A discussion of bisexual populations with Wolbachia infection as an evolution algebra

Abstract

In this paper, Wolbachia infection in a bisexual and diploid population with a fixed cytoplasmic incompatibility rate $w$ and maternal transmission rate $d$ is studied as an evolution algebra. As the cytoplasmic incompatibility (CI) of the population causes deaths in the offspring, the evolution algebra of this model is not baric, and is a dibaric algebra if and only if the cytoplasmic incompatibility rate $w$ is 1 and $d=1$. The idempotent elements are given in terms of $d$ and $w$. Moreover, this algebra has no absolute nilpotent elements when CI expression $w \neq 1$.