Abstract: Firstly, this paper introduces the development of bisexual Galton-Watson branching process. On the basis of past achievements, a model with population size dependent mating and immigration (BIPSDM) is established in random environments, that is more conform to the fact about bisexual biological reproduction. Then, applying some classical results on superadditive functions, the limit of mean growth rate per mating unit is obtained. Through discussing extinct probability of BIPSDM, a necessary and sufficient condition for BIPSDM to become extinct with probability one was found under certain conditions. Some properties known are enlarged in this article.

Key words: Galton-Watson branching process, bisexual Galton-Watson branching process, immigration, population size dependent mating, growth rate, extinction probability