Population Dynamics in a Changing Environment: Random versus Periodic Switching

Environmental changes greatly influence the evolution of populations. In this talk, we discuss the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modelled by a carrying capacity that switches either randomly or periodically between states of resources abundance and scarcity. The population dynamics is characterised by demographic noise (birth and death events) coupled to the fluctuating population size. By combining analytical and simulation methods, we elucidate the similarities and differences of evolving subject to stochastic and periodic switching. We show that the population size distribution is generally broader under intermediate and fast random switching than under periodic variations, with periodic changes leading to an abrupt transition from slow to fast switching regimes. The fixation probability under intermediate/fast random and periodic switching can hence vary significantly, with markedly different asymptotic behaviours. We also determine the conditions under which the fixation probability of the slow strain is maximum when the dynamics is driven by asymmetric switching. If time permits, I will outline how our methodology also allows us to analyse the complex eco-evolutionary dynamics arising when the slow strain produces public goods benefiting the entire population.