Bisexual Galton-Watson branching process with population-size-dependent mating

Abstract

In this paper, we introduce a bisexual Galton-Watson branching process with mating function dependent on the population size in each generation. Necessary and sufficient conditions for the process to become extinct with probability 1 are investigated for two possible conditions on the sequence of mating functions. Some results for the probability generating functions associated with the process are also given.

A class of controlled bisexual branching processes with mating depending on the number of progenitor couples

“…In such a particular case, the model (1) may be considered under the perspective of the class of processes studied in Molina et al (2002) (1) is reduced to the class of models given in Daley (1968).…”

“…Alsmeyer and Rösler (1996), Bruss (1984), Daley (1968), González et al (2000González et al ( , 2001, Molina et al (2002) or Xing and Wang (2005). We refer the reader to Hull (2003) or Haccou et al (2005) m a n u s c r i p t 2 M. Molina et al for surveys about these processes.…”

On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

“…By developing some techniques similar to those of Daley et al (1986) and Molina et al (2002), we obtain a criterion analogous to theirs for superadditive branching processes.…”

“…Molina et al (2002) suggested a bisexual Galton-Watson model with population-sizedependent mating. They obtained a necessary and sufficient condition for the process to become extinct with probability 1.…”

Moment Estimation in the Class of Bisexual Branching Processes With Population–size Dependent Mating

“…In particular, the bisexual branching process with population-size dependent mating, unlike Daley's model, introduces the novelty that the function governing mating is allowed to change in each generation according to the total number of mating units in the previous generation. Some results on its extinction probability and limiting behaviour are given in Molina et al (2002) and Molina, Mota & Ramos (2004).…”