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

AbstractIn this paper, Wolbachia infection in a bisexual and diploid population with a fixed cytoplasmic incompatibility rate <italic>w</italic> and maternal transmission rate <italic>d</italic> 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 <italic>w</italic> is 1 and d=1 . The idempotent elements are given in terms of <italic>d</italic> and <italic>w</italic>. Moreover, this algebra has no absolute nilpotent elements when CI expression w≠1 . [ABSTRACT FROM AUTHOR]