ON THE ASYMPTOTIC GROWTH FOR A BISEXUAL GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS

摘要

The bisexual Galton-Watson branching process (BP) is a two-type branching model with F_n~* females and M_n~* males in the nth generation, n = 1,2,..., which form Z_n~* = L(F_n~*, M_n~*) mating units. These reproduce independently of all other mating units with the same offspring probability distribution for each generation. The mating function L:R~+ x R~+ → R~+ is assumed to be monotonically nondecreasing in each coordinate, integer valued on integer arguments, and such that L(x, y) ≤ xy.