Negative‐assortative mating for color in wolves

There is strong negative‐assortative mating for gray and black pelage color in the iconic wolves in Yellowstone National Park. This is the first documented case of significant negative‐assortative mating in mammals and one of only a very few cases in vertebrates. Of 261 matings documented from 1995 to 2015, 63.6% were between gray and black wolves and the correlation between mates for color was –0.266. There was a similar excess of matings of both gray males × black females and black males × gray females. Using the observed frequency of negative‐assortative mating in a model with both random and negative‐assortative mating, the estimated proportion of negative‐assortative mating was 0.430. The estimated frequency of black wolves in the population from 1996 to 2014 was 0.452 and these frequencies appear stable over this 19‐year period. Using the estimated level of negative‐assortative mating, the predicted equilibrium frequency of the dominant allele was 0.278, very close to the mean value of 0.253 observed. In addition, the patterns of genotype frequencies, that is, the observed proportion of black homozygotes and the observed excess of black heterozygotes, are consistent with negative‐assortative mating. Importantly these results demonstrate that negative‐assortative mating could be entirely responsible for the maintenance of this well‐known color polymorphism.     

A model of assortative mating with partial dominance.

A model of assortative mating incorporating partial dominance is proposed for a single locus with two alleles. It is derived by starting from an arbitrary genotypic distribution and finding symmetric and non-selective mating frequencies which duplicate this distribution. Numerical values are imputed to genotypes, the homozygotes having numerically equal values, opposite in sign, and the heterozygote having a value determined by the gene and heterozygote frequencies. The model is specified in a canonical form which reveals the correlation between mates based on genotypic values, and relates the correlation to the fixation index. It permits negative as well as positive values of the fixation index. It is shown that this general model includes several particular cases, in equilibrium phase, occurring in the literature.     

Comparisons of positive assortative mating and sexual selection models

A series of theoretical models of positive assortative mating and sexual selection are contrasted. It is established that for a dominant trait partial positive assortative mating generally implies some fixation, whereas sexual selection exhibits a unique globally stable polymorphism exhibiting Hardy-Weinberg proportions. The effects of monogamy against polygamy do not qualitatively alter the equilibrium outcomes, although the rate of evolutionary change is generally slowed with monogamy vis-à-vis polygamy. For sexual selection the influence of timing of random mating as against preferential mating causes no change in the equilibrium states, although the rates of convergence can be slowed if sexual selection occurs late in the breeding season. Under assortative mating the timing can alter the equilibrium outcomes. The amount of heterozygosity is always deficient in cases of assortative mating, but always exhibits Hardy-Weinberg ratios under a sexual selection mechanism. This suggests that observations consistent with Hardy-Weinberg equilibrium states cannot preclude ipso facto certain forms of selection forces, including mating patterns and some natural selection structures.     

Quantitative characters under assortative mating: Gametic model

The gametic model introduced by Gimelfarb (1982, Theor. Pop. Biol. 22, 324-366) is applied to investigating the dynamics, represented in the model by a second-order recurrence equation, the the variance of sex-independent and sex-controlled characters under assortative mating. It is shown that, for any additive character, there always exists a unique equilibrium for the variance, which is stable. Dynamical properties of the variance under positive and negative matings are considered, and numerical evaluations of the equilibrium values as well as of the dynamical changes of the variance are presented. Comparisons with results from a biological experiment are made.     

Estimation of assortative mating preferences in the Arctic skua.

Methods are described for the maximum likelihood estimation of mating preferences in models of assortative mating for monogamous and polygamous organisms. These methods are applied to data of matings of the three phenotypes, pale, intermediated and dark of the Arctic Skua. The data were obtained by exhaustive surveys of the Arctic Skua populations on the islands of Fair Isle and Foula. The data give evidence of significant assortative mating of pale birds on Foula and intermediate birds on Fair Isle. The combined data show that there is very highly significant assortative mating, but only of intermediates. In previous surveys, data, in which intermediates and darks were not distinguished, were obtained from a number of islands in the Shetlands. These data, combined with the present data, show that the overall assortative mating of pale is very highly significant with no evidience of heterogeneity. The assortative mating of intermediate birds on Fair Isle agrees with other evidence showing that inermediate males have an advantage as a result of sexual selection.     

Evolution of disassortative and assortative mating preferences based on imprinting

A two-locus haploid model of sexual selection is investigated to explore evolution of disassortative and assortative mating preferences based on imprinting. In this model, individuals imprint on a genetically transmitted trait during early ontogeny and choosy females later use those parental images as a criterion of mate choice. It is assumed that the presence or absence of the female preference is determined by a genetic locus. In order to incorporate such mechanisms as inbreeding depression and heterozygous advantage into our haploid framework, we assume that same-type matings are less fertile than different-type mating. The model suggests that: if all the females have a disassortative mating preference a viability-reducing trait may be maintained even without the fertility cost of same-type matings; a disassortative mating preference can be established even if it is initially rare, when there is a fertility cost of same-type matings. Further, an assortative mating preference is less likely to evolve than a disassortative mating preference. The model may be applicable to the evolution of MHC-disassortative mating preferences documented in house mice and humans.     

