Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space

Abstract

Online enhancements: appendixes.abstract: Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individualbased 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 both in 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 efficient 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.

Evolution of resource specialisation in competitive metacommunities

“…For substitutable resources (), diversity declines abruptly at the diagonal , where the system undergoes a shift in selection regime. To understand this regime shift, we use ideas from Wickman et al (), who showed that selection in spatially heterogeneous systems described by reaction‐diffusion equations can be divided into sympatric and parapatric selection terms. Sympatric selection is a spatially weighted average of local disrupting or stabilising selection, and parapatric selection is, roughly speaking, a measure of the variance in local directional selection.…”

“…Ecologically, low or no movement corresponds to the species sorting scenario of metacommunity theory (Leibold et al ), for which regional coexistence of many resource competitors is possible if the landscape contains a broad range of local resource supply ratios (Tilman ). Wickman et al () showed that this also holds evolutionarily for perfectly substitutable resources and generalist‐favouring trade‐offs. The number of evolutionarily coexisting consumers increases as diffusion rates decrease, and as diffusion rates approach zero, an infinite number of consumers can coexist, which adapt locally to a continuum of spatially varying supply ratios (Wickman et al ).…”

“…Wickman et al () showed that this also holds evolutionarily for perfectly substitutable resources and generalist‐favouring trade‐offs. The number of evolutionarily coexisting consumers increases as diffusion rates decrease, and as diffusion rates approach zero, an infinite number of consumers can coexist, which adapt locally to a continuum of spatially varying supply ratios (Wickman et al ).…”

“…Conversely, the only study that included different resources types (antagonistic to substitutable to essential, Schreiber & Tobiason 2003) considered, in turn, only linear affinity trade-offs, which are neither specialist nor generalist-favouring. Finally, the few studies considering heterogeneous environments focused, again, on perfectly substitutable resources (Parvinen & Egas 2004;Nurmi & Parvinen 2008;D ebarre & Gandon 2010;Wickman et al 2017). Yet, resource types are rarely perfectly substitutable, and trade-offs are rarely perfectly linear, and their joint effects on trait evolution and coexistence of resource competitors are poorly understood.…”

Dirac-concentrations in an integro-pde model from evolutionary game theory

“…In general, they may be derived from density-and frequency-dependent interactions among phenotypes, in which case the relative advantage of a trait x against a different trait y depends on the context of their interaction. For instance, in [9,13,17,29] the invasion fitness between phenotypes with different dispersal strategies is obtained in the context of reaction-diffusion equations modeling the two competiting species in a bounded spatial domain. Those results concerning pairwise interactions has implications in the mutation-selection framework [12,11,18,19,24], which concerns populations structured by space and trait.…”