Costly defense traits in structured populations

TL;DR

This paper models the dynamics of a costly defense trait in structured populations, showing how spatial structure and ecological parameters influence whether the trait becomes fixed or extinct.

Contribution

It introduces a new model combining Lotka-Volterra dynamics with spatial structure, deriving conditions for fixation or extinction of defense traits.

Findings

Defense trait frequency converges to Wright-Fisher diffusions with frequency-dependent migration.

Fixation or extinction depends on the comparison between selective disadvantage and ecological parameters.

The model provides explicit criteria for the evolutionary fate of costly defense traits.

Abstract

We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population, where one type of prey individuals - modeling carriers of a defense trait - is more effective in defending against the predators but has a weak reproductive disadvantage. Under certain assumptions we prove that the relative frequency of these defenders in the total prey population converges to spatially structured Wright-Fisher diffusions with frequency-dependent migration rates. For the many-demes limit (mean-field approximation) hereof, we show that the defense trait goes to fixation/extinction if and only if the selective disadvantage is smaller/larger than an explicit function of the ecological model parameters.