Continuous-genotype models and assortative mating

Feldman and Cavalli-Sforza (1979a,b) have argued that the convergence properties of classical models of assortative mating are not known, and that these models involve arbitrary assumptions which assume rather than derive the achievement of equilibrium. A careful consideration of all models shows that the classical models are well defined and seem to achieve their equilibria. The model used by Feldman and Cavalli-Sforza involves an arbitrary assumption. Consideration of the models of Wright, Fisher, Bulmer, and Lande in the context of assortative mating or of selection versus mutation shows that these models are consistent with each other. The treatment of the balance between mutation and normalizing selection by Cavalli-Sforza and Feldman comes to conclusions sharply different from those of other authors, apparently as a result of this same arbitrary assumption.     

Sampling scale can cause bias in positive assortative mating estimates: evidence from two intertidal snails

Assortative mating in the wild is commonly estimated by correlating between traits in mating pairs (e.g. the size of males and females). Unfortunately, such an approach may suffer from considerable sampling bias when the distribution of different expressions of a trait in the wild is nonrandom (e.g. when segregation of different size classes of individuals occurs in different microhabitats or areas). Consequently, any observed trait correlation in the wild can be an artefact of pooling heterogeneous samples of mating pairs from different microhabitats or areas rather than true nonrandom matings. This bias in estimating trait correlations as a result of sampling scale is termed the scale‐of‐choice effect (SCE). In the present study, we use two intertidal littorinid species from Hong Kong to show how the SCE can bias size‐assortative mating estimates from mating pairs captured in the wild, empirically demonstrating the influence of this effect on measures of positive assortative mating. This finding cautions that studies overlooking the SCE may have misinterpreted the magnitude and the cause of assortative mating, and we provide a new analytical approach for protecting against this potential bias in future studies.     

Strong assortative mating between allopatric sticklebacks as a by-product of adaptation to different environments

Speciation involves the evolution of reproductive isolation between populations. One potentially important mechanism is the evolution of pre- or postzygotic isolation between populations as a by-product of adaptation to different environments. In this paper, we tested for assortative mating between allopatric stickleback populations adapted to different ecological niches. Our experimental design controlled for interpopulation interactions and non-adaptive explanations for assortative mating. We found that prezygotic isolation was surprisingly strong: when given a choice, the majority of matings occurred between individuals from similar environments. Our results indicate that the by-product mechanism is a potent source of reproductive isolation, and likely contributed to the origin of sympatric species of sticklebacks.     

Frequency-dependent selection and the evolution of assortative mating

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a "one-allele" model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to "reinforcement") regardless of the form of natural selection.     

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.     

Positive assortative mating between recently described sympatric morphs of Icelandic sticklebacks

Recently, models of sympatric speciation have suggested that assortative mating can develop between sympatric morphs due to divergence in an ecologically important character. For example, in sympatric pairs of threespine stickleback (Gasterosteus aculeatus L.) size-assortative mating seems to be instrumental in reproductive isolation. Here, we examine courtship behaviour and assortative mating of newly described sympatric stickleback morphs in Lake Thingvallavatn, Iceland. We find that the two morphs show strong positive assortative mating. However, the mechanism involved in mate choice does not seem to be as straightforward as in other similar systems of sympatric stickleback morphs and may involve variation in nest type.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.     

Intermediate inheritance of Tourette syndrome, assuming assortative mating.

Segregation analysis incorporating assortative mating was used to test for major locus inheritance of Tourette syndrome in a single large pedigree containing 182 members. The analysis provided evidence of a major locus with an intermediate inheritance pattern for which the penetrance was estimated from the data as 28% in heterozygotes and 98%-99% in homozygotes. A significant assortative mating correlation was estimated from the data as 70%-79%. In contrast, when assortative mating was not included in the model, intermediate inheritance was not inferred. If, in addition, constancy of the allele frequencies across generations was not assumed, Mendelian transmission was rejected. Each subject, affected or unaffected, was assigned a score reflecting the presence and severity of symptoms. Higher means scores in affected homozygotes than in affected heterozygotes suggested greater severity in homozygotes: genotype information was obtained from genotype probabilities computed assuming intermediate inheritance.     

