We explore the combined roles of stochasticity and migration on the ?statistical outcomes of commonly studied models of population ?dynamics. Specifically, we consider a distributed population with ?logistic growth at each location, subject to "seascape" ?fluctuations, 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, which we study within a mean-field perspective in ?which migration occurs between any pair of sites. 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 fitness-fluctuation amplitudes. The results are compared and ?contrasted with the more conventional choice of demographic noise due ?to stochasticity in reproduction. We anticipate that key features of ?the results hold beyond the mean-field limit, and potentially account ?for the many observations of the empirical Richard's growth law in ?natural settings.