Carrying capacity and demographic stochasticity: Scaling behavior of the stochastic logistic model

The stochastic logistic model is the simplest model that combines individua l-level demography with density dependence. It explicitly or implicitly und erlies many models of biodiversity of competing species, as well as non-spa tial or metapopulation models of persistence of individual species. The mod el has also been used to study persistence in simple disease models. The st ochastic logistic model has direct relevance for questions of limiting simi larity in ecological systems. This paper uses a biased random walk heuristi c to derive a scaling relationship for the persistence of a population unde r this model, and discusses its implications for models of biodiversity and persistence. Time to extinction of a species under the stochastic logistic model is approximated by the exponential of the scaling quantity U=(R-1)(2 ) N/R(R+1), where N is the habitat size and R is the basic reproductive num ber. (C) 2000 Academic Press.