The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

Abstract

By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs 1 when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates.

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits

“…This is also in line with previous results on the evolution of single traits that have found that evolutionary branching is inhibited by limited dispersal (e.g., Day ; Ajar ; Parvinen et al. ; Wakano and Lehmann ). In such models and ours, limited dispersal inhibits evolutionary branching because it creates genetic correlations among competing individuals, so that a mutant cannot be as different to common types as in well‐mixed population.…”

“…This finding is in line with a recent computational eco-evolutionary model, which found that when species can evolve cross-feeding interactions, mutualistic coexistence is compromised by spatial structure and limited dispersal (Oliveira et al 2014). This is also in line with previous results on the evolution of single traits that have found that evolutionary branching is inhibited by limited dispersal (e.g., Day 2001;Ajar 2003;Parvinen et al 2017;Wakano and Lehmann 2014). In such models and ours, limited dispersal inhibits evolutionary branching because it creates genetic correlations among competing individuals, so that a mutant cannot be as different to common types as in well-mixed population.…”

A quantitative genetics approach to the evolution of phenotypic (co)variance under limited dispersal, with an application to socially synergistic traits

“…This finding is in line with a recent computational eco-evolutionary model which found that when species can evolve cross-feeding interactions, mutualistic coexistence is compromised by spatial structure and limited dispersal (Oliveira et al, 2014). This is also in line with previous results on the evolution of single traits that have found that evolutionary branching is inhibited by limited dispersal (e.g., Day, 2001, Ajar, 2003, Wakano and Lehmann, 2014, Parvinen et al, 2017. In such models and ours, limited dispersal inhibits evolutionary branching because it creates genetic correlations among competing individuals, so that a mutant cannot be as different to common types as in well-mixed population.…”

The components of directional and disruptive selection in heterogeneous group-structured populations

“…(52) predicts that the sign of the disruptive selection coefficient is solely determined by the sign of d 2 fs/dz 2 1 no matter whether dispersal is complete or locally limited. A similar result has been shown inParvinen et al (2017) by assuming a Wright-Fisher process.…”