Origin and evolution of assortative mating in actively speciating mole rats

The origin and evolution of positive assortative mating in the actively speciating subterranean mole rats of the Spalax ehrenbergi superspecies in Israel, may be deciphered by comparing female mate preference in the laboratory between ancestral and derivative species. Estrous females of the recent derivative of speciation (chromosomal species 2n = 60) showed trimodal mate preference distribution significantly differing from a normal curve. Females consisted of three phenotypes, comprising negative, low positive, and high positive preference for homospecific males. By contrast, mate preference in encounters of ancestral species (2n = 52, 54, and 58) showed a prevalence of a positive homospecific mate preference. It is suggested that the three modal distribution is explicable even on the basis of one major gene with three genotypes. The evolution of ethological reproductive isolation proceeded presumably from a high polymorphism in the most recent derivative of speciation towards increasing monomorphism of positive assortative mating among ancestral species. If an assortative mating locus combines with sexual selection of the frequent male adapted optimally to the local environment, then speciation and adaptation will be tightly linked in the evolution of mole rats.     

The effect of positive assortative mating at one locus on a second linked locus

Summary Considerations proceed from a model of positive assortative mating based on genotype at one locus, with an arbitrary number of alleles, assuming no selection, mutation, or migration, hypothetically infinite population size, and discrete non-overlapping generations. From these conditions, inferences are made about the genotypic structure at a linked locus, as well as about the corresponding 2-locus gametic structure.The following main results are presented: in the course of the generations, the genotypic structure at the second locus and the 2-locus gametic structure always tend to a limit responsive to the initial conditions concerning the joint genotypic structure at the two loci and the degree of assortativity and linkage. A complete, analytical representation of the limits is given. In particular, if assortative mating is only partial and at the same time linkage is not complete, a population is not able to maintain a permanent deviation of the gametic structure from linkage equilibrium, and thus the genotypic structure at the second locus tends to Hardy-Weinberg proportions. On the other hand, if initial linkage disequilibrium is combined with partial assortative mating and complete linkage (or with complete assortative mating and unlinked loci) the population maintains this disequilibrium and thus the genotypic structure at the second locus need not tend to Hardy-Weinberg proportions. It turns out that the conditions not only of complete linkage, but also of unlinked loci together with complete assortativity, imply no change in gametic structure from the initial structure.In order to demonstrate the influence of several parameters on the speed of convergence to and the magnitude of the respective limits, several graphs are included.     

Emergence and loss of assortative mating in sympatric speciation

We have studied an agent model which presents the emergence of sexual barriers through the onset of assortative mating, a condition that might lead to sympatric speciation. In the model, individuals are characterized by two traits, each determined by a single locus A or B. Heterozygotes on A are penalized by introducing an adaptive difference from homozygotes. Two niches are available. Each A homozygote is adapted to one of the niches. The second trait, called the marker trait has no bearing on the fitness. The model includes mating preferences, which are inherited from the mother and subject to random variations. A parameter controlling recombination probabilities of the two loci is also introduced. We study the phase diagram by means of simulations, in the space of parameters (adaptive difference, carrying capacity, recombination probability). Three phases are found, characterized by (i) assortative mating, (ii) extinction of one of the A alleles and (iii) Hardy-Weinberg like equilibrium. We also make perturbations of these phases to see how robust they are. Assortative mating can be gained or lost with changes that present hysteresis loops, showing the resulting equilibrium to have partial memory of the initial state and that the process of going from a polymorphic panmictic phase to a phase where assortative mating acts as sexual barrier can be described as a first-order transition.     

On the origin of species by means of assortative mating.

Assortative mating may split a population even in the absence of natural selection. Here, we study when this happens if mating depends on one or two quantitative traits. Not surprisingly, the modes of assortative mating that can cause sympatric speciation without selection are rather strict. However, some of them may occur in nature. Slow elimination of intermediate individuals caused by the gradual tightening of assortative mating, which evolves owing to relatively weak disruptive selection, provides the alternative scenario for sympatric speciation, in addition to fast elimination of intermediate individuals as a result of the direct action of strong disruptive selection under an invariant mode of assortative mating. Even when assortative mating alone cannot split an initially coherent population, it may be able to prevent the merging of species after their secondary contact.     

Some multiallele partial assortative mating systems for a polygamous species

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA 74, 3476–3479), Wilbur et al. (1978, Evolution 32, 264–270), and Singh and Zouros (1978, Evolution 32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

The effect of positive assortative mating on genetic parameters in a simulated beef cattle population

Summary Two simulated data sets, representing random mating and positive assortative mating in a beef cattle population over 10 rounds of mating, were each composed of 100 replicates. Three correlated traits were considered; calving ease (CE), 200 day weight (WW) and postweaning gain (PG). All selection practiced in the simulation was random. Positive assortative mating, which was based on parental WW phenotypic records, increased the progeny additive genetic variance of WW. The absolute values of genetic covariances and correlations between WW with CE and PG were also increased by positive assortative mating. Variances or covariances did not reach their expected equilibrium values due to overlapping generations, low replacement rates and only 10 rounds of mating.The financial assistance of Agriculture Canada and the Natural Sciences and Engineering Research Council of Canada are gratefully acknowledged