Evolutionary stability in an eco-evolutionary game dynamics with density dependence

Based on the concept of eco-evolutionary game dynamics proposed by Tilman et al. (2020) the dynamical stability and the ecologically evolutionarily stable strategy (eco-ESS) of a simple eco-evolutionary game dynamics with density dependence are investigated. In this model, for simplicity, we assume that only birth rate of individuals depends on the pairwise interactions between individuals and that the payoff matrix is density-dependent. Our main results show clearly that, compared with the condition of ESS in classic evolutionary game dynamics, the condition of the eco-ESS is more stringent in our eco-evolutionary game dynamics.