ESS in a River Network with Two Branches

Abstract

In a recent work by Jiang et al. [Bull. Math. Biol., 2020, Paper No. 131, 42pp], to discuss the impact of differing topology of river networks on the evolution of dispersal, the authors proposed three different models and found the winning of slower/faster diffuser or evolutionarily singular strategies. However, it is unknown whether there is an evolutionarily stable strategy (ESS, a central concept in evolution game theory) for these three models. In this paper, focusing on the Model (III) proposed by them (the most complicated one as they stated), we give a confirmed answer to this issue, that is, there does exist ESS.