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@@ -7,7 +7,7 @@
<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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<meta name="src" content="canal.tex">
-<meta name="date" content="2011-11-23 15:07:00">
+<meta name="date" content="2011-12-16 14:40:00">
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>
@@ -29,16 +29,16 @@ <h2 class="titleHead"> Canalization of the evolutionary trajectory of the
class="cmr-10">1,2</span></sup><br /><br />
<sup class="textsuperscript"><span
class="cmr-10">1</span></sup><span
-class="cmr-10">Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA.</span><br />
+class="cmr-10">Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA.</span>
<sup class="textsuperscript"><span
class="cmr-10">2</span></sup><span
-class="cmr-10">Howard Hughes Medical Institute, University of Michigan, Ann Arbor, MI, USA.</span><br />
+class="cmr-10">Howard Hughes Medical Institute, University of Michigan, Ann Arbor, MI, USA.</span>
<sup class="textsuperscript"><span
class="cmr-10">3</span></sup><span
-class="cmr-10">Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK.</span><br />
+class="cmr-10">Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK.</span>
<sup class="textsuperscript"><span
class="cmr-10">4</span></sup><span
-class="cmr-10">Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.</span><br />
+class="cmr-10">Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.</span>
<sup class="textsuperscript"><span
class="cmsy-10">&#8224;</span></sup><span
class="cmr-10">Present address: Institute of Evolutionary Biology, University of Edinburgh, Edinburgh, UK.</span></div>
@@ -145,22 +145,18 @@ <h3 class="likesectionHead"><a
id="x1-4000"></a>Results</h3>
<!--l. 105--><p class="noindent" >The virus persists over the course of the 40-year simulation, infecting a significant fraction of the
host population through annual winter epidemics in temperate regions and through less periodic
-epidemics in the tropics (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>A). Across replicate simulations, we observe average yearly
+epidemics in the tropics (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->A</a>). Across replicate simulations, we observe average yearly
attack rates of 6.8% in temperate regions and rates of 7.1% in the tropics, comparable with
estimated attack rates of influenza A (H3N2) of 3&#8211;8% per year <span class="cite">[<a
href="#XMonto93">10</a>,&#x00A0;<a
href="#XKoelle09">11</a>]</span>. Over the course of the
simulation, the virus population evolves in antigenic phenotype exhibiting, at any point, a
handful of highly abundant phenotypes sampled repeatedly and a large number of phenotypes
-appearing at low abundance (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>B). By including measurement noise on antigenic locations,
-we approximate an experimental antigenic map of H3N2 influenza (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>D). The appearance
+appearing at low abundance (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->B</a>). By including measurement noise on antigenic locations,
+we approximate an experimental antigenic map of H3N2 influenza (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->D</a>). The appearance
of clusters in the antigenic map comes from the regular spacing of high abundance
phenotypes combined with measurement noise. Over time, clusters of antigenically
-similar strains are replaced by novel clusters of more advanced strains (Figure&#x00A0;<a
-href="#x1-17001r1">S1<!--tex4ht:ref: phenotypes --></a>A).
+similar strains are replaced by novel clusters of more advanced strains (<a href="#x1-17001r1">Figure S1<!--tex4ht:ref: phenotypes -->A</a>).
