Analysis of some nonrandom mating models

In this paper a few asymmetric models are presented taking account of the effects of assortative mating on an autosomal trait controlled by a single locus possibly with multiple alleles. The models are developed by specifying the intensities for preference mating for various phenotypes. The analysis is confined to the case in which preference is exercised by the individuals of one sex only. It is assumed that males possess unlimited fertility.The dynamics of the population and its equilibrium distribution are discussed. The gene frequency usually changes with time and equilibrium distribution in most cases depends only on the assortment parameters. Expressions are obtained giving the additive and dominance components of variance, and covariances for relatives for populations in equilibrium for some of the models.     

A rapid generalized least squares model for a genome-wide quantitative trait association analysis in families

Genome-wide association studies (GWAS) using family data involve association analyses between hundreds of thousands of markers and a trait for a large number of related individuals. The correlations among relatives bring statistical and computational challenges when performing these large-scale association analyses. Recently, several rapid methods accounting for both within- and between-family variation have been proposed. However, these techniques mostly model the phenotypic similarities in terms of genetic relatedness. The familial resemblances in many family-based studies such as twin studies are not only due to the genetic relatedness, but also derive from shared environmental effects and assortative mating. In this paper, we propose 2 generalized least squares (GLS) models for rapid association analysis of family-based GWAS, which accommodate both genetic and environmental contributions to familial resemblance. In our first model, we estimated the joint genetic and environmental variations. In our second model, we estimated the genetic and environmental components separately. Through simulation studies, we demonstrated that our proposed approaches are more powerful and computationally efficient than a number of existing methods are. We show that estimating the residual variance-covariance matrix in the GLS models without SNP effects does not lead to an appreciable bias in the p values as long as the SNP effect is small (i.e. accounting for no more than 1% of trait variance).     

PARTITIONING THE EFFECTS OF SPATIAL ISOLATION,NEST HABITAT,AND INDIVIDUAL DIET IN CAUSING ASSORTATIVE MATING WITHIN A POPULATION OF THREESPINE STICKLEBACK

Assortative mating is measured as a phenotypic or genotypic correlation between mates. Although biologists typically view assortative mating in terms of mate preference for similar partners, correlations between mates can also arise from phenotypic spatial structure arising from spatial isolation or habitat preferences. Here, we test whether diet‐assortative mating within an ecologically variable population of threespine stickleback results from small‐scale geographic isolation or microhabitat preference. We find evidence for assortative mating in the form of a positive correlation between mated pairs’ diets (measured using stable isotopes). Stable isotopes reveal diet differences between different nesting areas and among individuals using different nest habitat within a nesting area. This spatial segregation of diet types should generate some assortative mating, but is insufficient to explain the observed assortment strength. Significant male–female isotope correlations remain after controlling for spatial variables. We therefore conclude that sticklebacks’ diet‐assortative mating arises from additional behavioral preference. More generally, our results illustrate the point that spatial segregation can only drive appreciable levels of phenotypic assortative mating when environment‐phenotype correlations are parallel and strong in both sexes. Consequently, intraspecific assortative mating may typically entail mating preferences rather than just spatial cosegregation of phenotypes.     

The population genetics of assortative mating based on imprinting

This paper is concerned with the population effects of mating preferences for inherited traits. We suppose that the trait is determined by a pair of alleles and concentrate on the autosomal case with complete dominance. We are interested in the case when the mating preferences are determined by the phenotype of relatives, such as parents or sibs. This is a possible consequence of imprinting, a kind of learning process which occurs early after birth in warmblooded vertebrates. In spite of the greater analytical complexity of these models, their results are very similar to those found when the preference is determined by the phenotype of the mating individual itself. In particular the preference for the same phenotype as that of relatives usually leads to the fixation of either morph, depending on the initial frequency. Polymorphism, on the other hand, always results when the preference is for a phenotype which differs from that of relatives.     

Response to Selection Under Non-Random Mating I. Partitioning Genetic Variance

In analogy to the concept of breeding value defined for random mating equilibrium populations, the “transmittable genetic value” of an individual is defined as the average value of its expected progeny for any system of mating. The genotypic value is then characterised in terms of transmittable and residual genetic values and components of genetic variance redefined which can be estimated by the conventional procedure based on resemblance between relatives.     

The effect of cultural transmission on continuous variation.

Cultural transmission may depend on the non-genetic transfer of information from parent to offspring. The consequences of such cultural transmission for continuous variation are investigated theoretically for randomly mating populations. Cultural inheritance may act on genetical and environmental differences between individuals. The consequences for cultural inheritance of polygenic variation and variation due to chance environmental factors are considered. An equilibrium may occur in which the population variance and the covariances between relatives can be expressed as functions of estimable parameters of genetical and environmental variation. Whatever the ultimate origin of culturally inherited differences they are expected to lead to environmental differences between families ("E2" variation). In addition, if cultural transmission maintains differences due ultimately to segregation at many gene loci we may find genotype-environmental covariation is generated.     

