Two-Sex Galton-Watson Branching Processes
Ali Falahati
Dept of Math Statistics, Chalmers Univ of Technology, Gothenburg, Sweden
Abstract
In this talk we present a model for studying a bisexual
population called Two-Sex
Galton-Watson Branching Processes (2S-GWBP for short). Our model follows
that of Asmussen and Hering (1983), where population
developments proceeds in two stages, first reproduction
and then mating. Our model, emphasizes on the notion of the family,
i. e. children born from a couple (or a mating unite).
The total number of couples in a coming generation will be
the sum of marriages of daughters of each family. In the model studied by
Asmussen and Hering (1983), it is the total numbers of
the female and male in the present generation which determine the
distribution of number of the couples in the coming generation,
where in our model we allow this distribution depends not only
on the number of couples in the present generation but also
to a suitable function of size of all families in that generation.
Also in our model we allow the distribution of number of children born
into each family depends on the number of family (or couples) of
that generation. The results for a simple case both for a
supercritical and critical case will be given.
