Reinforcement and the genetics of nonrandom mating

Abstract.— The occurrence of reinforcement is compared when premating isolation is caused by the spread of a gene causing females to prefer to mate with males carrying a population-specific trait (a "preference" model) and by a gene that causes females to prefer to mate with males that share their own trait phenotype (an "assortative mating" model). Both two-island models, which have symmetric gene flow, and continent-island models, which have one-way gene flow, are explored. Reinforcement is found to occur much more easily in a two-island assortative mating model than in any of the other three models. This is due primarily to the fact that in this model the assortative mating allele will automatically become genetically associated in each population with the trait allele that is favored by natural selection on that island. In contrast, natural selection on the trait both favors and opposes the evolution of premating isolation in the two-island preference model, depending on the particular population. These results imply that species recognition in the context of mating may evolve particularly easily when it targets cues that are favored by natural selection in each population. In the continent-island models, reinforcement is found to occur more often under the preference model than the assortative mating model, thus reversing the trend from the two-island models. Patterns of population subdivision may therefore play a role in determining what types of premating isolation may evolve.     

Bisexual branching processes in a genetic context: rates of growth for Y-linked genes

A multitype bisexual branching process is considered to model the behaviour of a Y-linked gene with two genotypes in a two-sex population. It is assumed perfect fidelity mating with preference of females for the males carrying certain allele of the gene. Under these assumptions, we study the rate of growth of each genotype on the event of non-extinction. The rate of growth of a genotype may depend on whether the other survives or becomes extinct and, in general, both genotype frequencies grow at different rates. We also investigate conditions for the simultaneous explosion of both genotypes to have positive or zero probability.     

A single-locus model of speciation

The crucial phase of speciation is argued to be the evolution of mating cross-incompatibility (prezygotic incompatibility) between the genotypes distinguishing the prospective species populations. Based on this idea, a single-locus model of speciation is presented, which is shown to be biologically plausible and may help to settle the controversy as to the biological significance of single-locus modes of speciation. The model involves three alleles, two of which characterize in homozygous state the prospective species populations and in heterozygous state their hybrids. The third allele represents a mutant which is equivalent to one of the first two alleles with the exception that it inhibits mating with carriers of the third allele. This third allele is fixed in one population and immigrates into a second population which contains the mutant inhibiting matings with members of the former population. Migration in the reverse direction does not occur. Proceeding from a widely applicable concept of fitness and mating preference it is shown that postzygotic incompatibility (hybrid or heterozygote disadvantage) alone suffices to trigger evolutionary replacement of the extant mating relations in the population receiving immigrants by any arbitrary degree of prezygotic incompatibility. This corroborates Wallace's hypothesis and emphasizes the potential biological relevance of speciation by reinforcement (parapatric speciation) at single gene loci.     

Joint Frequencies of Alleles Determined by Separate Formulations for the Mating and Mutation Systems

A method to calculate joint gene frequencies, which are the probabilities that two neutral genes taken at random from a population have certain allelic states, is developed taking into account the effects of the mating system and the mutation scheme. We assume that the mutation rates are constant in the population and that the mating system does not depend on allelic states. Under either--the condition that mutation rates are symmetric or that the mating unit is large and the mutation rate is small--the general formula is represented by two terms, one for the mating system and the other for the mutation scheme. The term for the mating system is expressed using the coancestry coefficient in the infinite allele model, and the term for the mutation scheme is a function of the eigenvalues and the eigenvectors of the mutation matrix. Several examples are presented as applications of the method, including homozygosity in a stepping-stone model with a symmetric mutation scheme.     

Molecular evidence for multiple paternity in a feral population of green swordtails

Genetic parentage analyses provide insights into mating systems and have revealed widespread evidence for polyandry in natural populations. Here, we use 5 microsatellite markers to estimate female mating rates in a feral population of green swordtails, Xiphophorus helleri, a live-bearing poeciliid fish that has become a model system in the study of precopulatory mate choice and mating competition. Although heralded as a potential model for investigating sperm competition as early as 1950, there has been no attempt to explore postcopulatory sexual selection in its mating system. We thus obtained information on the prevalence, and therefore biological relevance, of polyandry from a wild population. We genotyped the offspring from 14 wild-caught gravid females and determined the number of fathers in each brood using allele counting methods and the programs GERUD and PARENTAGE. Our analyses revealed that 57% (allele counts and GERUD) and 71% (PARENTAGE) of the sampled broods had at least 2 sires, with a global mean 1.74 fathers per brood. Paternity skew was generally high in mixed paternity broods so that our analyses almost certainly underestimate actual mating frequencies in the wild. Our data provide a solid underpinning for future studies of postcopulatory sexual selection in this species.     

