rid="fig2s2">Figure 2–figure supplement 2</xref>, purple).</p><fig id="fig9" position="float"><label>Author response image 2.</label><caption><title>Well-mixed evolved cocultures of heterotypic cooperators and cheaters showed a steady change in the <inline-formula><mml:math id="inf297"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf298"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratio. (<bold>A</bold>) To pre-adapt cooperators and cheaters in the lysine-limited coculture environment so that no new mutations of large fitness benefits could quickly arise, we started eight well-mixed replicates (marked by different symbols) consisting of <italic>rsp5</italic> <inline-formula><mml:math id="inf299"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <italic>rsp5</italic> <inline-formula><mml:math id="inf300"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and the ancestral <inline-formula><mml:math id="inf301"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> (Materials and methods). The <italic>rsp5</italic> mutation was previously found to be highly adaptive for the lysine-requiring cells in a lysine-limited environment (Waite & Shou 2012). The initial stochastic phase at 150 hours is indicative of additional rounds of adaptive races<sup>21</sup> between <italic>rsp5</italic> <inline-formula><mml:math id="inf302"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <italic>rsp5</italic> <inline-formula><mml:math id="inf303"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>. After 250 hours, the <inline-formula><mml:math id="inf304"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf305"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ratios showed steady trends, suggesting no additional rapid adaptive races. Two of these cultures (purple) were revived from frozen stocks. (<bold>B</bold>) In the two revived cocultures where the evolved populations were denoted with a “ <bold>ʹ</bold> ”, <inline-formula><mml:math id="inf306"><mml:mrow><mml:mrow><mml:msubsup><mml:msup><mml:mi>R</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> :<inline-formula><mml:math id="inf307"><mml:mrow><mml:mrow><mml:msup><mml:msup><mml:mi>C</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> continued to decline steadily before being used for experiments in <xref ref-type="fig" rid="fig2s2">Figure 2–figure supplement 2</xref>. Broken axis indicates the period of time elapsed during which a small revived inoculum (30 μl into 200 μl minimal medium and then expanded to 2 ml minimal medium) grew to detectable densities.</title></caption><graphic xlink:href="elife00960f009"/></fig><p>In a spatial environment, the same selective pressure of lysine-limitation on <inline-formula><mml:math id="inf308"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf309"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> cells also exists, but the best mutants are restricted to their original birth locations and thus could not take over the coculture. Hence, deterministic rather than stochastic outcomes were observed when <inline-formula><mml:math id="inf310"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf311"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf312"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> were grown on a spatial environment either in the absence or the presence of lysine and adenine supplements (<xref ref-type="fig" rid="fig1">Figure 1C</xref> in the original and revised manuscript). We have transferred these explanations from supplemental files into the main text.</p><p><italic>“…so the system could simply be a case of negative frequency dependent selection. Even in this case, one could have a case of cooperation, but it still remains to be shown that pure cooperator populations maximize fitness (see e.g., MacLean et al, PLoS Biology,</italic> <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1371/journal.pbio.1000486">http://dx.doi.org/10.1371/journal.pbio.1000486</ext-link><italic>; please check also definitions of ““cooperator” in Nowack, Science 314, 1560 and Doebeli & Hauert, Ecology Letters 8, 748)</italic>.</p><p><italic>(ii) In any mixture, defectors outcompete co-operators. Probably this is what you refer to when you write that “C had a growth advantage over R”, but this crucial point remains unclear. Instead, you turn off the interaction by providing lysine and adenine in the medium, but this is not the same.</italic>”</p><p>The MacLean et al. work used the yeast invertase system, which is known to show negative frequency-dependent selection (i.e., cooperators have an advantage over cheaters when cooperators are rare). In this case, “common goods” – glucose and fructose generated from invertase produced and released from cooperators and not cheaters – are “privatized” to a certain extent so that cooperators have preferential access to the common goods they produced (Gore et al. 2009). Thus, when cooperators are rare, cheaters at high abundance do not have much access to scarce common goods while cooperators do. This advantage of cooperator over cheater when cooperators are rare contributes to the coexistence of cooperators and cheaters. We do not believe that there is negative frequency-dependent selection in our experimental system, for two reasons. First, in a heterotypic cooperative system, an individual needs the common goods supplied by its partner, and therefore privatization of common goods produced by self is futile. Second, as discussed above, we see no signs of negative frequency-dependent selection in our pre-adapted cocultures (<xref ref-type="fig" rid="fig2s2">Figure 2–figure supplement 2</xref>, no trend of stable coexistence of <inline-formula><mml:math id="inf313"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf314"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> in a well-mixed environment).