Die Hard: the route to extinction in variable environments

Per Lundberg

Theoretical Ecology, Lund University, Sweden

Abstract

Our aim is to formulate a population model that can account for a variety of routes to extinction and still retain the desired properties of commonly used discrete time models. We also attempt to derive the stochastic parts of our model from "first principles" to make the inclusion of stochasticity more realistic and general. We start our analysis with the simplest possible projection of the population density at time t, N(t), to the next time step N(t+1), i.e.,

N(t+1) = N(t) + B(t) - D(t)

where B(t) is the number of offspring born in year t, surviving at least till t+1 and D(t) is the number of adults that die in year t. In this way, juveniles and adults have different mortality rates. They are often of different magnitude and distribution, and we will make B(t) and D(t) independent of each other. The problem is now to find appropriate statistical distributions of B(t) and D(t). The population model thus derived will be able to explain a range of extinction behaviors and we will show that the model structure and its predictions are relatively robust to assumptions about underlieing statistical distributions of environmental noise and demographic processes.