A clarification of the Hardy-Weinberg law

C. C. Li showed that Hardy-Weinberg proportions (HWP) can be maintained in a large population by nonrandom mating as well as random mating. In particular he gave the mating matrix for the symmetric case in the most general form possible. Thus Li showed that, once HWP are attained, the same proportions can be maintained by what he called pseudorandom mating. This article shows that, starting from any genotypic distribution at a single locus with two alleles, the same in each sex, HWP can be reached in one round of nonrandom mating with no change in allele frequency. In the model that demonstrates this fact, random mating is represented by a single point in a continuum of nonrandom possibilities.     

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.     

Regular systems of inbreeding with mutation

Probability of identity by type is studied for regular systems of inbreeding in the presence of mutation. Analytic results are presented for half-sib mating, first cousin mating, and half nth cousin mating under both infinite allele and two allele (back mutation) models. Reasonable rates of mutation do not provide significantly different results from probability of identity by descent in the absence of mutation. Homozygosity is higher under half-sib mating than under first cousin mating, but the expected number of copies of a gene in the population is higher under first cousin mating than under half-sib mating.     

Gene duplication and divergence produce divergent MHC genotypes without disassortative mating

Genes of the major histocompatibility complex (MHC) exhibit heterozygote advantage in immune defence, which in turn can select for MHC‐disassortative mate choice. However, many species lack this expected pattern of MHC‐disassortative mating. A possible explanation lies in evolutionary processes following gene duplication: if two duplicated MHC genes become functionally diverged from each other, offspring will inherit diverse multilocus genotypes even under random mating. We used locus‐specific primers for high‐throughput sequencing of two expressed MHC Class II B genes in Leach's storm‐petrels, Oceanodroma leucorhoa, and found that exon 2 alleles fall into two gene‐specific monophyletic clades. We tested for disassortative vs. random mating at these two functionally diverged Class II B genes, using multiple metrics and different subsets of exon 2 sequence data. With good statistical power, we consistently found random assortment of mates at MHC. Despite random mating, birds had MHC genotypes with functionally diverged alleles, averaging 13 amino acid differences in pairwise comparisons of exon 2 alleles within individuals. To test whether this high MHC diversity in individuals is driven by evolutionary divergence of the two duplicated genes, we built a phylogenetic permutation model. The model showed that genotypic diversity was strongly impacted by sequence divergence between the most common allele of each gene, with a smaller additional impact of monophyly of the two genes. Divergence of allele sequences between genes may have reduced the benefits of actively seeking MHC‐dissimilar mates, in which case the evolutionary history of duplicated genes is shaping the adaptive landscape of sexual selection.     

Structure, function, and phylogeny of the mating locus in the Rhizopus oryzae complex

The Rhizopus oryzae species complex is a group of zygomycete fungi that are common, cosmopolitan saprotrophs. Some strains are used beneficially for production of Asian fermented foods but they can also act as opportunistic human pathogens. Although R. oryzae reportedly has a heterothallic (+/-) mating system, most strains have not been observed to undergo sexual reproduction and the genetic structure of its mating locus has not been characterized. Here we report on the mating behavior and genetic structure of the mating locus for 54 isolates of the R. oryzae complex. All 54 strains have a mating locus similar in overall organization to Phycomyces blakesleeanus and Mucor circinelloides (Mucoromycotina, Zygomycota). In all of these fungi, the minus (-) allele features the SexM high mobility group (HMG) gene flanked by an RNA helicase gene and a TP transporter gene (TPT). Within the R. oryzae complex, the plus (+) mating allele includes an inserted region that codes for a BTB/POZ domain gene and the SexP HMG gene. Phylogenetic analyses of multiple genes, including the mating loci (HMG, TPT, RNA helicase), ITS1-5.8S-ITS2 rDNA, RPB2, and LDH genes, identified two distinct groups of strains. These correspond to previously described sibling species R. oryzae sensu stricto and R. delemar. Within each species, discordant gene phylogenies among multiple loci suggest an outcrossing population structure. The hypothesis of random-mating is also supported by a 50:50 ratio of plus and minus mating types in both cryptic species. When crossed with tester strains of the opposite mating type, most isolates of R. delemar failed to produce zygospores, while isolates of R. oryzae produced sterile zygospores. In spite of the reluctance of most strains to mate in vitro, the conserved sex locus structure and evidence for outcrossing suggest that a normal sexual cycle occurs in both species.     

Bisexual branching processes in a genetic context: the extinction problem for Y-linked genes

In this paper the inheritance of a Y-linked gene with alleles R and r in a population with both females and males is modelled using a two-type bisexual branching process. It is assumed that the reproductive distribution associated with the R allele can differ from the associated with the r allele and that females prefer to mate with a male having the R allele rather than with a male with the r allele. Under these assumptions, we provide some conditions for the extinction and/or survival of both alleles in the population. These conditions depend on the magnitudes of the average number of females and males per mating unit. Moreover, the almost sure extinction of the r allele is independent of the behaviour of the R allele. On the other hand, the survival of the R allele with positive probability may depend strongly on the reproductive behaviour of the other allele. Theoretical results are illustrated by means of simulated examples and some open problems are proposed to the reader as conjectures.     