</p><p>Importantly, in our mathematical model, we assumed a fixed cheater advantage over cooperator under all conditions. Experiments and modeling yielded similar results: spatial self-organization favors heterotypic cooperation. Thus, we conclude that negative frequency dependent selection is not a pre-requisite of our conclusions on spatial self-organization favoring heterotypic cooperation over cheating.</p><p><italic>“To clarify these issues, it will be necessary to repeat the experiments (in both supplemented and un-supplemented media) with monocultures of both the cooperator and cheater strains, showing that growth rate is higher for the cheaters when supplemented…</italic>”</p><p>As discussed above, we have competed <inline-formula><mml:math id="inf315"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf316"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in a well-mixed environment, and we observed an advantage of <inline-formula><mml:math id="inf317"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf318"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> when lysine is abundant and no disadvantage of <inline-formula><mml:math id="inf319"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf320"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> when lysine is absent (Waite & Shou 2012). Since in abundant lysine, the fitness advantage of <inline-formula><mml:math id="inf321"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf322"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> was ∼2%, we cannot simply measure monoculture growth rates. This is because, for example, small differences in growth temperature can give rise to growth rate difference greater than 2%. A competition assay with both <inline-formula><mml:math id="inf323"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf324"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> ensures that the two competing strains experience the same environment and go through the same amount of dilutions during propagation.</p><p><italic>“but [the growth rate of the cheaters] is lower when un-supplemented.</italic>”</p><p>We have also shown that <inline-formula><mml:math id="inf325"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> + <inline-formula><mml:math id="inf326"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> but not <inline-formula><mml:math id="inf327"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> + <inline-formula><mml:math id="inf328"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> can grow to high density (<xref ref-type="fig" rid="fig8">Author response image 1</xref>).</p><p><italic>“However, it is acknowledged that this relies on an unstructured environment, so you would need to add a non-spatial treatment. If this is feasible it would be great, but other approaches to solve this issue might also be acceptable.</italic>”</p><p>Using pre-adapted cocultures of <inline-formula><mml:math id="inf329"><mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msubsup><mml:mo>’</mml:mo><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="inf330"><mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:msup><mml:mo>’</mml:mo><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf331"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in which <inline-formula><mml:math id="inf332"><mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:msup><mml:mo>’</mml:mo><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> was steadily favored over <inline-formula><mml:math id="inf333"><mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msubsup><mml:mo>’</mml:mo><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> in unstructured (well-mixed or periodically disrupted spatial) environments, we have shown that a spatial environment favors <inline-formula><mml:math id="inf334"><mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msubsup><mml:mo>’</mml:mo><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> over <inline-formula><mml:math id="inf335"><mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:msup><mml:mo>’</mml:mo><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig2">Figure 2</xref> in the revised manuscript).</p><p><italic>“With respect to mutualism, referee 2 sees a need to revisit and properly discuss previous concepts. Currently you posit partner choice/recognition as a possible mechanism favouring mutualism and contrast a spatial environment as an alternative explanation. You state however that the “mechanism is unclear” and that there is a “paradox” in terms of the effect of space. In fact this is an example of “partner fidelity feedback”, a mechanism that is well known in the mutualism literature, so there is no paradox. The essence of partner fidelity feedback is that increasing the fitness of a mutualistic partner itself leads to increased fitness for the other partner. The results can thus be easily explained within this framework: cooperators increase the local fitness of their mutualist partners, thus receiving more cooperation themselves. Empty space is required for cooperators and their partners to grow into in order to self-organise.</italic>”</p><p>We have modified our text to link self-organization to partner fidelity feedback.