Across replicate simulations, clusters persist for an average of 5.0 years measured as
the time it takes for a new cluster to reach 10% frequency, peak and decline to 10%
frequency. The transition between clusters occurs quickly, taking an average of 1.8
@@ -178,7 +174,7 @@ <h3 class="likesectionHead"><a
<!--l. 110--><p class="noindent" > <img
src="figures/evol.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;1: </span><span
class="content"><span
class="cmbx-10x-x-109">Simulation results showing epidemiological, antigenic and genealogical</span>
@@ -199,30 +195,22 @@ <h3 class="likesectionHead"><a
<!--l. 115--><p class="noindent" ></div><hr class="endfigure">
<!--l. 117--><p class="noindent" >Remarkably, although antigenic phenotype is free to mutate in any direction in the
two-dimensional space, selection pressures force the virus population to move in nearly a
-straight line in antigenic space (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>B). Across replicate simulations, 94% of the
+straight line in antigenic space (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->B</a>). Across replicate simulations, 94% of the
variance of antigenic phenotype can be explained by a single dimension of variation. This
mirrors the empirical results showing a largely linear antigenic map for H3N2 influenza
isolates from 1968 to 2003 <span class="cite">[<a
href="#XSmith04">9</a>]</span>. Because of the primarily one-dimensional movement,
antigenic distance from the original phenotype increases nearly linearly with time
-(Figure&#x00A0;<a
-href="#x1-17001r1">S1<!--tex4ht:ref: phenotypes --></a>B). Antigenic evolution occurs in a punctuated fashion; periods of relative
-stasis are interspersed with more rapid antigenic change (Figure&#x00A0;<a
-href="#x1-17001r1">S1<!--tex4ht:ref: phenotypes --></a>B). Antigenic and
+(<a href="#x1-17001r1">Figure S1<!--tex4ht:ref: phenotypes -->B</a>). Antigenic evolution occurs in a punctuated fashion; periods of relative
+stasis are interspersed with more rapid antigenic change (<a href="#x1-17001r1">Figure S1<!--tex4ht:ref: phenotypes -->B</a>). Antigenic and
epidemiological dynamics show a fundamental linkage, so that large jumps of antigenic
-phenotype result in increased rates of infection (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>, Figure&#x00A0;<a
-href="#x1-17002r2">S2<!--tex4ht:ref: driftvsinc --></a>). In general, evolution
+phenotype result in increased rates of infection (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol --></a>, <a href="#x1-17002r2">Figure S2<!--tex4ht:ref: driftvsinc --></a>). In general, evolution
via many smaller mutations results in a smoother antigenic map and less variation
-in yearly epidemics (Figure&#x00A0;<a
-href="#x1-17003r3">S3<!--tex4ht:ref: incmaptree_smooth --></a>), while evolution via rare mutations of large effect
+in yearly epidemics (<a href="#x1-17003r3">Figure S3<!--tex4ht:ref: incmaptree_smooth --></a>), while evolution via rare mutations of large effect
exhibits a more clustered antigenic map and wider variation in seasonal incidence
-(Figure&#x00A0;<a
-href="#x1-17004r4">S4<!--tex4ht:ref: incmaptree_rough --></a>).
+(<a href="#x1-17004r4">Figure S4<!--tex4ht:ref: incmaptree_rough --></a>).
<!--l. 119--><p class="noindent" >The genealogical tree connecting the evolving virus population appears characteristically sparse
-with pronounced trunk and short-lived side branches (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>C). This tree shape is reflected in
+with pronounced trunk and short-lived side branches (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->C</a>). This tree shape is reflected in
low levels of standing diversity; across replicates, an average of 5.68 years of evolution separate
two randomly sampled viruses in the population. This level of diversity matches what is observed
in phylogenies of influenza A (H3N2) <span class="cite">[<a
@@ -235,17 +223,13 @@ <h3 class="likesectionHead"><a
for pervasive positive selection for antigenic change (Table&#x00A0;<a
href="#x1-4002r1">1<!--tex4ht:ref: mktable --></a>). Trunk mutations tend
to push antigenic phenotype forward along the line of primary antigenic variation
-(Figure&#x00A0;<a
-href="#x1-17005r5">S5<!--tex4ht:ref: mutspectrum --></a>). We find a roughly linear relationship between the antigenic effect of a
+(<a href="#x1-17005r5">Figure S5<!--tex4ht:ref: mutspectrum --></a>). We find a roughly linear relationship between the antigenic effect of a
mutation and the likelihood that this mutation becomes incorporated into the trunk
-(Figure&#x00A0;<a
-href="#x1-17006r6">S6<!--tex4ht:ref: probtrunk --></a>). Additionally, we find that trunk mutations occur at strikingly regular
+(<a href="#x1-17006r6">Figure S6<!--tex4ht:ref: probtrunk --></a>). Additionally, we find that trunk mutations occur at strikingly regular
intervals, with less variation of waiting times than expected under a simple random
-process (Figure&#x00A0;<a
-href="#x1-17007r7">S7<!--tex4ht:ref: waittimes --></a>). There is a relative scarcity of mutation events occurring in intervals
+process (<a href="#x1-17007r7">Figure S7<!--tex4ht:ref: waittimes --></a>). There is a relative scarcity of mutation events occurring in intervals
under 1 year and a relative excess of a mutation events occurring in 2&#8211;3 year intervals
-(Figure&#x00A0;<a
-href="#x1-17007r7">S7<!--tex4ht:ref: waittimes --></a>).
+(<a href="#x1-17007r7">Figure S7<!--tex4ht:ref: waittimes --></a>).