Sex ratio polymorphism: The impact of mutation and drift on evolution

This paper addresses the question, which sex ratio will evolve in a population that is subject to mutation and drift. The problem is analyzed using a simulation model as well as analytical methods. A detailed simulation model for the evolution of a population's allele distribution shows that for the sex ratio game a wide spectrum of different population states may evolve from on the one hand a monomorphic state with one predominant allele and with all other alleles suppressed by the forces of selection, to on the other hand a polymorphism determined by recurrent mutations. Which of these states will evolve depends on the population size, the mating system and the rate of mutations. For the sex ratio game the evolutionary stable strategy (ESS), as defined by evolutionary game theory, can only predict the population sex ratio but not the underlying stable population state. A comparison of different approaches to the problem shows that false predictions of the stable population states might result from two simplifying assumptions that are fairly common in evolutionary biology: a) it is assumed that mutations are rare events and there is never more than one mutant gene present in a population at any one time; b) a deterministic relationship is assumed between the fitness assigned to an individual's strategy and the individual's contribution to the gene pool of future generations.     

Genetic diversity and population structure of the invasive alien red swamp crayfish

High genetic diversity is thought to characterize successful invasive species, as the potential to adapt to new environments is enhanced and inbreeding is reduced. The red swamp crayfish, Procambarus clarkii, native to northeastern Mexico and south-central USA was introduced to Nanjing, China from Japan in 1929. Little is known about the genetic diversity and population structure of this species in China. We examined the genetic diversity and population structure of six P. clarkii populations using nine polymorphic microsatellites. Among the six populations, Nanjing population showed the highest allele number, allele richness and gene diversity, which is consistent with records indicating Nanjing may be the first site of introduction. In all six populations, significant heterozygote deficit was observed, suggesting founder effects and non-random mating. Analysis of bottleneck under infinite allele model, stepwise mutation model and two-phased model of mutation revealed evidence of a recent bottleneck in all these populations. Pairwise genetic distance analysis, AMOVA and assignment tests demonstrated high genetic differentiation between populations. Pairwise genetic distance did not fit the pairwise geographic distance, suggesting that human mediated dispersal have played a role in the population expansion and genetic differentiation.     

On Nonrandom Mating Systems for Attaining Hardy-Weinberg Equilibrium

LI (1988) showed that random mating is a sufficient, not a necessary condition for the Hardy-Weinberg principle. A nonrandom mating population that behaves like a random mating population is thus called a ‘pseudo-random mating population’ by him. The pseudo-random mating system studied by him has been focused on those populations in which the parental generation is in Hardy-Weinberg proportions. In other words, the mating type frequency deviations from random mating for each parental genotype add up to zero. In this article these restrictions are relaxed and new pseudo-random mating systems that immediately yield Hardy-Weinberg offspring are also obtained. This is possible because reciprocal crosses have identical segregation probabilities for an autosomal locus, and the manipulation of the combined frequency of reciprocal crosses does not change the gene frequency of the population. A comparison of these new patterns with that of Li is given in the Discussion.     

Stochastic modelling of shifts in allele frequencies reveals a strongly polygynous mating system in the re‐introduced Asiatic wild ass

Small populations are prone to loss of genetic variation and hence to a reduction in their evolutionary potential. Therefore, studying the mating system of small populations and its potential effects on genetic drift and genetic diversity is of high importance for their viability assessments. The traditional method for studying genetic mating systems is paternity analysis. Yet, as small populations are often rare and elusive, the genetic data required for paternity analysis are frequently unavailable. The endangered Asiatic wild ass (Equus hemionus), like all equids, displays a behaviourally polygynous mating system; however, the level of polygyny has never been measured genetically in wild equids. Combining noninvasive genetic data with stochastic modelling of shifts in allele frequencies, we developed an alternative approach to paternity analysis for studying the genetic mating system of the re‐introduced Asiatic wild ass in the Negev Desert, Israel. We compared the shifts in allele frequencies (as a measure of genetic drift) that have occurred in the wild ass population since re‐introduction onset to simulated scenarios under different proportions of mating males. We revealed a strongly polygynous mating system in which less than 25% of all males participate in the mating process each generation. This strongly polygynous mating system and its potential effect on the re‐introduced population's genetic diversity could have significant consequences for the long‐term persistence of the population in the Negev. The stochastic modelling approach and the use of allele‐frequency shifts can be further applied to systems that are affected by genetic drift and for which genetic data are limited.     

