Population Extinction on a Random Fitness Seascape*

We explore the role of stochasticity and noise in the statistical outcomes of commonly studied population dynamics models within a space-independent (mean-field) perspective. Specifically, we consider a distributed population with logistic growth at each location, subject to ``seascape'' noise, wherein the population's fitness randomly varies with location and time. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.