<div class="table">
@@ -312,8 +296,7 @@ <h3 class="likesectionHead"><a
regions. We find that, consistent with empirical estimates <span class="cite">[<a
href="#XRussell08">14</a>,&#x00A0;<a
href="#XBedford10">15</a>]</span>, the trunk resides primarily
-within the tropics, where seasonal dynamics are less prevalent (Figure&#x00A0;<a
-href="#x1-4003r2">2<!--tex4ht:ref: spatial --></a>A). Across
+within the tropics, where seasonal dynamics are less prevalent (<a href="#x1-4003r2">Figure 2<!--tex4ht:ref: spatial -->A</a>). Across
replicate simulations, we observe 72% of the trunk&#8217;s history within the tropics and
28% within temperate regions. With symmetric host contact rates and equal host
population sizes, and without seasonal forcing, we would expect trunk proportions of one
@@ -322,8 +305,7 @@ <h3 class="likesectionHead"><a
region-specific rates on trunk branches. We find that migration patterns on side branches are
close to symmetric, with similar rates between all regions, while migration patterns on
trunk branches are highly asymmetric, with high rates of movement between temperate
-regions and from temperate regions into the tropics (Figure&#x00A0;<a
-href="#x1-4003r2">2<!--tex4ht:ref: spatial --></a>B). Extrapolating from
+regions and from temperate regions into the tropics (<a href="#x1-4003r2">Figure 2<!--tex4ht:ref: spatial -->B</a>). Extrapolating from
these rates, we arrive at an expected stationary distribution of 76% tropics and 24%
temperate regions, in line with the observed residency patterns of the trunk. It may at first
seem counter-intuitive to see higher rates of movement from the temperate regions
@@ -344,7 +326,7 @@ <h3 class="likesectionHead"><a
<!--l. 143--><p class="noindent" ><img
src="figures/spatial.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;2: </span><span
class="content"><span
class="cmbx-10x-x-109">Patterns of geographic movement of virus lineages</span>. (A) Evolutionary
@@ -385,37 +367,31 @@ <h4 class="likesubsectionHead"><a
href="#XKoelle06">6</a>,&#x00A0;<a
href="#XRecker07">7</a>]</span>, our results show that a simple model coupling antigenic and
genealogical evolution exhibits broad explanatory power. We find a strong correspondence
-between the antigenic and genealogical patterns generated by our model (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>) and
+between the antigenic and genealogical patterns generated by our model (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol --></a>) and
patterns of genetic and antigenic evolution exhibited by influenza A (H3N2) <span class="cite">[<a
href="#XFitch97">3</a>,&#x00A0;<a
href="#XSmith04">9</a>]</span>. Our
model suggests that punctuated antigenic evolution need only be explained by a lack of
mutational opportunity and predicts that more detailed classification of influenza strains
-will support a relatively small number of predominant phenotypes (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>B). We
+will support a relatively small number of predominant phenotypes (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->B</a>). We
suggest that a large proportion of intra-cluster variation in the observed antigenic map
is due to experimental noise, rather than each strain possessing a unique antigenic
location. Additionally, our model accurately predicts the contrasting dynamics of other
types/subtypes of influenza. We find that lowering mutation size/effect or lowering intrinsic <span
class="cmmi-10x-x-109">R</span><sub><span
class="cmr-8">0</span></sub>
results in decreased incidence, slower antigenic movement and greater genealogical
-diversity, all distinguishing characteristics of H1N1 influenza and influenza B (Figure&#x00A0;<a
-href="#x1-17008r8">S8<!--tex4ht:ref: h1n1_mut --></a>,
-Figure&#x00A0;<a
-href="#x1-17009r9">S9<!--tex4ht:ref: h1n1_r0 --></a>).
+diversity, all distinguishing characteristics of H1N1 influenza and influenza B (<a href="#x1-17008r8">Figure S8<!--tex4ht:ref: h1n1_mut --></a>,
+<a href="#x1-17009r9">Figure S9<!--tex4ht:ref: h1n1_r0 --></a>).