Covariance between relatives for X-chromosomal loci in a population in disequilibrium

Summary According to Hardy-Weinberg, for a single autosomal locus, a population achieves equilibrium in one generation of random mating if allelic frequency is the same in the sexes, or in two generations if the frequency is not. For a single X-chromosomal locus, however, the approach to equilibrium oscillates and is gradual. Covariances between relatives for autosomal and for X-chromosomal loci are in the literature for a random mating population in equilibrium. Although assumption of equilibrium is defensible for an autosomal locus, it is less defensible for an X-chromosomal locus. Covariances between collateral and between lineal relatives are derived for X-chromosomal loci in a random mating population not in equilibrium. Collateral relatives such as sibs are of the same generation, and lineal relatives such as parent-offspring are of different generations. Coefficient of co-ancestry between relatives, based on identity by descent, was used in this development. Results are applicable to crossbreeding in livestock and poultry, and also to haplo-diploid organisms, such as the honeybee, in which the entire genome is equivalent to being X-chromosomal.Supported in part by the Illinois Agricultural Experiment Station, Hatch Project 35-0367     

Fatal or Harmless: Extreme Bistability Induced by Sterilizing,Sexually Transmitted Pathogens

Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.     

Polyploidy and self-fertilization in flowering plants

Mating systems directly control the transmission of genes across generations, and understanding the diversity and distribution of mating systems is central to understanding the evolution of any group of organisms. This basic idea has been the motivation for many studies that have explored the relationships between plant mating systems and other biological and/or ecological phenomena, including a variety of floral and environmental characteristics, conspecific and pollinator densities, growth form, parity, and genetic architecture. In addition to these examples, a potentially important but poorly understood association is the relationship between plant mating systems and genome duplication, i.e., polyploidy. It is widely held that polyploid plants self-fertilize more than their diploid relatives, yet a formal analysis of this pattern does not exist. Data from 235 species of flowering plants were used to analyze the association between self-fertilization and ploidy. Phylogenetically independent contrasts and cross-species analyses both lend support to the hypothesis that polyploids self-fertilize more than diploids. Because polyploidy and self-fertilization are so common among angiosperms, these results contribute not only to our understanding of the relationship between mating systems and polyploidy in particular, but more generally, to our understanding of the evolution of flowering plants.     

Consanguineous marriages in Italy: A Note

Abstract

A general multifactorial model is given for the inheritance of traits that exhibit a sexual dimorphism. The model allows for polygenic inheritance, cultural transmission, phenotypic assortative mating, and a common environment of rearing. Several cultural mechanisms are described for which transmission from parent to offspring is sex‐dependent and for which many different patterns of sex‐specific correlations can result. A special case of the general model is described in which phenotypic differences between males and females are due only to differences in nontransmissible environmental factors and/or genetic factors that do not contribute to variability within a sex. Application of these models to human spatial visualizing ability, using data reported by others, gives an estimate of 45 per cent for the proportion of the variance that is accounted for by transmissible factors. Neither an X‐linked hypothesis nor a sex‐specific cultural mechanism is required to explain the transmission of spatial ability.     

On the Role of Schistosome Mating Structure in the Maintenance of Drug-resistant Strains

The effects of drug treatment of human hosts on a population of schistosome parasites depends on a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.     

CORRELATED INBREEDING AMONG RELATIVES: OCCURRENCE,MAGNITUDE, AND IMPLICATIONS

Understanding the magnitude and causes of genetic and phenotypic resemblance among relatives is key to understanding evolutionary processes. Contrary to basic expectation, individual coefficients of inbreeding ( f) were recently hypothesized to be intrinsically correlated across parents and offspring in structured populations, potentially creating an additional source of phenotypic resemblance in traits that show inbreeding depression. To test this hypothesis, we used individual‐based simulations to quantify the parent–offspring correlations in f arising under random mating in populations of different size, immigration rate, and mating system. Parent–offspring correlations in f were typically positive (median r≈ 0.2–0.4) in relatively small and isolated populations. Relatively inbred parents therefore produced relatively inbred offspring on average, although the magnitude of this effect varied considerably among replicate populations. Correlations were higher given more generations of random mating, greater variance in reproductive success, polygynous rather than monogamous mating, and for midparent–offspring rather than parent–offspring relationships. Furthermore, f was also positively correlated across half‐siblings, and closer relatives had more similar inbreeding coefficients across entire generations. Such intrinsic resemblance in f among relatives could provide an additional genetic benefit of mate choice and bias quantitative genetic analyses that do not account for correlated inbreeding depression.     

Is Fisher's model necessary for the theory of population improvement?

Summary It is shown here that genetic advance in one cycle of recurrent selection can be formulated directly in terms of covariances between relatives by application of the general statistical principle of linear prediction. For practical use of such formulae it is necessary to estimate the corresponding covariance between relatives from the mating design used. With General Combining Ability selection such estimation is direct. For other types of selection, it is necessary to derive associated covariances from other types of covariances but it is not necessary to use classical results of covariances between relatives in terms of genetic effects. Indeed, covariances can be derived without factorial decomposition of the genetic effects at one locus, i.e., without the concept of additivity and dominance. This approach allows a simple derivation of the genetic advance after n cycles of selection, followed by m generations of intercrossing, with a minimum of assumptions.     

