A necessary condition for extinction in those bisexual Galton-Watson branching processes governed by superadditive mating functions

Abstract

Mating functions considered by Asmussen (1980) and Daley (1968) for the class of bisexual Galton-Watson branching processes (GWBP) are shown to be superadditive. Consideration of a process that allows only sibling mating leads to a necessary condition for almost sure extinction in bisexual GWBP governed by superadditive mating functions. A simple example shows that the condition is not sufficient.

Weighted conditional least square estimators for bisexual branching processes with immigration

“…As was pointed out in Hull (1982), this is not a serious restriction. Indeed, it is reasonable to assume that a given number of females and males living together in the same environment will give rise to more mating units than if they form separate groups living in different non-communicated environments.…”

Stochastic modeling in biological populations with sexual reproduction through branching models: Application to Coho salmon populations

“…[2], [9] or [14]) and models where mating or reproduction (or both processes) are affected by the number of couples in the population (see Refs. [23], [25,26] or [34]).…”

“…According to(13), when mf −1 ≤ c −1 2 , or equivalently when f m −1 ≥ c 2 , then the mating strategy 1 is applied; when mf −1 ≥ c 2 then the mating strategy 3 is put in practice; and otherwise, the mating strategy 2 is carried out. From(14), when the number of female smolts is less than or equal to the number of male smolts then, the reproduction strategy 1 is assumed, where the production of female smolts is promoted. On the contrary, if the number of female…”

Bisexual branching processes with offspring and mating depending on the number of couples in the population

“…In Daley's model the offspring distribution and the function governing the matings between females and males are the same for each generation. Such a model has received some attention in the literature; see, for example, Rösler (1996, 2002), Bagley (1986), Bruss (1984), Daley et al (1986), González and Molina (1996, 1997), or Hull (1982. More recently, with the objective to model the probabilistic evolution of more complex two-sex populations, various classes of bisexual branching processes have been introduced and some theory about them developed; see, for instance, González et al (2000González et al ( , 2001, Molina et al (2002Molina et al ( , 2003Molina et al ( , 2004aMolina et al ( , 2004b or Xing and Wang (2005).…”