<!--l. 156--><p class="noindent" >In our model, when antigenic phenotype remains static, there may be multiple consecutive
-seasons without appreciable incidence (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>A), a pattern apparently absent from H3N2
+seasons without appreciable incidence (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->A</a>), a pattern apparently absent from H3N2
influenza <span class="cite">[<a
href="#XFinkelman07">16</a>]</span>. We suggest that any model exhibiting punctuated evolution broadly consistent
with the punctuated change seen in the experimental antigenic map will show similar patterns of
incidence. We can &#8216;fix&#8217; the incidence patterns, but at the cost of too smooth an antigenic map
-(Figure&#x00A0;<a
-href="#x1-17003r3">S3<!--tex4ht:ref: incmaptree_smooth --></a>). Evolutionary patterns of the neuraminidase (NA) protein may provide an
+(<a href="#x1-17003r3">Figure S3<!--tex4ht:ref: incmaptree_smooth --></a>). Evolutionary patterns of the neuraminidase (NA) protein may provide an
explanation. Epitopes in the HA and NA proteins are jointly responsible for determining
antigenicity <span class="cite">[<a
href="#XNelson07NatRevGenet">2</a>]</span>, and it is now clear that levels of adaptive evolution are similar between HA and
@@ -455,8 +431,7 @@ <h4 class="likesubsectionHead"><a
another lineage moves tangentially, eventually resulting in two non-interacting viral
lineages. Instead, we find that only movement in a single antigenic direction is favored.
The origins of this pattern can be seen in the interaction between virus evolution and
-host immunity (Figure&#x00A0;<a
-href="#x1-7001r3">3<!--tex4ht:ref: immunity --></a>). As the virus population evolves forward it leaves a wake of
+host immunity (<a href="#x1-7001r3">Figure 3<!--tex4ht:ref: immunity --></a>). As the virus population evolves forward it leaves a wake of
immunity in the host population, and evolution away from this immunity results in the
canalization of the antigenic phenotype; mutations that continue along the line of primary
antigenic variation will show a transmission advantage compared to more tangential
@@ -473,7 +448,7 @@ <h4 class="likesubsectionHead"><a
<!--l. 166--><p class="noindent" ><img
src="figures/immunity.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;3: </span><span
class="content"><span
class="cmbx-10x-x-109">Host immunity and antigenic history of the virus population</span>. Contour
@@ -509,8 +484,7 @@ <h4 class="likesubsectionHead"><a
mutation is the same as in the previous two-dimensional formulation. We arrive at nearly
the same results with this model; principal components analysis shows that the first
and second dimensions of variation account for 87% and 7%, respectively, of the total
-variance (Figure&#x00A0;<a
-href="#x1-17010r10">S10<!--tex4ht:ref: 10dgrid --></a>). Thus, our model predicts that future work probing mutational
+variance (<a href="#x1-17010r10">Figure S10<!--tex4ht:ref: 10dgrid --></a>). Thus, our model predicts that future work probing mutational
effects will support an underlying high-dimensional antigenic space, even though a
two-dimensional map is sufficient to explain observed antigenic relationships among
strains.
@@ -521,21 +495,14 @@ <h4 class="likesubsectionHead"><a
trajectories, and thereby test what happens when we &#8220;wind back the tape&#8221; <span class="cite">[<a
href="#XGouldWonderfulLife">20</a>]</span> on the evolution
of the virus. We ran 100 replicate simulations, each starting from the endpoint of the original
-40-year simulation (Figure&#x00A0;<a
-href="#x1-8001r4">4<!--tex4ht:ref: replicateevol --></a>, Figure&#x00A0;<a
-href="#x1-8002r5">5<!--tex4ht:ref: replicateinc --></a>). Initially, we find a great detail of repeatability; during
+40-year simulation (<a href="#x1-8001r4">Figure 4<!--tex4ht:ref: replicateevol --></a>, <a href="#x1-8002r5">Figure 5<!--tex4ht:ref: replicateinc --></a>). Initially, we find a great detail of repeatability; during
the first year of evolution, every replicate virus population undergoes a similar antigenic
-transition (Figure&#x00A0;<a
-href="#x1-8001r4">4<!--tex4ht:ref: replicateevol --></a>), resulting in a repeatable peak in northern hemisphere incidence (Figure&#x00A0;<a
-href="#x1-8002r5">5<!--tex4ht:ref: replicateinc --></a>).
+transition (<a href="#x1-8001r4">Figure 4<!--tex4ht:ref: replicateevol --></a>), resulting in a repeatable peak in northern hemisphere incidence (<a href="#x1-8002r5">Figure 5<!--tex4ht:ref: replicateinc --></a>).
