THE DISTRIBUTION OF POPULATION SURVIVAL TIMES

A discrete unstructured population model with nonoverlapping generatio ns is used to calculate the probability of extinction as a function of the number of generations elapsed and the initial population size. Th is formulation accounts for demographic effects, environmental variati on, and catastrophic mortality. Accurate approximations are developed for large carrying capacity and large time. The main qualitative resul ts are as follows: The probability of early extinction depends strongl y on the initial population size. A substantial fraction of small star ting populations become extinct within a short time. Those that surviv e the initial period typically survive for a long time. This skew in e xtinction times makes the expected time to extinction a misleading ind icator. Probabilities of extinction are sensitive to environmental var iation in the net reproductive rate and the shape of the distribution of disturbances, not just its mean. Probabilities of extinction are li kewise sensitive to the rate of catastrophe occurrences and the shape of the catastrophe distribution, not just its mean. Diffusion approxim ations are likely to be inaccurate for small populations or for popula tions that show large changes in size in a single generation. These di fficulties may be overcome by use of an extrapolation based on solutio ns for discrete population size and time.