A necessary condition for extinction in those bisexual Galton-Watson branching processes governed by superadditive mating functions

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Abstract
Mating functions considered by Asmussen (1980) and Daley (1968) for the class of bisexual Galton-Watson branching processes (GWBP) are shown to be superadditive. Consideration of a process that allows only sibling mating leads to a necessary condition for almost sure extinction in bisexual GWBP governed by superadditive mating functions. A simple example shows that the condition is not sufficient.

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