STOCHASTIC EXTINCTION MODELS DISCRETE IN TIME

We analyse the stochastic dynamics of a population with non-overlapping generations by a Markov chain model with discrete time steps. It is demonstrated that one can calculate mean lifetimes and colonization probabilities from the elements of the corresponding transition matrix. Our model includes demographic as well as environmental noise. An important contribution to demographic noise comes from sexual reproduction which our model takes into account. Introducing comparatively low mating probabilities results in an Allee effect which has a great influence on the mean lifetimes and colonization abilities of small populations. The non-overlapping of generations allows us to reduce the two-dimensional model including both sexes to the one-dimensional case. If there is no environmental stochasticity we find that the long mean lifetimes of asexual populations are extremely reduced in models with two sexes. But the stronger the environmental variations are, the more the large difference between sexual and asexual models disappears. Another important result is that the mean lifetime grows very fast (exponentially) with the capacity if we assume slight environmental variations (or exclude them totally), but only slowly (linearly) if we include them. These trends are supported by the findings from models with overlapping generations that exist in the literature.