Determining selection across heterogeneous landscapes: a perturbation-based method and its application to modeling evolution in space

Wickman, J., Diehl, S., Blasius, B., Klausmeier, C., Ryabov, A., & Brännström, Å. (2017). Determining selection across heterogeneous landscapes: a perturbation-based method and its application to modeling evolution in space. American Naturalist 189 (4) 381-395. 10.1086/690908.

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Abstract

Spatial structure can decisively influence the way evolutionary processes unfold. Several methods have thus far been used to study evolution in spatial systems, including population genetics, quantitative genetics, momentclosure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply in both continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very effi- cient, and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

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