Rules for assortative mating in relation to selection for linear merit functions

Summary This study examined how assortative mating (without selection) based on linear combinations of two traits could be used to change genetic parameters so as to increase efficiency of selection. The efficiency of the Smith-Hazel index for improvement of multiple traits is a function of phenotypic and genetic variances and covariances, and of the relative economic values of the traits involved. Assortative mating is known to change genetic variances and covariances. Recursive formulae were derived to obtain these variances and covariances after t generations of assortative mating on linear combinations (mating rules) of phenotypic values for two traits, with a given correlation between mates. Selection efficiency after t generations of assortative mating without selection was expressed as a function of random mating genetic parameters, economic values, the mating rule, and the correlation between mates. Selection efficiency was maximized with respect to the coefficients in the mating rule. Because the objective function was nonlinear, a computer routine was used for maximizing it. Two cases were considered. When random mating heritabilities for the two traits were h _X ² =0.25 and h _Y ² =0.50, the genetic correlation r_XY=-0.60, and the economic values were a_X=3 and a_Y=1, continued assortative mating based on the optimal mating rule for 31 generations (with a correlation of 0.80 between mates) increased selection efficiency by 29%. Heritabilities changed to 0.38 and 0.66, respectively, and the genetic correlation became – 0.79. When h _X ² =0.60, h _Y ² =0.60, r_XY=– 0.20, a₁=1 and a₂=1, 36 generations of continued assortative mating with the optimal mating rule increased the efficiency of selection by 17%, heritabilities became h _X ² = h _Y ² =0.71, and the genetic correlation changed to 0.25. Only three generations of assortative mating were required to change the sign of the genetic correlation.     

Transfer systems and covariance under assortative mating

Summary This paper introduces the concept of a transfer system of random variables and uses it ot study various types of assortative mating. The standard correlation structure between relatives under phenotypic and genetic assortative mating are obtained easily and these results are then extended to multiple characters by means of multivariate transfer systems. Equilibrium values for the parameters are found and index assortative mating is considered with specific applications.     

Two-trait selection response with marker-based assortative mating

 Marker-based assortative mating (MAM) – the mating of individuals that have similar genotypes at random marker loci – can increase selection response for a single trait by 3–8% over random mating (RM). Genetic gain is usually desired for multiple traits rather than for a single trait. My objectives in this study were to (1) compare MAM, phenotypic assortative mating (PAM), and RM of selected individuals for improving two traits and (2) determine when MAM will be most useful for improving two traits. I simulated 20 generations of selecting 32 out of 200 individuals in an F₂ population. The individuals were selected based on an index (SI) of two traits and were intermated by MAM, PAM, or RM. I studied eight genetic models that differed in three contrasts: (1) weight, number of quantitative trait loci (QTL), and heritability (h ²) for each trait; (2) linkage of QTL for each trait; and (3) trait means of the inbred parents of the F₂. For SI and the two component traits, MAM increased short-term selection response by 5–8% in six out of the eight genetic models. The MAM procedure was least effective in two genetic models, wherein the QTL for one trait were unlinked to the QTL for the other trait and the parents of the F₂ had divergent means for each trait. The loss of QTL heterozygosity was much greater with MAM than with PAM or RM. Consequently, the advantage of MAM over RM dissipated after 5–7 generations. Differences were small between selection responses with PAM and RM. The MAM procedure can enhance short-term selection response for two traits when selection is not stringent, h ² is low, and the means of the parents of the F₂ are equal for each trait. Received: 10 June 1998 / Accepted: 5 August 1998     

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we numerically analyze the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with two alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, here we add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductively isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.     

Analysis of “nontraditional” relationships under assortative mating

The set of conditions on the genetical and developmental mechanisms of quantitative characters as well as on selection and mating system presented in (Gimelfarb, 1981) is expanded, thus enabling one to obtain the genotypic covariances between relatives for a larger variety of relationships. It is also demonstrated that the frequency of a relationship in a population under assortative mating may in general be different from the frequency of this relationship in the population under random mating. A subpopulation of relatives is not necessarily a representative sample of the whole population with respect to the quantitative character distribution. However, for any relationship which is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships, its frequency in a population under assortative mating is the same as in the population under random mating, and the subpopulation of such relatives is a representative sample of the whole population.Paper No. 6620 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, North Carolina. This investigation was supported in part by NIH Research Grant No. GM 11546 from the National Institute of General Medical Sciences     

Effects of assortative mating for pupa weight on genetic parameters of unselected Tribolium castaneum

