Limiting similarity of competitive species and demographic stochasticity

Stochastic replicator dynamics and evolutionary stability

To develop the concept of evolutionary stability in a stochastic environment, we investigate the continuous-time dynamics of a two-phenotype linear evolutionary game with generally correlated random payoffs in pairwise interactions. By using the Gram-Schmidt orthogonalization procedure and Itô's formula, we deduce a stochastic differential equation for the phenotype frequencies that extends the replicator equation, called the stochastic replicator equation. We give conditions for stochastic stability of a fixation state or a constant interior equilibrium point with respect to the stochastic dynamics of the two phenotypes. We show that, if a fixation state is stochastically stable, then the pure strategy corresponding to this fixation state must be stochastically evolutionarily stable with respect to mixed strategies. However, this is not the case for a mixed strategy that corresponds to a stochastically stable constant interior equilibrium point with respect to the two phenotypes.

Stochastic evolutionary stability in matrix games with random payoffs

Evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behavior, but also widely used in economics and social sciences. Recently, in order to reveal the stochastic dynamical properties of evolutionary games in randomly fluctuating environments, the concept of stochastic evolutionary stability based on conditions for stochastic local stability for a fixation state was developed in the context of a symmetric matrix game with two phenotypes and random payoffs in pairwise interactions [Zheng et al., Phys. Rev. E 96, 032414 (2017)2470-004510.1103/PhysRevE.96.032414]. In this paper, we extend this study to more general situations, namely, multiphenotype symmetric as well as asymmetric matrix games with random payoffs. Conditions for stochastic local stability and stochastic evolutionary stability are established. Conditions for a fixation state to be stochastically unstable and almost everywhere stochastically unstable are distinguished in a multiphenotype setting according to the initial population state. Our results provide some alternative perspective and a more general theoretical framework for a better understanding of the evolution of animal behavior in a stochastic environment.

Empirical Support for the Pattern of Competitive Exclusion between Insect Parasitic Fungi

Fungal entomopathogens are largely facultative parasites and play an important role in controlling the density of insect populations in nature. A few species of these fungi have been used for biocontrol of insect pests. The pattern of the entomopathogen competition for insect individuals is still elusive. Here, we report the empirical competition for hosts or niches between the inter- and intra-species of the entomopathogens Metarhizium robertsii and Beauveria bassiana. It was found that the synergistic effect of coinfection on virulence increase was not evident, and the insects were largely killed and mycosed by M. robertsii independent of its initial co-inoculation dosage and infection order. For example, >90% dead insects were mycosed by M. robertsii even after immersion in a spore suspension with a mixture ratio of 9:1 for B. bassiana versus M. robertsii. The results thus support the pattern of competitive exclusion between insect pathogenic fungi that occurred from outside to inside the insect hosts. Even being inferior to compete for insects, B. bassiana could outcompete M. robertsii during co-culturing in liquid medium. It was also found that the one-sided mycosis of insects occurred during coinfection with different genotypic strains of either fungi. However, parasexual recombination was evident to take place between the compatible strains after coinfection. The data of this study can help explain the phenomena of the exclusive mycosis of insect individuals, but co-occurrence of entomopathogens in the fields, and suggest that the synergistic effect is questionable regarding the mixed use of fungal parasites for insect pest control.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Evolutionary stability concepts in a stochastic environment

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.