After three years, repeatability has mostly disappeared, with antigenic phenotype and
-incidence appearing highly variable across replicates (Figure&#x00A0;<a
-href="#x1-8001r4">4<!--tex4ht:ref: replicateevol --></a>, Figure&#x00A0;<a
-href="#x1-8002r5">5<!--tex4ht:ref: replicateinc --></a>). The 1&#8211;2 year
+incidence appearing highly variable across replicates (<a href="#x1-8001r4">Figure 4<!--tex4ht:ref: replicateevol --></a>, <a href="#x1-8002r5">Figure 5<!--tex4ht:ref: replicateinc --></a>). The 1&#8211;2 year
timescale of repeatability can be explained by the presence of standing antigenic variation.
In the initial virus population, there are several novel antigenic variants present at
-low frequency (Figure&#x00A0;<a
-href="#x1-7001r3">3<!--tex4ht:ref: immunity --></a>), one of which, without fail, comes to predominate the virus
+low frequency (<a href="#x1-7001r3">Figure 3<!--tex4ht:ref: immunity --></a>), one of which, without fail, comes to predominate the virus
population.
<!--l. 179--><p class="noindent" ><hr class="figure"><div class="figure"
>
@@ -548,30 +515,20 @@ <h4 class="likesubsectionHead"><a
<!--l. 181--><p class="noindent" > <img
src="figures/replicateevol.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;4: </span><span
class="content"><span
class="cmbx-10x-x-109">Antigenic phenotypes over the course of 4 years of evolution across</span>
<span
class="cmbx-10x-x-109">100 replicate simulations starting from identical initial conditions</span>. Replicate
-simulations were initialized with the end state of the 40-year simulation shown in Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>.
+simulations were initialized with the end state of the 40-year simulation shown in <a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol --></a>.
Each panel shows an additional year of evolution, with black points representing the mean
antigenic phenotypes of the 100 replicate simulations and gray lines representing the history
of each mean antigenic phenotype.</span></div><!--tex4ht:label?: x1-8001r4 -->
<!--l. 186--><p class="noindent" ></div><hr class="endfigure">
-<!--l. 188--><p class="noindent" >We see that the initial evolutionary trajectory, during which time standing variation plays out, is
-highly repeatable, and thus predictable given enough information and the right methods of
-analysis. However, prediction of longer-term evolutionary scenarios will necessarily be difficult or
-impossible except in a vague sense. Through careful surveillance efforts and genetic and antigenic
-characterization of influenza strains, the World Health Organization makes twice-yearly vaccine
-strain recommendations <span class="cite">[<a
-href="#XBarr10">21</a>]</span>. It should be possible to combine these sorts of modeling approaches
-with surveillance data to gauge the likelihood that a sampled variant will spread through the
-population.
-<!--l. 190--><p class="noindent" ><hr class="figure"><div class="figure"
+<!--l. 188--><p class="noindent" ><hr class="figure"><div class="figure"
>
@@ -580,10 +537,10 @@ <h4 class="likesubsectionHead"><a
-<!--l. 192--><p class="noindent" ><img
+<!--l. 190--><p class="noindent" ><img
src="figures/replicateinc.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;5: </span><span
class="content"><span
class="cmbx-10x-x-109">Timeseries of incidence across 100 replicate simulations with identical</span>
@@ -592,11 +549,19 @@ <h4 class="likesubsectionHead"><a
the course of 6 years. Solid black lines represent the median weekly incidence across the
100 replicate simulations, while gray intervals represent the interquartile range across
simulations. There is little variability for the first year of replicate simulations. Replicate
-simulations were initialized with the end state of the 40-year simulation shown in Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>.</span></div><!--tex4ht:label?: x1-8002r5 -->
+simulations were initialized with the end state of the 40-year simulation shown in <a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol --></a>.</span></div><!--tex4ht:label?: x1-8002r5 -->
-<!--l. 195--><p class="noindent" ></div><hr class="endfigure">
+<!--l. 193--><p class="noindent" ></div><hr class="endfigure">
+<!--l. 195--><p class="noindent" >We see that the initial evolutionary trajectory, during which time standing variation plays out, is
+highly repeatable, and thus predictable given enough information and the right methods of
+analysis. However, prediction of longer-term evolutionary scenarios will necessarily be difficult or
+impossible except in a vague sense. Through careful surveillance efforts and genetic and antigenic
+characterization of influenza strains, the World Health Organization makes twice-yearly vaccine
+strain recommendations <span class="cite">[<a
+href="#XBarr10">21</a>]</span>. It should be possible to combine these sorts of modeling approaches
+with surveillance data to gauge the likelihood that a sampled variant will spread through the
+population.