</p><p><italic>“The reason for performing simulations given in line 122 are obscure. Do you indeed imply that simulation results “ensure that no biological mechanism beyond cell growth [...] where required for spatial self organisation”? It seems that modeling efforts would only help to arrive at such statements, but would not be sufficient to “ensure” this.</italic>”</p><p>We have changed our text to “We also eliminated the confounding influence of adaptive mutations using mathematical simulations.” Thus, no more use of language such as “ensure.” The original intention was to state that we could use a mathematical model to verify whether a certain set of assumptions is sufficient to generate experimental outcomes.</p><p><italic>“Even more problematic is the fact that the model description is far from sufficient to repeat the simulations. In the equation, D is treated as a spatially varying function, but then referred to as a constant. With two different constant values, there are two different equations, but the position of D in the equation in line 235 suggests an unnecessary complication. The text suggests that this equation is solved numerically, but no details are given except the boundary conditions. Instead, you give many simulation results as figures, but it is e.g. completely unclear how randomness emerges in the deterministic equations. Is this based on some stochastic initial condition (although you speak of densities)? Or do you use a stochastic algorithm to numerically solve a deterministic equation? In the supplement, you list many parameters (enough to fit all kinds of things), but there is no information on how exactly these enter. The only equation in the paper seems to be almost decoration.</italic>”</p><p>We have rewritten the modeling aspect of our paper. We have changed diffusion “constant” to diffusion “coefficient” to avoid confusion.</p><p>We have added substantially more details on modeling in the main text and in “The diffusion model” section of Materials and methods. In addition, we are enclosing our source code. We also added a sentence addressing stochasticity and determinism All parameters have been experimentally measured except for the three parameters on the carrying-capacity-determining metabolite (such as glucose) required by all three strains (<italic>a</italic><sub><italic>G</italic>,</sub> <italic>K</italic><sub><italic>G</italic>,</sub> and <italic>S</italic><sub><italic>G</italic></sub>)<sub>.</sub> The equation section has also been expanded to be comprehensive.</p><p><italic>“The figures combining simulations and experiments are impressive, but it remains unclear how the various parameters of the model where chosen to generate this similarity (which appears to be difficult to quantify).</italic>”</p><p>Most parameters for simulations were experimentally measured, and presumably this is the reason why experiments and simulations shared the same trend. We have added a supplementary figure (<xref ref-type="fig" rid="fig6s1">Figure 6–figure supplement 1</xref>). In this figure, we varied the benefit supply amount and diffusion coefficient in simulations to show that spatial localization of benefits is required to generate results that are similar to experiments.</p><p><italic>“Moreover, a closer inspection of cluster size and form does suggest that there is some qualitative difference between simulations and experiments. Note that it would not be enough to only clarify the source of parameters - so far, the model is not described in a way that one could repeat this study. Please describe it in a way that anyone who reads the paper should be able to come up with his own numerical code that leads to the same results.</italic>”</p><p>The difference between simulations and experiments could be due to a variety of reasons. First, our assumption on how cells rearrange to accommodate new cells is clearly simplified. We assumed that with a probability of 0.7, a confined cell will send its new daughter cell straight up and with a probability of 0.3, the new daughter displaces a neighbor cell, causing the displaced neighbor cell and all cells above it to “bulge” up. In reality, the new daughter cell could divide diagonally up. So far, we don’t have ways to experimentally track all possible ways of cell rearrangement and thus our assumption is a simplification of experimental reality. We have now discussed this in Materials and methods. Second, genetically identical cells in the same environment may behave very differently. For example, cells in the top crown of a community are always much brighter than cells down below, even though many cells down below retain the ability to divide (i.e., they are live). We don’t know how these physiological differences may impact nutrient consumption and growth.</p><p><italic>“Finally, the current version of the manuscript is unnecessarily condensed, i.e. Results and Discussion are combined and much important information is relegated to the supplementary material. Given that there are no space constraints, an extended version of the manuscript should be envisaged, including all figures that document results and use supplementary files primarily for additional documentation that would in it self not be required for understanding the work.</italic>”</p><p>We have rewritten introduction and added a separate discussion. We have also moved some originally supplemental figures into the main text.</p><p><italic>[Editors’ note: before acceptance, the following revisions were also requested.</italic>]</p><p><italic>“The presentation at the places referee 3 has pointed to is a big issue. Taking the perspective of someone reading the paper for the first time, they would quite likely be left confused on many points. A significant improvement in presentation, and addressing the use of non-isogenic lines are the main things the authors need to address</italic>.