Modelling coevolution in ecological networks with adaptive dynamics

Abstract

Coevolution can impose density‐dependent selection through reciprocal biotic interactions on the fitness of involved species, driving directional and disruptive trait evolution and rich evolutionary possibilities. Coevolution has since Darwin been considered a potential path leading to adaptive diversification that could explain the emergence of ecological networks of biotic interactions that harbour multiple interacting species (eg, pollination networks and food webs). Here, we present adaptive dynamics, a powerful tool of evolutionary invasion analysis that explores how quantitative traits undergo incremental evolution, to exploring the emergence of multi‐species networks through coevolution. Specifically, we exemplify the feasibility of using adaptive dynamics to investigate trait evolution in 4 ecological networks, driven, respectively, by resource competition, trophic interactions, as well as bipartite mutualistic and antagonistic interactions. We use a set of ordinary differential equations to describe, at different paces, the population dynamics and trait dynamics of involved species assemblages. Through computing ecological equilibrium, invasion fitness, selection gradient and evolutionary singularity, and testing for evolutionary stability and the coexistence criterion of mutual invasibility, we illustrate the typical evolutionary dynamics and the criteria of evolutionary stability and branching in these ecological networks. Results highlight the importance of the form of trait‐mediated interaction kernel (ie, interaction strength as a function of trait difference) to adaptive diversification in these coevolutionary systems. We conclude by advocating that biotic interactions between two species can indeed lead to diffuse and even escape‐and‐radiate coevolution, making the emerged ecological networks an ideal model for studying complex adaptive systems.