<!--l. 197--><p class="noindent" >Recent work on empirical fitness landscapes has shown that natural selection follows few
mutational paths <span class="cite">[<a
href="#XWeinreich06">22</a>]</span>. The spindly genealogical tree and the almost linear serial replacement of
@@ -652,6 +617,8 @@ <h4 class="likesubsectionHead"><a
class="cmmi-10x-x-109">R</span><sub><span
class="cmr-8">0</span></sub> in a naive host population is 1.8. There is no super-infection in the
model.
+
+
<!--l. 207--><p class="noindent" >Each virus possesses an antigenic phenotype, represented as a location in Euclidean space. Here,
we primarily use a two-dimensional antigenic location. After recovery, a host &#8216;remembers&#8217; the
phenotype of its infecting virus as part of its immune history. When a contact event occurs and a
@@ -672,8 +639,6 @@ <h4 class="likesubsectionHead"><a
href="#XSmith04">9</a>]</span>. The probability that infection occurs after exposure is
proportional to the distance <span
class="cmmi-10x-x-109">d </span>to the closest phenotype in the host immune history. Risk of
-
-
infection follows the form <span
class="cmmi-10x-x-109">&#x03C1; </span>= min<span
class="cmsy-10x-x-109">{</span><span
@@ -734,6 +699,8 @@ <h4 class="likesubsectionHead"><a
Instead, the viral genealogy is directly recorded. This is made possible by tracking transmission
events connecting infections during the simulation; infections record the ID of their
&#8216;parent&#8217; infection. Proceeding from a sample of infections, their genealogical history can
+
+
be reconstructed by following consecutive links to parental infections. During this
procedure, lineages coalesce to the ancestral lineages shared by the sampled infections,
eventually arriving at the initial infection introduced at the beginning of the simulation.
@@ -747,17 +714,12 @@ <h4 class="likesubsectionHead"><a
have implemented similar tracking of infection trees <span class="cite">[<a
href="#XVolz09">26</a>,&#x00A0;<a
href="#XOdea11">27</a>]</span>. This genealogy-centric
-
-
approach makes many otherwise difficult calculations transparent, such as calculating
-lineage-specific region-specific migration rates (Figure&#x00A0;<a
-href="#x1-4003r2">2<!--tex4ht:ref: spatial --></a>) and lineage-specific mutation effects
-(Figure&#x00A0;<a
-href="#x1-17005r5">S5<!--tex4ht:ref: mutspectrum --></a>).
+lineage-specific region-specific migration rates (<a href="#x1-4003r2">Figure 2<!--tex4ht:ref: spatial --></a>) and lineage-specific mutation effects
+(<a href="#x1-17005r5">Figure S5<!--tex4ht:ref: mutspectrum --></a>).
<!--l. 217--><p class="noindent" >Infections are sampled at a rate designed to give approximately 6000 samples over the course of
the simulation, with genealogies constructed from a subsample of approximately 300 samples.
-The results presented in Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a> represent a single representative model output; one hundred
+The results presented in <a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol --></a> represent a single representative model output; one hundred
replicate simulations were conducted to arrive at statistical estimates.
<!--l. 219--><p class="noindent" >
<h4 class="likesubsectionHead"><a
@@ -819,18 +781,18 @@ <h4 class="likesubsectionHead"><a
effect size (mean = 0<span
class="cmmi-10x-x-109">.</span>6, sd = 0<span
class="cmmi-10x-x-109">.</span>2), then antigenic drift occurs in a more continuous
+
+
fashion, resulting in less variation in seasonal incidence and a smoother distribution of
-antigenic phenotypes (Figure&#x00A0;<a
-href="#x1-17003r3">S3<!--tex4ht:ref: incmaptree_smooth --></a>). If mutations are less common (<span
+antigenic phenotypes (<a href="#x1-17003r3">Figure S3<!--tex4ht:ref: incmaptree_smooth --></a>). If mutations are less common (<span
class="cmmi-10x-x-109">&#x03BC; </span>= 5 <span
class="cmsy-10x-x-109">&#x00D7; </span>10<sup><span
class="cmsy-8">-</span><span
class="cmr-8">5</span></sup>) and show
more variance in effect (mean = 0<span
class="cmmi-10x-x-109">.</span>7, sd = 0<span
class="cmmi-10x-x-109">.</span>5), then antigenic change occurs in a more
-punctuated fashion (Figure&#x00A0;<a
-href="#x1-17004r4">S4<!--tex4ht:ref: incmaptree_rough --></a>). Basic reproductive number <span
+punctuated fashion (<a href="#x1-17004r4">Figure S4<!--tex4ht:ref: incmaptree_rough --></a>). Basic reproductive number <span
class="cmmi-10x-x-109">R</span><sub><span
class="cmr-8">0</span></sub> can be traded off with
mutational parameters to some extent. Less mutational input and higher <span
@@ -842,8 +804,6 @@ <h4 class="likesubsectionHead"><a
class="cmmi-10x-x-109">R</span><sub><span
class="cmr-8">0</span></sub> results in increased rates of emergence of antigenically novel
strains.
