Dynamics of populations in a changing environment

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Abstract
We present an individual-based model of a population that lives in a changing environment. The individuals forming the population are subject to mutations and selection pressure. Using Monte Carlo simulations we have shown that, depending on the values of the mutation rate and selection, the population may reach either an active phase (it will survive) or an absorbing phase (it will become extinct). We have determined that the transition between the two states (phases) is continuous. We have shown that when the selection is weaker the population lives in all available space, while if the selection is stronger, it will move to the regions where the living conditions are better, avoiding those with more difficult conditions. The dependence of the mean time to extinction on the rate of mutations has been determined and discussed.