Non-random mating and information theory

Abstract

In this work, mate choice is modeled by means of the abstract concept of mutual mating propensity. This only assumes that different types of couples can have different mating success. The model is adequate for any population where mating occurs among distinct types. There is no extra assumption about particular mating scheme or preference model. The concept of mutual mating propensity permits to express the observed change in the mating phenotypes as the gain in information with respect to random mating. The obtained expression is a form of the Price equation in which the mapping between ancestral and descendant population is substituted by a mapping between random mating and non random mating population. At the same time, this framework provides the connection between mate choice and the exact mathematical partition of the choice effects, namely sexual isolation, sexual selection and a mixed effect. The sexual selection component is the sum of the intra-sexual male and female selection. The proposed framework helps to unveil previously hidden invariants. For example, if the mutual preference between partner types is multiplicative there is no sexual isolation (inter-sexual selection) effect on the frequencies, i.e. the only possible effect of mate choice is intra-sexual selection. On the contrary, whatever the contribution of each partner to the mutual preference, if it comes as a non-multiplicative factor, there is at least an inter-sexual selection detectable effect. This new view over the mate choice problem, permits to develop general mating propensity models and to make predictions of the mate choice effects that may emerge from such models. This possibility opens up the way for setting a general theory of model fitting and multimodel inference for mate choice. Thus, it is suggested that the proposed framework, by describing mate choice as the flow of information due to non-random mating, provides a new important setting for exploring different mating models and their consequences.

The information theory formalism unifies the detection of the patterns of sexual selection and assortative mating for both discrete and quantitative traits

“…The objective of this work is twofold. Firstly, we aim to demonstrate that the previous theoretical development, which is rooted in information theory and the concept of mutual mating propensity (Carvajal-Rodríguez 2018b, 2020), seamlessly aligns with the new sexual selection definition put forth by Shuker and Kvarnemo (2021). In this context, sexual selection emerges as a consequence of variations in the mutual mating propensity, without requiring specific assumptions about the genetic basis of the involved traits.…”

“…To compare different types’ fitness fairly, we compute the relative fitness, w i , as the ratio of their absolute fitness to the mean population fitness. Thus, for a given type i with frequency p i , the new frequency p ’ i after a selection episode will be given by (Bürger 2000; Hansen 2018) Recently, a simple theoretical framework, similar to the model presented in (1), has been developed to describe the influence of mating competition and mate choice on the emergence of sexual selection and assortative mating patterns (Carvajal-Rodríguez 2018b, 2019, 2020). This theoretical framework has enabled the development of new statistical tests for detecting sexual selection and assortative mating.…”

“…The probability q ’ ij of mating or gamete access for fertilization between any pair having such a combination of traits is (Carvajal-Rodríguez 2018b) Equation (2) represents the expected frequencies of mating between types i and j as a function of the expected frequencies per random gamete encounter and the relative values of mutual propensity. The equation clearly resembles equation (1) for the change in frequencies because of selection.…”

“…Having formalized the concepts of mutual propensity and mating fitness it is then possible to model mate competition and choice and the patterns of sexual selection and assortative mating they produce (see Carvajal-Rodríguez 2018b, 2020). The pattern of sexual selection is caused mainly by two biological mechanisms: mate competition and mate choice (Lewontin et al 1968; Arnold and Wade 1984; Endler 1986; Rolán-Alvarez and Caballero 2000; Rolán-Alvarez et al 2015).…”

“…In earlier work, Carvajal-Rodríguez (2018b) showed for discrete traits, that non-random mating can be characterized as the divergence between the mating distribution, Q ’, derived from mutual mating propensities, and the distribution of random mating, Q . For the continuous case we have that the divergence between the two distributions Q ’ and Q is given by where q ( x,y )= f ( x ) g ( y ).…”