</p><p><italic>“Reviewer #2</italic>:</p><p><italic>I have major reservations about the experiments presented in</italic> <xref ref-type="fig" rid="fig2"><italic>Figure 2</italic></xref> <italic>of the revised manuscript, which I feel must be addressed before I can suggest acceptance of the manuscript</italic>.</p><p><italic>In attempting to demonstrate that a cooperative dilemma occurs the authors pre-adapted both cooperators and cheaters to a lysine-limited environment in order to attempt to remove the confounding effect of adaptation to this environment. While I appreciate that the “adaptive race” could be a large confounding effect, I feel the potential biases introduced are not acceptable. As the strains have been pre-adapted they are likely to no longer be isogenic. As such, all fitness effects observed thereafter could be owing to differing mutations between cooperators and cheaters that have different effects depending on the environment. While much early research on social behaviour in microbes used similarly non-isogenic lines, this has resulted in reduced impact of this work in molecular microbiology. The gold standard now is clearly to use isogenic lines, and I do not feel that I can recommend publication of results using non-isogenic lines in a journal with the aspirations of</italic> eLife.</p><p><italic>The obvious solution to this problem for me would be to remove the experiments presented in</italic> <xref ref-type="fig" rid="fig2"><italic>Figure 2</italic></xref> <italic>from the paper and simply point to the evidence from Shou et al. 2007 and Waite & Shou 2012 supporting the existence of a cooperative dilemma. Alternatively, if the authors could analyse co-cultures on a short enough timescale so that the adaptive race is not a problem this would be preferable, but I don’t know whether this is possible. Regardless I don’t think inclusion of experiments with non-isogenic lines is acceptable for a journal of</italic> eLife<italic>’s standing.</italic>”</p><p>The cooperating and cheating populations resulting from the pre-adaptation process are not clonal, let alone isogenic. Nonetheless, the growth rate of well-mixed cultures decreased as the ratio of cheaters to cooperators increased, suggesting that cheaters remained cheaters. Top-views of the communities were similar to results from isogenic strains: spatial association of cooperators with the partner and isolation of cheaters. These, and the fact that in nature, cooperators have to face cheaters some of which are of different species and therefore non-isogenic (such as the non-pollinating wasps of fig), and most importantly, the need to show that perturbation of spatial environment causes cheaters to rise in abundance, originally made us to include the experimental result in <xref ref-type="fig" rid="fig2">Figure 2</xref>. However, we understand the reviewer’s concern about possible confounding factors due to the usage of non-clonal, non-isogenic populations. We have replaced <xref ref-type="fig" rid="fig2">Figure 2</xref> with simulation data, showing that disruption of spatial organization favors cheaters, which is a very important point we would not want to miss. We have moved the original <xref ref-type="fig" rid="fig2">Figure 2</xref> to supplementary information, and modified the text.</p><p><italic>“Reviewer #3</italic>:</p><p><italic>After reading the manuscript carefully, I still do have several concerns. Most importantly, the results are presented in a way that is confusing and most probably not beneficial to the community. For example</italic>:</p><p><italic>- I have checked with several colleagues and the terms “homotypic cooperation” and “heterotypic cooperation” are not at all familiar terms. From the authors reply, I have not understood why they phrase their work in their own terms.</italic>”</p><p>In the literature, mutually beneficial interactions between two species have been referred to as “mutualism” (Foster & Wenseleers 2006), “cooperation” (Harcombe 2010), or “interspecific cooperation” (Sachs et al. 2004). We opted to use “cooperation” rather than “mutualism” to emphasize that the act of helping the partner confers a cost to self. This leads to the social dilemma where cheaters that do not help the partner have fitness advantage over their cooperating counterparts. We believe that using just the term “cooperation” is not adequate, because we want to emphasize that in our system, cooperation involves exchange of distinct benefits between two distinct populations rather than cooperation involving exchanging of identical benefits between identical individuals which the majority of the field has been studying. The term “interspecific cooperation” implies that cooperators are between different species. Even though our yeast strains can be regarded as different “species” because they do not mate with each other, they can also be considered the same species if one uses the divergence in ribosomal RNA sequences to define species (a field standard)! Most importantly, heterotypic cooperation can apply to cooperation between phenotypically differentiated subpopulations, such as between different cell types in a multicellular organism. We have thus chosen to use “homotypic cooperation” and “heterotypic cooperation” to most precisely represent the context of our work. We feel that using precisely defined terms, even if they are unfamiliar, is less confusing than using familiar terms that are not quite appropriate.