On Asymptotic Behavior of Extinction Moment of Critical Bisexual Branching Process in Random Environment

Abstract: We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction time is of the order $\ln^2 N$. Interestingly, this result is valid for a general class of mating functions. Among them are the functions describing the monogamous and polygamous behavior of couples, as well as the function reducing the bisexual branching process to the simple one.