-
-
<!--l. 225--><p class="noindent" >In 20 out of the 100 replicate simulations, we observed a major bifurcation of antigenic phenotype
and a consequent increase in incidence and genealogical diversity. These simulations were
removed from the analysis. Similar to Koelle et al. <span class="cite">[<a
@@ -868,8 +828,7 @@ <h4 class="likesubsectionHead"><a
distance between them averages 0.83 antigenic units with a standard deviation of 0.64
units.
<!--l. 231--><p class="noindent" >We added noise to each of the 5943 sampled viruses in this fashion resulting in an approximated
-antigenic map (Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>D). Virus samples were then clustering following standard clustering
+antigenic map (<a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->D</a>). Virus samples were then clustering following standard clustering
algorithms. We tried clustering by the <span
class="cmmi-10x-x-109">k</span>-means algorithm and also agglomerative hierarchical
clustering with a variety of linkage criterion. We found that clustering by Ward&#8217;s criterion
@@ -879,13 +838,13 @@ <h4 class="likesubsectionHead"><a
<!--l. 234--><p class="noindent" >
<h4 class="likesubsectionHead"><a
id="x1-14000"></a>Acknowledgments</h4>
+
+
<!--l. 235--><p class="noindent" >We would like to thank Sarah Cobey, Aaron King, Pejman Rohani and the attendees of the 2011
RAPIDD Workshop on Phylodynamics for helpful discussion. We would also like to thank Ed
Baskerville and Daniel Zinder for programming advice. The term &#8216;canalization&#8217; was originally
suggested by Micaela Martinez-Bakker.
<!--l. 238--><p class="noindent" >
-
-
<h4 class="likesubsectionHead"><a
id="x1-15000"></a>Funding</h4>
<!--l. 239--><p class="noindent" >TB is supported by the Howard Hughes Medical Institute and by the European Molecular
@@ -919,6 +878,8 @@ <h3 class="likesectionHead"><a
id="XFerguson03"></a>Ferguson NM, Galvani AP, Bush RM (2003) Ecological and immunological
determinants of influenza evolution. Nature 422: 428&#8211;433.
</p>
+
+
<p class="bibitem" ><span class="biblabel">
5.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XTria05"></a>Tria F, Lässig M, Peliti L, S F (2005) A minimal stochastic model for influenza
@@ -929,8 +890,6 @@ <h3 class="likesectionHead"><a
id="XKoelle06"></a>Koelle K, Cobey S, Grenfell B, Pascual M (2006) Epochal evolution shapes
the phylodynamics of interpandemic influenza A (H3N2) in humans. Science 314:
1898&#8211;1903.
-
-
</p>
<p class="bibitem" ><span class="biblabel">
7.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
@@ -966,6 +925,8 @@ <h3 class="likesectionHead"><a
The genomic and epidemiological dynamics of human influenza A virus. Nature 453:
615&#8211;619.
</p>
+
+
<p class="bibitem" ><span class="biblabel">
13.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XBedfordBMC11"></a>Bedford T, Cobey S, Pascual M (2011) Strength and temp of selection revealed
@@ -976,8 +937,6 @@ <h3 class="likesectionHead"><a
id="XRussell08"></a>Russell CA, Jones TC, Barr IG, Cox NJ, Garten RJ, et&#x00A0;al. (2008) The global
circulation of seasonal influenza A (H3N2) viruses. Science 320: 340&#8211;346.
</p>
-
-
<p class="bibitem" ><span class="biblabel">
15.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XBedford10"></a>Bedford T, Cobey S, Beerli P, Pascual M (2010) Global migration dynamics
@@ -1015,6 +974,8 @@ <h3 class="likesectionHead"><a
21.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XBarr10"></a>Barr I, McCauley J, Cox N, Daniels R, Engelhardt O, et&#x00A0;al. (2010)
Epidemiological, antigenic and genetic characteristics of seasonal influenza A (H1N1),
+
+
A (H3N2) and B influenza viruses: basis for the WHO recommendation on the
composition of influenza vaccines for use in the 2009-2010 Northern Hemisphere
season. Vaccine 28: 1156&#8211;1167.
