Limit behaviour for a supercritical bisexual Galton–Watson branching process with population-size-dependent mating

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

“…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.…”

“…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.…”

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

“…The asymptotic behaviour of a BPSDM given P1 and P2 is studied in Molina et al . (2004), in which sufficient conditions for P3 are also provided.…”

“…With respect to (v), it is clear that . Then, since { r − n Z n } n ≥0 and { r − n ( F n , M n )} n ≥1 converge almost surely to W and r −1 W μ, respectively (see Molina et al ., 2004), considering P4, converges almost surely to μ on Q .…”

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.…”