The Multi-type Bisexual Galton-Watson Branching Process

Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo

Publication date: 20 June 2022

Abstract: In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a mating function and form couples of different types. We assume that this function is superadditive, which in simple words implies that two groups of females and males will form a larger number of couples together rather than separate. In the absence of a linear reproduction operator which is the key to understand the behaviour of the model in the asexual case, we build a concave reproduction operator and use a concave Perron-Frobenius theory to ensure the existence of eigenelements. Using this tool, we find a necessary and sufficient condition for almost sure extinction as well as a law of large numbers. Finally, we study the almost sure long-time convergence of the rescaled process through the identification of a supermartingale, and we give sufficient conditions to ensure a convergence in

L^{1}

to a non-degenerate limit.

This page was built for publication: The Multi-type Bisexual Galton-Watson Branching Process

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6402563)