Linear analysis solves two puzzles in population dynamics: the route to extinction and extinction in coloured environments

In this paper, we give simple explanations to two unsolved puzzles that have emerged in recent theoretical studies in population dynamics. First, the tendency of some model populations to go extinct from high population densities, and second, the positive effect of autocorrelated environments on extinction risks for some model populations. Both phenomena are given general explanations by simple, linear, sto-chastic models. We emphasize the predictive and explanatory power of such models.