Differences in mating propensities: some models for examining the genetic consequences

Fluid limit for the Poisson encounter-mating model

Stochastic encounter-mating (SEM) models describe monogamous permanent pair formation in finite zoological populations of multitype females and males. In this paper we study SEM models with Poisson firing times. First, we prove that the model enjoys a fluid limit as the population size diverges, that is, the stochastic dynamics converges to a deterministic system governed by coupled ordinary differential equations (ODEs). Then we convert these ODEs to the well-known Lotka–Volterra and replicator equations from population dynamics. Next, under the so-called fine balance condition which characterizes panmixia, we solve the corresponding replicator equations and give an exact expression for the fluid limit. Finally, we consider the case with two types of female and male. Without the fine balance assumption, but under certain symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to characterize assortative mating.

Nonadditive genetic effects in animal behavior

Heritabilities, commonly used to predict evolutionary potential, are notoriously low for behaviors. Apart from strong contributions of environmental variance in reducing heritabilities, the additive genetic components can be very low, especially when they are camouflaged by nonadditive genetic effects. We first report the heritabilities of courtship traits in founder-flush and control populations of the housefly (Musca domestica L.). We estimated the heritability of each male and female display through the regression of the courtships involving daughters and sons (with randomly selected mates) onto the "midparental" courtship values of their parents. Overall, the average heritability was significantly (P = .012) higher for the parent-daughter assays than for the parent-son assays. We attributed the low (even negative) heritabilities to genotype-by-environment interactions whereby the male's behavior is influenced by the "environment" of his mating partner's preferences for the display, generating epistasis through indirect genetic effects. Moreover, bottlenecked lines had up to 800% of the heritability of the controls, suggesting "conversion" of additive genetic variance from nonadditive components. Second, we used line-cross assays on separate populations that had been selected for divergence in mating behavior to identify dominance and epistasis through heterosis and outbreeding depression in courtship. Finally, our literature review confirms the prevalence of such low heritabilities (i.e., a conservative mean of 0.38) and nonadditive genetics in other behavioral repertoires (64% of the studies). We conclude that animal behavior is especially prone to the gamut of quantitative genetic complexities that can result in negative heritabilities, negative selection responses, inbreeding depression, conversion, heterosis, and outbreeding depression.

The Genetic Architecture of House Fly Mating Behavior

This chapter summarizes several experimental approaches used to identify the effects of dominance, epistasis, and genotype-by-environment interactions in the genetic architecture of the mating behavior of the common house fly (Musca domestica L.). Quantitative genetic investigations of mating behavior hold special intrigue for unraveling the complexities of fitness traits, with applications to theory on sexual selection and speciation. Besides being well suited to large-scale quantitative genetic protocols, the house fly has a remarkably complex courtship repertoire, affording special opportunities for studies on communication, social interactions, and learning. Increased additive genetic variances for the courtship repertoire of experimentally bottlenecked populations provided evidence for the presence of dominance and/or epistasis. Negative genetic variances in these populations suggested genotype-by-environment interactions, where the environment is the mating partner. Line cross assays of populations that had been subjected to selection for divergent courtship repertoire confirmed that both dominance and epistasis have significant effects. These crosses also showed more directly that the expression of the male's genotype is dependent upon the preferences of his mating partner. Repeatability studies also detailed how males alter their courtship performances with successive encounters within and across females, such that the males learn to improve their techniques in securing copulations. A review of 41 animal behavior studies found that a wide range of traits and taxa have dominance, epistasis, and genotype-y-environment interactions, although house fly courtship may remain a unique model where learning is an intersexually selected trait. Future development of more sophisticated molecular techniques for the M. domestica genome will help unravel the underlying biochemical and developmental pathways of these quantitative genetic interactions for a more complete understanding of the processes of inbreeding depression, outbreeding depression, and pleiotropy.

Male-male interactions and mating kinetics in Drosophila

Male-male interaction (K) has been estimated from data on the attrition rate of virgin females per minute in a study of the mating kinetics in Drosophila. K is expressed as the time males expend on other males relative to that expended while searching for, courting, and copulating with females. The value of K in these studies ranged from 0 (approximately) to .695; it was affected both by strain (sepia or ebony D. melanogaster and wild-type D. simulans) and by size of the mating chamber. Host-parasitoid models of ecologists appear to be appropriate for examining mating kinetics in Drosophila.

A model describing the kinetics of mating in Drosophila

The kinetics of mating in species of Drosophila that copulate for periods of time greater than the duration of experimental observation can be described precisely by an equation that combines second order reaction kinetics with the exponential decay of a lag factor. The two rate constants for this kinetic system were estimated from mating data using a wild-type D. simulans strain, a wild-type D. melanogaster strain, and vestigial mutant D. melanogaster males with wild-type females. The results confirm the applicability of second order kinetics, and demonstrate the usefulness of the model in comparisons of mating rates among strains of flies. In most cases, the model explains more than 95% of the variance in the data, and in addition sheds light on the mechanics of the process of mating.