Forward and backward processes in bisexual models with fixed population sizes. (English) Zbl 0812.92017

Möhle, M.

J. Appl. Probab. 31, No. 2, 309-332 (1994).

Exchangeable bisexual models with fixed population size and non overlapping generations are introduced, where in each generation there are \(N\) pairs of individuals consisting of a female and a male. The \(N\) pairs of a generation produce \(N\) daughters and \(N\) sons altogether forming the \(N\) pairs of the next generation at random. The author studies the extinction of the lines of descendants of a fixed number of pairs when the population size becomes large and the process of the ancestor-pair number of all pairs of a generation.

Reviewer: R.Manthey (Jena)

MSC:

92D25	Population dynamics (general)
60J85	Applications of branching processes

Keywords:

Galton-Watson process; Ornstein-Uhlenbeck process; Wright-Fisher model; exchangeable bisexual models; fixed population size; overlapping generations; extinction; lines of descendants