Probability of Extinction in a Finite Population with Truncation Selection

Abstract

SUMMARY A model is considered for a finite population in the presence of a combination of natural and artificial selection. The population is assumed to contain two types of individuals which reproduce according to a Poisson distribution. The probability that a given type is lost within a certain time is obtained. An expression is derived which gives the expected number of individuals present in the population at a given time. Some numerical results are presented for various values of the parameters. A procedure to obtain the approximate value of the probability of extinction is discussed, and the probability of ultimate extinction is approximated using a diffusion approximation with the backward diffusion equation. The expected response to selection in the long term is discussed.