A population process with offspring distribution depending on both population size and generation

Abstract

A population process {Zn} is defined, with offspring distribution depending on both population size and generation number. As is well known, in models where the offspring distribution depends only on the size, under most conditions extinction surely results. The model we now introduce would mean that if history has an influence on evolution of the population, it is possible to obtain models for which a probability as high as desired exists that the population size balances between two given values.