Abstract: In this paper, we study the limiting behavior of the conditional mean growth rate for the bisexual Galton-Watson branching process with population-size-dependent mating in random environments. Using the properties of superadditive functions, we obtain the limit properties of the mean growth rate per mating unit, and the upper bound and lower bound of the conditional mean. We introduce two sequences on the conditional mean growth rate, whose limit properties are established by utilizing the properties of the mean growth rate per mating unit. The bisexual Galton-Watson branching process with population-size-dependent mating is rather complex, so our results improve and extend the related known works in the literature.

Key words: bisexual branching process, the mean growth rate per mating unit, conditional mean growth rate, limit properties