</p><p><italic>“ “Kin selection can achieve positive assortment” makes no sense.</italic>”</p><p>We have modified the paragraph to: “In homotypic cooperation that involves genetic relatives, positive assortment can be achieved through “kin selection”…”</p><p><italic>“ “Can increase in frequency if it leads to more offspring that are genetically related to the original co-operator” seems to hold for anything that evolves - this statement seems to be empty unless you indicate that the “more offspring” is not produced by the focal individual.</italic>”</p><p>This sentence, which turned out to be unnecessary, has been deleted.</p><p><italic>“ “Spatial environment, which allows repeated interactions” is a weird formulation. Usually, these two are treated separately, as repeated interactions allow for sophisticated behaviour conditioned on the past, whereas spatial structure per se does not.</italic>”</p><p>In a spatial environment, it is more likely (compared to a well-mixed environment) that two neighboring individuals remain neighbors. We have modified the sentence to read: “Spatial environment, which facilitates repeated interactions because two neighboring individuals are likely to remain neighbors, has been shown to promote heterotypic cooperation.”</p><p><italic>“ “Can act as a cheater of the system” is a weird formulation. C cheats G by not providing A, but does it cheat R?</italic>”</p><p>For more clarity, we have changed the sentence to:</p><p>“These results collectively suggest that <inline-formula><mml:math id="inf336"><mml:mrow><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math></inline-formula> acts as a cheater variant of <inline-formula><mml:math id="inf337"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula>.”</p><p><italic>“ “break of symmetry from the initial symmetric distribution can be due to stochastic effects such as differences in the initial state of cells” - this seems to be self-contradictory.</italic>”</p><p>We have changed the sentence to:</p><p>“Break of symmetry from the initial symmetric spatial distribution can be due to stochastic effects such as differences in the initial amounts of metabolites cells possessed, death of cells, or the random direction of cell division.”</p><p><italic>“ “cells attached to the glass rod” - are you sure all cells equally attach? Is this some biased sample?</italic>”</p><p>In pilot experiments, the results were similar when we compared the ratios of samples obtained using the glass rod with the ratios measured for the rest of the sampled community. Thus, based on the pilot experiment and the estimates of ratios from top-view images, we think the sampling bias, even if present, will not affect our conclusions.</p><p><italic>“I am still not convinced that</italic> <xref ref-type="fig" rid="fig3"><italic>Figure 3</italic></xref> <italic>shows a good agreement between experiment and simulations beyond “red-green domains grow, whereas blue regions remain constrained”. Simulations suggest a more complex micro-structure, which is absent ion the experiment.</italic> <xref ref-type="fig" rid="fig3"><italic>Figure 3 C and F</italic></xref> <italic>suggests a much stronger association in the Co&Ch treatment than the experiment. I was also wondering why the authors look at frequencies of the two strains throughout - are absolute population sizes not relevant for the interaction? Why?</italic>”</p><p>There are differences in the details of patterns even between replicates of simulated or experimental communities. However, the feature that we are focusing on, i.e., more association of cooperators compared to cheaters with the partner, is consistent in all cases. This is the aspect that we are focusing on as self-organization, and it is supported by both simulations and experiments. The microstructure in simulated results that the reviewer is referring to is likely caused by the cell rearrangement assumption in the model. Each new daughter cell in simulations can divide in a random direction, and each division event independently causes rearrangement of some cells in the community. In contrast, in experimental communities, presumably cells rearrange according to the collective pressure exerted by all growing cells. As such, some artifacts, including finer structure at the individual cell level, is expected in the simulation results, which would explain larger values of association index compared to the experiment. Alternatively, some of the finer spatial features in the experimental cross-sections may have been lost in fixing and cryosectioning processes, leading to smaller association indexes when compared to the simulations. Nevertheless, when compared with the competition control, both simulations and experiments clearly show self-organization, which is the main message of our paper.</p><p>Since we are focusing on whether cooperator or cheater is favored, we have chosen to focus on the ratio of the two. When cheater frequency is high, population growth is reduced (in blue-dominated region, growth is restricted – see <xref ref-type="fig" rid="fig3">Figure 3</xref> vertical cross-sections). In a strict sense, population size matters. For example, when the total population size and/or density are too low, the community fails to grow even in absence of cheater because the released metabolites are so diluted that cells could not take them up fast enough to remain viable. However, our experiments never used such low population sizes.