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ESS in a River Network with Two Branches
  
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KeyWord:Evolution of dispersal, evolutionarily stable strategy, advective patchy environment, selection gradient
Author NameAffiliation
Gongyi Jin Department of Mathematics, Shanghai Normal University, Shanghai 200234, P.R. China 
Xiaoqian Feng Department of Mathematics, Shanghai Normal University, Shanghai 200234, P.R. China 
Peng Zhou Department of Mathematics, Shanghai Normal University, Shanghai 200234, P.R. China 
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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.