Summary Effects of random (R) or positive assortative (A) mating for pupal weight (PW) on genetic parameters of pupation time (PT), pupal and larval weights (LW) were studied in unselected populations of Tribolium castaneum. Two groups, each with 50 males mated to 100 females in each of 5 replicates, were either R-mated or A-mated for 3 generations. Genetic parameters were estimated from covariances between sibs (R group) or by an iterative method (A group). Estimates of heritability in R and A groups were 0.30±0.12 and 0.39±0.02 (PW); 0.26±0.13 and 0.49±0.04 (LW); and 0.39±0.10 and 0.25±0.03 (PT). Estimates of genetic correlations in the R group were –0.21±0.23 (PW and LW); 0.45±0.10 (PW and PT); and –0.77±0.14 (LW and PT). Those in the A group were 0.27±0.10 (PW and LW); 0.15±0.14 (PW and PT); the genetic correlation between LW and PT was not estimable in this group. Within-family variances (grams squared) of PW by generation (1, 2, and 3) were, respectively: 0.048 (R) and 0.047 (A); 0.054 (R) and 0.041 (A); and 0.050 (R) and 0.046 (A). In agreement with theory, estimates of heritability of PW and LW were larger in the A group. Estimates of genetic correlations in the A group were inconsistent with expectations from theory. Assortative mating tended to decrease within-family variance of PW.     

Stress-induced assortative mating and the evolution of stress resistance

We show with a model that variation in environmental stress between generations facilitates the evolution of stress resistance through assortative mating. Stress induces delayed maturation of susceptible phenotypes, segregating their fertile period from resistant phenotypes. Assortment of mates enhances the responsiveness of populations to natural selection by inflating genetic variance. Thus, positive selection and inflated genetic variance in stressful environments can cause a strong evolutionary increase in resistance. By contrast, benign environments do not segregate phenotypes, and the random mating among phenotypes deflates genetic variance, leading to a weaker response to selection against resistance, assuming that resistance is costly. When environments vary randomly from benign to stressful, populations respond asymmetrically to negative and positive selection. This asymmetry (1) accelerates fixation of a resistance allele if resistance is generally favoured (stressful generations more frequent) but delays the loss of the allele if it is generally disfavoured (benign generations more frequent), and (2) it can push a resistance allele to fixation even when long‐term costs modestly exceed benefits. When resistance alleles pleiotropically delay mating, stress‐induced random mating has complementary effects. Serial autocorrelation in the stressor amplifies these effects. These results suggest a novel mechanism for the persistence of resistance polymorphisms.     

A general linear model for the genotypic covariance between relatives under assortative mating

A linear model for the genotypic covariance between relatives under assortative mating comprising the classical linear model and the model of selective assortative mating is proposed. The general conditions on the genetical and developmental mechanisms of quantitative characters, as well as on selection and the mating system, on which the model is based, are explicitly stated and discussed. A classification of different relationships is presented and it is shown that these conditions are sufficient to obtain the genotypic covariance between relatives only if the relationship is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships. All the traditional relationships, i.e., those for which the covariances of the relatives have been obtained in the literature, fall into this category. These conditions also ensure that the regression of the individual's genotypic value on the genotypic value or phenotype of any of its ancestors is always linear.Paper No. 6619 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, North Carolina. This investigation was supported in part by NIH Research Grant No. GM 11546 from the National Institute of General Medical Sciences     

Sexual size dimorphism and assortative mating for morphological traits in Passer domesticus

In this study, assortative mating for different morphological traits was studied in a captive population of house sparrows (Passer domesticus). Males were larger than females. Assortative mating was found for tail length, wing length and general body size. Males with larger badge size mated with females with longer tails. The strongest assortative mating occurred for tail length (r=0.77), and this assortative mating remained significant after controlling for wing length, mass and tarsus length, suggesting that it was not an artefact of assortative mating for body size. The possibility of sexual selection for tail length in the house sparrow is discussed.     

Convergence of genotypic frequencies for differential selfing and positive assortative mating at a biallelic locus

For a biallelic model of differential self-fertilization and differential positive assortative mating based on genotype, it is shown that the genotypic frequencies converge for all sets of mating system parameters. Overdominance and underdominance with respect to the parameters are necessary but not sufficient conditions for global convergence to a polymorphic equilibrium and local attractiveness of both the fixation states, respectively. There are cases of overdominance and underdominance for which one fixation state is globally attractive. The relationship of the result to those known from the classical viability selection model are briefly discussed. For the multiallelic version, it is shown that after the first generation all of the homozygote frequencies are always in excess of the corresponding Hardy-Weinberg proportions if at least one homozygote rate of self-fertilization or assortment probability is positive.     

