This research demonstrates the time until extinction in a critical bisexual branching process, suggesting significant implications for ecological models.
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 order ln² N . Interestingly, this result is valid for a general class of mating functions. Among these 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.
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Zhiyanov et al. (2026) studied this question.
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