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We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two evolutionarily stable strategies: the efficient one in which the population is in a state with a maximal payoff and the risk-dominant one where players are averse to risk. We show that for a large range of parameters of our dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy.
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is shown that ran
We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to Chinas one-child policy. By allowing any number of births, but with an imposed dela
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evoluti
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a ca
In addition to their unusually long life cycle, periodical cicadas, {it Magicicada} spp., provide an exceptional example of spatially synchronized life stage phenology in nature. Within regions (broods) spanning 50,000 to 500,000 km$^2$, adults emerg