Estimating sexual selection and sexual isolation effects from mating frequencies

Sexual selection (defined as the change in genotypic or phenotypic frequencies of mated versus total population frequencies) and sexual isolation (defined as the deviation from random mating in mated individuals) show different evolutionary consequences and partially confounded causes. Traditionally, the cross-product estimator has been used to quantify sexual selection, whereas a variety of indexes, such as Yule V, Yule Q, YA, joint I, and others have been used to quantify sexual isolation. Because the two types of estimators use different scales, the effects of both processes cannot be monitored simultaneously. We describe three new related statistics that quantify both sexual selection (PSS) and sexual isolation (PSI) effects for every mating pair combination in polymorphic traits, as well as measure their combined effects (PTI = PSI x PSS). The new statistics have the advantage of providing information on every mating pair combination, quantifying the effects of sexual selection and isolation in the same units, and detecting asymmetry in sexual isolation. The ability of the new statistics to ascertain the biological causes of sexual selection and sexual isolation are investigated under different models involving distinct marginal frequencies, mate propensity, and mate choice coefficients. We also studied the use of classical isolation indexes applied on PSI coefficients, instead of on raw data. The use of the classical indexes applied to PSI coefficients considerably reduces the statistical bias of the estimates, revealing the good estimation properties of the new statistics.