Quantifying and comparing mating systems using normalized mutual entropy

Methods for quantifying mating systems have been debated for over 30 years. Existing quantification methods rely on inequality indexes, producing a single number from a vector of data for all females or males in a population. Such methods do not account for interactions between members of the two sexes because they do not use the natural matrix (dyadic) structure of the data, where each matrix entry reflects how often a given pair of individuals mated or how many offspring they produced. These inequality indexes also suffer from being a function of population size. Here, we propose mutual entropy as a way to account for the matrix structure, along with a normalization that makes this index independent of population size, thereby robustly quantifying the continuum between monogamy and polygyny/polyandry. Normalized mutual entropy: (1) is a measure of diversity, so it can serve as an upper bound for sexual selection and (2) can accommodate hermaphrodites and self-fertilizing individuals. Normalized mutual entropy thereby provides a measure of mating systems, promiscuity, inbreeding and social cohesion.