code for Fronhofer et al. (2015) Journal of Theoretical Biology
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Evolution of dispersal distance: maternal investment leads to bimodal dispersal kernels

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Fronhofer, E. A.; Poethke, H. J. & Dieckmann, U. Evolution of dispersal distance: maternal investment leads to bimodal dispersal kernels J. Theor. Biol., 2015, 365, 270-279.

Abstract: Since dispersal research has mainly focused on the evolutionary dynamics of dispersal rates, it remains unclear what shape evolutionarily stable dispersal kernels have. Yet, detailed knowledge about dispersal kernels, quantifying the statistical distribution of dispersal distances, is of pivotal importance for understanding biogeographic diversity, predicting species invasions, and explaining range shifts. We therefore examine the evolution of dispersal kernels in an individual-based model of a population of sessile organisms, such as trees or corals. Specifically, we analyze the influence of three potentially important factors on the shape of dispersal kernels: distance-dependent competition, distance-dependent dispersal costs, and maternal investment reducing an offspring׳s dispersal costs through a trade-off with maternal fecundity. We find that without maternal investment, competition and dispersal costs lead to unimodal kernels, with increasing dispersal costs reducing the kernel׳s width and tail weight. Unexpectedly, maternal investment inverts this effect: kernels become bimodal at high dispersal costs. This increases a kernel׳s width and tail weight, and thus the fraction of long-distance dispersers, at the expense of simultaneously increasing the fraction of non-dispersers. We demonstrate that the qualitative robustness of our results against variations in the tested parameter combinations.