Theory of inbreeding and covariances between relatives under full-sib mating in diploids.

A generation matrix theory of full-sib mating is developed in which 13 mating "classes" are distinguished according to identity of genes in individuals mated and identity of genotypes as belonging to homozygous, parental, or offspring sets. The 13 times 13 matrix reveals some properties of the full-sib mating system not shown by previous work. The eigenvalues and a set of eigenvectors for the generation matrix, and the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab times cd, are given. The genotypic array of descendants in an arbitrary generation is also given. A new formula is derived for the coefficient of inbreeding in generation n + m in terms of coefficients of inbreeding in earlier generations. An algorithm is presented for calculating the probability of a given situation of identity of alleles carried by two individuals given only the indices of their own respective generations and the generation of their most recent common ancestor. The application of such probabilities to obtaining covariances between relatives in a full-sib mating system, under the assumptions of independence and non-interaction among loci, is illustrated. All results are shown to agree with previous work in special cases. All possible full sib, generation n - 1 parent-generation n + m offspring, and generation n uncle-generation n + m nephew covariances for 1 less than n + m less than or equal to 8 are obtained using the given algorithm.     

Covariances of relatives stemming from a population undergoing mixed self and random mating

We consider covariances of all parent and first-generation relatives from outcrossing or self-fertilization in a parent population that is in equilibrium with respect to these processes. The results, which are for any number of alleles and loci with additive and dominance effects, are phrased in terms of six quadratic genetic components whose coefficients are given by descent measures for equilibrium populations. Because of the variation in the inbreeding coefficients for this system of mating, the expressions include joint contributions of loci to the variances and covariances of relatives. By inclusion of the full complement of relatives, all quadratic components can be estimated. The findings of Ghai (1982, Biometrics 38, 87-92) for compound functions of the covariances with two alleles at a single locus are analyzed in terms of the more general model.     

Inbreeding Depression and Inbreeding Avoidance in a Natural Population of Guppies (Poecilia reticulata)

Maintenance of genetic variation in the face of strong natural selection is a long‐standing problem in evolutionary biology. One of the most extreme examples of within‐population variation is the polymorphic, genetically determined color pattern of male Trinidad guppies (Poecilia reticulata). Female mating preference for rare or novel patterns has been implicated as a factor in maintaining this variation. The origin of this preference is not understood, although inbreeding avoidance has been proposed as a mechanism. Inbreeding avoidance is advantageous when populations exhibit inbreeding depression and the opportunity for mating between relatives exists. To determine whether these conditions are met in a natural guppy population, we assessed mating and reproductive patterns using polymorphic molecular markers. Females produced more offspring with less‐related males than with more‐related ones. In addition, females were more likely to have mated with less‐related males, but this trend was only marginally significant. Male heterozygosity was positively correlated with mating success and with the number of offspring sired, consistent with strong inbreeding depression for adult male fitness. These results provide substantial insight into mating patterns of a wild guppy population: strong inbreeding depression occurs, and individuals tend to avoid mating with relatives.     

Inbreeding avoidance behaviors

Inbreeding is defined as mating between individuals related by common ancestry. Thus, the degree to which a particular mating is inbred depends on how far back in a pedigree one begins counting common ancestors. In general practice, the term inbreeding is used to describe mating between close relatives (first cousins or closer). Animal breeders have known for centuries that inbreeding causes a loss of constitutional vigor and fertility in domestic livestock. A growing literature now demonstrates that the offspring of matings between close relatives in species of undomesticated birds and mammals are less fit than outbred offspring. The deleterious consequences of inbreeding suggest the possibility that many species have evolved behaviors that lower the frequency of inbreeding.     

The use of twins in the analysis of assortative mating

The simulations illustrated show that a plausible model for mate selection can generate data on the similarity of twins and their spouses which are remarkably consistent with a transitive model for the effects of mate selection. This is, biological considerations impose constraints upon the relative values of correlations which are not foreseen, for example, by the some advocates of conventional path models although they might be predicted by common sense. In particular, the correlation between the spouses of twins is expected to be non-zero under a model of phenotypic assortment and turns out to be approximately equal to the product of the twin correlation and the square of the marital correlation. The relative magnitudes of the correlations derived from an empirical study of such relationships should enable models of phenotypic assortment to be tested more rigorously. Including both identical and non-identical twins in the sample studied should permit the inherited and cultural components of the mating system to be identified with more conviction. In the event of one sex playing a more significant role in mate selection for particular traits, such studies should reveal diagnostic patterns of familial correlations as long as male and female twins and their spouses are analysed separately. If the analysis is restricted to phenotypic correlations of the parents, the qualitative findings do not appear to be greatly affected by selection due to assortative mating although a reduction in variance is to be expected if a large proportion of individuals is unable to mate. In such cases twins will also be significantly concordant for mating. The consequences of such varied regimes of assortation for the population structure and the relationship between traits in subsequent generations remain the object of future inquiry.     

On the role of schistosome mating structure in the maintenance of drug resistant strains

The effects of drug treatment of human hosts upon a population of schistosome parasites depend upon a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.