</p><p><italic>“In the new, slightly improved model section, the notation should be streamlined and made readable. E.g. K always has two indices, but MM is always the same. This is unusual and not necessary. The nabla operator is not defined and nothing is mentioned on its (probably) discrete spatial version. The metabolite model is basically a time discrete version of a stochastic partial differential equation, is there a reason to use a first order algorithm? Why use two separate grid sizes? All this suggests a high level of sophistication in terms of numerically formulating the model, but it is not clear that the model results are robust. The dynamics of yeast cells is of course individual based, but some formulations suggest that many choices in this model have been made that are not explicitly described in the text. Thus, the model cannot be understood in detail without looking into the source code, which must be commented in a way that it could be read more easily.</italic>”</p><p>We have deleted the MM. <inline-formula><mml:math id="inf338"><mml:mrow><mml:mo>∇</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>z</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math></inline-formula> is the standard vector differential operator.</p><p>The following sentence is added:</p><p>“<inline-formula><mml:math id="inf339"><mml:mrow><mml:mo>∇</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mrow><mml:mover accent="true"><mml:mi>z</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math></inline-formula> is the vector differential operator.”</p><p>We explained why we are using two separate spatial domains:</p><p>“These grid sizes accommodated different diffusion coefficients in agarose and in community and represented the average distance nutrient molecules diffuse in 3.5 sec.”</p><p>Using a first-order algorithm seems to work, since we did not see numerical instability (such as metabolite concentrations going negative). Also, the simulation results qualitatively matched experimental results. For example, growth rates of simulated communities are similar to those of experimental communities.</p><p>With regard to the robustness of model results, we have tried altered assumptions and obtained similar results. For example, in <xref ref-type="fig" rid="fig3s1">Figure 3–figure supplement 1</xref>, “Sim w/ delay” incorporated a 60-hour delay in the death of <inline-formula><mml:math id="inf340"><mml:mrow><mml:mrow><mml:msubsup><mml:mi>G</mml:mi><mml:mrow><mml:mo>→</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>←</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:math></inline-formula> and in the consequent release of lysine according to experimental observations. This simulation generated qualitatively similar results as simulations without incorporating the delay. We have also tried to use the same diffusion coefficient for agarose and community, and obtained the same result. We have added:</p><p>“When we used the same diffusion coefficient (360 μm<sup>2</sup>/sec and grid size of 50 μm) for agarose and community, similar results were obtained.”</p><p>With regard to cell rearrangement, we have added:</p><p>“Time-lapse images of the growth of a single fluorescent cell into a microcolony showed that the center of the microcolony became brighter due to multiple cell layers when the microcolony grew to larger than 5-cell radius.”</p><p>The details of the diffusion model, including the choice of the discrete version to solve for the diffusion of metabolites, the use of two separate grids, and the details of the rearrangement scheme are discussed thoroughly in our previous <italic>eLife</italic> publication (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>). We have added a sentence in the description of the model (Materials and Methods) to make this point clear:</p><p>“We provide a summary of the most relevant features of the model below, without repeating the implementation details that can be found in (<xref ref-type="bibr" rid="bib30">Momeni et al., 2013</xref>).”</p><p>We have also added more comments to the source code, and partitioned the code to different sections for improved readability.</p><p><italic>“While I find the experimental system and the experimental results interesting, it seems that they follow in a straightforward way from the interactions in the system. Partners and co-operators can coexist and grow to high densities, whereas partners and cheaters cannot, which isolates cheaters.</italic>”</p><p>Many papers, theoretical and experimental, have been devoted to demonstrating that spatial environment stabilizes homotypic cooperation, which seems very straightforward: cooperators cluster with their cooperative offspring and cheaters with their cheating offspring, so of course this favors cooperation, especially if other resources are non-limiting. This straightforwardness did not prevent those reports from having a high impact on how we think, because scientific demonstration rests on different standards from intuition (which is also very important).</p><p>One of the most important aspects of our work is perhaps to make the field more aware of how tricky it can be to distinguish partner choice from partner fidelity feedback in natural systems. Our community is a bona-fide partner fidelity feedback system devoid of any possibility for partner recognition, and it looks very much like the situation between legume and cooperating and cheater rhizobia: exclusion of cheaters. Thus, in the absence of direct evidence of recognition, interpreting an “apparent” discrimination of cheaters as “partner choice” can be flawed. We have added this sentence to the Discussion:</p><p>“Our work suggests that any argument on partner recognition in a system that is intrinsically spatial…”</p></body></sub-article></article> |