Serial founder effects during range expansion: a spatial analog of genetic drift

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1-1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population.     

Host mating system and the prevalence of disease in a plant population

A modified susceptible-infected-recovered (SIR) host-pathogen model is used to determine the influence of plant mating system on the outcome of a host-pathogen interaction. Unlike previous models describing how interactions between mating system and pathogen infection affect individual fitness, this model considers the potential consequences of varying mating systems on the prevalence of resistance alleles and disease within the population. If a single allele for disease resistance is sufficient to confer complete resistance in an individual and if both homozygote and heterozygote resistant individuals have the same mean birth and death rates, then, for any parameter set, the selfing rate does not affect the proportions of resistant, susceptible or infected individuals at equilibrium. If homozygote and heterozygote individual birth rates differ, however, the mating system can make a difference in these proportions. In that case, depending on other parameters, increased selfing can either increase or decrease the rate of infection in the population. Results from this model also predict higher frequencies of resistance alleles in predominantly selfing compared to predominantly outcrossing populations for most model conditions. In populations that have higher selfing rates, the resistance alleles are concentrated in homozygotes, whereas in more outcrossing populations, there are more resistant heterozygotes.     

Limiting genotype frequencies of Y-linked genes through bisexual branching processes with blind choice

The limiting genotype growth rates and the limiting genotype frequencies of Y-linked genes are studied in a two-sex monogamous population. To this end, the evolution of the numbers of females, males, and mating units of each genotype is modelled by a multitype bisexual branching process in which it assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit of a genotype determine its growth rate, which does not depend on the behaviour of the other genotypes. Hence, the dominant genotype is found. Conditions for the simultaneous survival of genotypes to have positive probability are also investigated. Finally, the main results are illustrated by means of examples.     

Nuclear–mitochondrial epistasis: a gene's eye view of genomic conflict

We use population genetic models to investigate the cooperative and conflicting synergistic fitness effects between genes from the nucleus and the mitochondrion. By varying fitness parameters, we examine the scope for conflict relative to cooperation among genomes and the utility of the “gene's eye view” analytical approach, which is based on the marginal average fitness of specific alleles. Because sexual conflict can maintain polymorphism of mitochondrial haplotypes, we can explore two types of evolutionary conflict (genomic and sexual) with one epistatic model. We find that the nuclear genetic architecture (autosomal, X‐linked, or Z‐linked) and the mating system change the regions of parameter space corresponding to the evolution by sexual and genomic conflict. For all models, regardless of conflict or cooperation, we find that population mean fitness increases monotonically as evolution proceeds. Moreover, we find that the process of gene frequency change with positive, synergistic fitnesses is self‐accelerating, as the success of an allele in one genome or in one sex increases the frequency of the interacting allele upon which its success depends. This results in runaway evolutionary dynamics caused by the positive intergenomic associations generated by selection. An inbreeding mating system tends to further accelerate these runaway dynamics because it maintains favorable host–symbiont or male–female gene combinations. In contrast, where conflict predominates, the success of an allele in one genome or in one sex diminishes the frequency of the corresponding allele in the other, resulting in considerably slower evolutionary dynamics. The rate of change of mean fitness is also much faster with positive, synergistic fitnesses and much slower where conflict is predominant. Consequently, selection rapidly fixes cooperative gene combinations, while leaving behind a slowing evolving residue of conflicting gene combinations at mutation–selection balance. We discuss how an emphasis on marginal fitness averages may obscure the interdependence of allelic fitness across genomes, making the evolutionary trajectories appear independent of one another when they are not.     

Sperm competition and the dynamics of X chromosome drive: stability and extinction

Several empirical studies of sperm competition in populations polymorphic for a driving X chromosome have revealed that Sex-ratio males (those carrying a driving X) are at a disadvantage relative to Standard males. Because the frequency of the driving X chromosome determines the population-level sex ratio and thus alters male and female mating rates, the evolutionary consequences of sperm competition for sex chromosome meiotic drive are subtle. As the SR allele increases in frequency, the ratio of females to males also increases, causing an increase in the male mating rate and a decrease in the female mating rate. While the former change may exacerbate the disadvantage of Sex-ratio males during sperm competition, the latter change decreases the incidence of sperm competition within the population. We analyze a model of the effects of sperm competition on a driving X chromosome and show that these opposing trends in male and female mating rates can result in two coexisting locally stable equilibria, one corresponding to a balanced polymorphism of the SR and ST alleles and the second to fixation of the ST allele. Stochastic fluctuations of either the population sex ratio or the SR frequency can then drive the population away from the balanced polymorphism and into the basin of attraction for the second equilibrium, resulting in fixation of the SR allele and extinction of the population.