@@ -1024,8 +985,6 @@ <h3 class="likesectionHead"><a
id="XWeinreich06"></a>Weinreich D, Delaney N, DePristo M, Hartl D (2006) Darwinian evolution can
follow only very few mutational paths to fitter proteins. Science 312: 111&#8211;114.
</p>
-
-
<p class="bibitem" ><span class="biblabel">
23.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XGog02"></a>Gog J, Grenfell B (2002) Dynamics and selection of many-strain pathogens. Proc
@@ -1060,6 +1019,8 @@ <h3 class="likesectionHead"><a
France, and Australia: transmission and prospects for control. Epidemiol Infect 136:
852&#8211;864.
</p>
+
+
<p class="bibitem" ><span class="biblabel">
29.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XViboud06"></a>Viboud C, Bjørnstad O, Smith D, Simonsen L, Miller M, et&#x00A0;al. (2006) Synchrony,
@@ -1071,8 +1032,6 @@ <h3 class="likesectionHead"><a
lines of infection and disease in human influenza: a review of volunteer challenge
studies. Am J Epidemiol 167: 775&#8211;785.
</p>
-
-
<p class="bibitem" ><span class="biblabel">
31.<span class="bibsp">&#x00A0;&#x00A0;&#x00A0;</span></span><a
id="XPark09"></a>Park A, Daly J, Lewis N, Smith D, Wood J, et&#x00A0;al. (2009) Quantifying the impact
@@ -1118,7 +1077,7 @@ <h3 class="likesectionHead"><a
<!--l. 260--><p class="noindent" ><img
src="figures/phenotypes.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S1: </span><span
class="content"><span
class="cmbx-10x-x-109">Antigenic evolution over the course of the 40-year simulation</span>. (A)
@@ -1127,8 +1086,7 @@ <h3 class="likesectionHead"><a
class="cmmi-10x-x-109">x </span>= 0, <span
class="cmmi-10x-x-109">y </span>= 0) for each of 5943 virus samples
relative to time of virus sampling. Viruses were sampled at a constant rate proportional to
-prevalence and coloring was determined from the antigenic map in Figure&#x00A0;<a
-href="#x1-4001r1">1<!--tex4ht:ref: evol --></a>D.</span></div><!--tex4ht:label?: x1-17001r1 -->
+prevalence and coloring was determined from the antigenic map in <a href="#x1-4001r1">Figure 1<!--tex4ht:ref: evol -->D</a>.</span></div><!--tex4ht:label?: x1-17001r1 -->
<!--l. 263--><p class="noindent" ></div><hr class="endfigure">
@@ -1146,7 +1104,7 @@ <h3 class="likesectionHead"><a
<!--l. 272--><p class="noindent" ><img
src="figures/driftvsinc.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S2: </span><span
class="content"><span
class="cmbx-10x-x-109">Correlation between antigenic drift and attack rate</span>. Antigenic drift is
@@ -1234,7 +1192,7 @@ <h3 class="likesectionHead"><a
<!--l. 312--><p class="noindent" > <img
src="figures/mutspectrum.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S5: </span><span
class="content"><span
class="cmbx-10x-x-109">Mutation spectrum in two-dimensional antigenic space of side branch</span>
@@ -1262,7 +1220,7 @@ <h3 class="likesectionHead"><a
<!--l. 326--><p class="noindent" ><img
src="figures/probtrunk.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S6: </span><span
class="content"><span
class="cmbx-10x-x-109">Relationship between a mutation&#8217;s phenotypic effect and its</span>
@@ -1290,7 +1248,7 @@ <h3 class="likesectionHead"><a
<!--l. 338--><p class="noindent" ><img
src="figures/waittimes.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S7: </span><span
class="content"><span
class="cmbx-10x-x-109">Observed vs.</span><span
@@ -1385,7 +1343,7 @@ <h3 class="likesectionHead"><a
<!--l. 378--><p class="noindent" > <img
src="figures/10dgrid.png" alt="PIC"
>
-<br /> <div class="caption"
+<img style="float:none; padding:0px;" src="spanner.png"><br><div class="caption"
><span class="id">Figure&#x00A0;S10: </span><span
class="content"><span
class="cmbx-10x-x-109">Principal components of antigenic variation under a 10-sphere</span>

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