Criteria for extinction of certain population growth processes with interacting types

Abstract

A study is made of a series of stochastic growth processes related to multi-type branching models with interaction phenomena among the types with aim to ascertain criteria for extinction or non-extinction of the population. It is established that trends depicting changes of expected sizes of types generally overwhelm any effects of statistical fluctuations such that the conditions for extinction reduce to natural conditions on expected values. Three models are developed. The first two involve special mating systems for certain two sex populations. The last model is a neutralization phenomenon for two types of particles.