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.

Bayesian estimation in the class of bisexual branching processes with population-size dependent mating

“…Under Assumption (A), Molina et al (2002) proved the existence of the growth rate r = lim k→∞ r k . This asymptotic rate plays a major role in the research of the extinction probability, partial and total progeny and limiting evolution of a BPSDM, see Molina et al (2002Molina et al ( , 2004aMolina et al ( , 2004b.…”

“…We now consider the Bayes estimation of the growth rate r. Using the fact that, from a practical viewpoint, the growth rate can be calculated as r = lim k→∞ k −1 × L k (kμ 1 , kμ 2 ), see Molina et al (2002), the Bayes estimator of r iŝ r = Θ lim k→∞ k −1 L k kμ 1 (θ 1 , θ 2 ), kμ 2 (θ 1 , θ 2 ) π(θ 1 , θ 2 |F n ) dθ 1 dθ 2 . Proposition 3.2 Suppose a BPSDM with offspring distribution (3.1) is given.…”

“…In particular, Molina et al (2002) introduced the class of bisexual processes with population-size dependent mating where, unlike other bisexual models, the function governing the mating is allowed to change in each generation depending on the total number of couples in the previous one. Some theory about such processes has been developed in Molina et al (2002Molina et al ( , 2004aMolina et al ( , 2004b.…”

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

“…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). We refer the reader to Hull (2003) for a survey about the literature associated with the bisexual branching processes.…”

Bisexual Galton-Watson Branching Processes in Random Environments

“…[2,3,[5][6][7][8][9]13,14]). Recently, some modified BGWP such as BGWP with immigration and BGWP in varying environments (see e.g.…”