Assortative mating through a mechanism of sexual selection

We propose that assortative mating can arise through a mechanism of sexual selection by active female choice of partners based on a 'self-seeking like' decision rule. Using a mathematical model, we show that a gene can be selected that make females to choose mates that are similar to themselves with respect to an arbitrary tag, even if two independent and unlinked genes determine the preference and the tag. The necessary requisite for this process to apply is an asymmetry between partners, such that the female can choose the male but this one must always accept to mate. The fitness advantage is due to linkage disequilibrium built up between both genes. Simulations have been run to check the algebraic results and to analyse the influence of several factors on the evolution of the system. Any factor that favors linkage disequilibrium also favors the evolution of the preference allele. Moreover, in a large population subdivided in small subpopulations connected by migration, the assortative mating homogenizes the population genotypic structure for the tags in contrast to random mating that maintains most of the variation.     

Assortative mating and the genetic correlation

Summary The effect of assortative mating on the genetic correlation between traits X and Y is considered. Assortation on trait X changes the magnitude of the genetic correlation but not its sign. There are two situations depending on the signs of the correlation between mates () and of the random mating genetic correlation (): 1) if sign () = sign (), then >, where is the genetic correlation at equilibrium after continued assortation, and 2) if sign () = sign (), then < . However, negative assortative mating is virtually powerless to alter the magnitude of the genetic correlation. The consequences of a mixed assortation model, e.g., high milk production females mated to fast growing males and lesser productive females mated to slower growing sires, were also studied. Mixed positive assortation always increases the genetic correlation, but negative assortation decreases it. The implications of assortative mating on correlated responses to selection and on the equilibrium covariances between relatives for pairs of traits are discussed.     

Self seeks like: many humans choose their dog pets following rules used for assortative mating

Theoretical and experimental studies suggest that mating and pair formation are not likely to be random. Assortative mating, characterized as self seeking like, seems to be widely practiced in nature. Experimental evidence for it is strong among humans seeking a mate. Assortative mating increases the probability of finding a genetically similar mate, without fomenting inbreeding, achieving assortative mating without hindering the working of other mate-selection strategies that aim to maximize the search for good genes, optimizing the working of sex in evolutionary terms. Self seeking like seems to be a behavioural inborn trait among humans, and here we present evidence that the same behavioural mechanism seems to be at work when humans choose a pet. We show that in a significant proportion of human–pet pairs, sampled in pet beauty contests, the partners show much higher facial resemblances than can be expected by random pair formation.     

Incipient allochronic speciation due to non-selective assortative mating by flowering time, mutation and genetic drift

We model the evolution of flowering time using a multilocus quantitative genetic model with non-selective assortative mating and mutation to investigate incipient allochronic speciation in a finite population. For quantitative characters with evolutionary parameters satisfying empirical observations and two approximate inequalities that we derived, disjunct clusters in the population flowering phenology originated within a few thousand generations in the absence of disruptive natural or sexual selection. Our simulations and the conditions we derived showed that cluster formation was promoted by limited population size, high mutational variance of flowering time, short individual flowering phenology and a long flowering season. By contrast, cluster formation was hindered by inbreeding depression, stabilizing selection and pollinator limitation. Our results suggest that incipient allochronic speciation in populations of limited size (satisfying two inequalities) could be a common phenomenon.     

Estimating sexual selection and sexual isolation effects from mating frequencies

Abstract.— 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.     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating

We consider mating strategies for females who search for males sequentially during a season of limited length. We show that the best strategy rejects a given male type if encountered before a time‐threshold but accepts him after. For frequency‐independent benefits, we obtain the optimal time‐thresholds explicitly for both discrete and continuous distributions of males, and allow for mistakes being made in assessing the correct male type. When the benefits are indirect (genes for the offspring) and the population is under frequency‐dependent ecological selection, the benefits depend on the mating strategy of other females as well. This case is particularly relevant to speciation models that seek to explore the stability of reproductive isolation by assortative mating under frequency‐dependent ecological selection. We show that the indirect benefits are to be quantified by the reproductive values of couples, and describe how the evolutionarily stable time‐thresholds can be found. We conclude with an example based on the Levene model, in which we analyze the evolutionarily stable assortative mating strategies and the strength of reproductive isolation provided by them.     

Differential contribution of stature phenotypes to assortative mating in parents of Philadelphia Black and White school children

Assortative mating for stature, weight, and the ponderal and Quetelet's indices is considered in a large sample of Philadelphia Blacks and Whites. The husband-wife correlation for stature is positive and significant in Whites (r = 0.34, d.f. = 382), but negligible in Blacks (r = 0.06, d.f. = 420). Correlations for weight and the body indices are positive and significant in both samples, those for body indices showing some dependency on the husband-wife correlations for stature and weight. When couples are grouped into statural mating combinations on the basis of short (S), medium (M) and tall (T), White spouses' statures show an approximately linear relationship to one another. The distribution of Black spouses' statures, however, is not completely independent, even though the husband-wife correlation is close to zero. There are elements of both positive and negative assortative mating among Blacks, resulting in an excess of certain mating types over that expected on the basis of chance. These mating types are usually those in which the husband is shorter than the wife, except at the heterogeneous extremes of the bivariate array.