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.     

PHENOTYPIC SELECTION IN AN ARTIFICIAL POPULATION OF IMPATIENS PALLIDA: THE IMPORTANCE OF THE INVISIBLE FRACTION

Multiple-regression techniques for measuring phenotypic selection have been used in a large number of recent field studies. One benefit of this technique is its ability to discern the direct action of selection on traits by removing effects of correlated traits. However, covariation among traits expressed at different stages in an organism's life history is often poorly estimated because individuals that die before reaching adulthood cannot be measured as adults. Accurate estimates of trait covariances are necessary for the correct interpretation of the direct action of selection on a trait. If phenotypic characters expressed at different life-history stages are of interest, and mortality occurs between stages, the components of the selection model will be biased by not including those individuals that died (the “invisible fraction”).     

Estimating fluctuating selection in age-structured populations

In age-structured populations, viability and fecundity selection of varying strength may occur in different age classes. On the basis of an original idea by Fisher of weighting individuals by their reproductive value, we show that the combined effect of selection on traits at different ages acts through the individual reproductive value defined as the stochastic contribution of an individual to the total reproductive value of the population the following year. The selection differential is a weighted sum of age-specific differentials that are the covariances between the phenotype and the age-specific relative fitness defined by the individual reproductive value. This enables estimation of weak selection on a multivariate quantitative character in populations with no density regulation by combinations of age-specific linear regressions of individual reproductive values on the traits. Demographic stochasticity produces random variation in fitness components in finite samples of individuals and affects the statistical inference of the temporal average directional selection as well as the magnitude of fluctuating selection. Uncertainties in parameter estimates and test power depend strongly on the demographic stochasticity. Large demographic variance results in large uncertainties in yearly estimates of selection that complicates detection of significant fluctuating selection. The method is illustrated by an analysis of age-specific selection in house sparrows on a fitness-related two-dimensional morphological trait, tarsus length and body mass of fledglings.     

Indirect genetic effects from ecological interactions in Arabidopsis thaliana

Indirect genetic effects arise when genes expressed in one individual affect the expression of traits in other individuals. The importance of indirect genetic effects has been recognized for a diversity of evolutionary processes including kin selection, sexual selection, community structure and multilevel selection, but data regarding their genetic architecture and prevalence throughout the genome remain scarce, especially for interactions between unrelated individuals. Using a set of 411 Bay-0 x Shahdara Arabidopsis recombinant inbred lines grown with Landsberg neighbours, we examined quantitative trait loci (QTL) having direct and indirect effects on size, developmental, and fitness related traits. Using an interval mapping approach, we identified 15 QTL with direct effects and found that 13 of these QTL had significant indirect effects on trait expression in neighbouring plants. These results suggest widespread pleiotropy, as nearly all direct effect QTL have associated pleiotropic indirect effects. Paradoxically, most indirect effects were of the same sign as direct effects, creating a pattern of nearly universal positive pleiotropy that makes most covariances between direct and indirect effects positive. These results are consistent with a complex genetic basis for intraspecific interactions, but suggest that interactions between neighbouring plants are largely positive, rather than negative as would be expected for competition. In addition to their evolutionary and ecological importance, these pleiotropic relationships between DGE and IGE loci have implications for quantitative genetic studies of natural populations as well as experimental design considerations. Additionally, studies that ignore IGEs may over- or underestimate quantitative genetic parameters, as well as the effect of and variance contributed by QTL.     

Influence of mom and dad: quantitative genetic models for maternal effects and genomic imprinting

The expression of an imprinted gene is dependent on the sex of the parent it was inherited from, and as a result reciprocal heterozygotes may display different phenotypes. In contrast, maternal genetic terms arise when the phenotype of an offspring is influenced by the phenotype of its mother beyond the direct inheritance of alleles. Both maternal effects and imprinting may contribute to resemblance between offspring of the same mother. We demonstrate that two standard quantitative genetic models for deriving breeding values, population variances and covariances between relatives, are not equivalent when maternal genetic effects and imprinting are acting. Maternal and imprinting effects introduce both sex-dependent and generation-dependent effects that result in differences in the way additive and dominance effects are defined for the two approaches. We use a simple example to demonstrate that both imprinting and maternal genetic effects add extra terms to covariances between relatives and that model misspecification may over- or underestimate true covariances or lead to extremely variable parameter estimation. Thus, an understanding of various forms of parental effects is essential in correctly estimating quantitative genetic variance components.     

BoLA class I allele diversity and polymorphism in a herd of cattle

Major histocompatibility complex class I genes are among the most polymorphic genes characterized. The high level of polymorphism is essential for generating host immune responses. In humans, three distinct genomic loci encode human leukocyte antigen (HLA) class I genes, allowing individuals to express up to six different HLA class I molecules. In cattle, the number of distinct genomic loci are currently at least six, and the number of different bovine leukocyte antigens (BoLA) class I molecules that are expressed in individual animals are variable. The extent of allele variation within the cattle population is unknown. In this study, the number and variety of BoLA class I sequences expressed by 36 individuals were determined from full-length BoLA class I cDNA clones. Twenty distinct BoLA class I alleles were identified, with only four being previously reported. The number of expressed BoLA class I alleles in individual animals ranged between one and four, with none of the animals having an identical complement of BoLA class I molecules. Variation existed in the number of BoLA class I alleles expressed as well as the composition of expressed alleles, however, several BoLA class I alleles were found in multiple individual animals. Polymorphic amino acid sites were analyzed for positive and negative selection using the ADAPTSITE program. In the antigen recognition sites (ARS), there were eight positions that were predicted to be under positive selection and three positions that were predicted to be under negative selection from 62 positions. In contrast, for non-antigen recognition sites (non-ARS), there were three positions that were predicted to be under positive selection and 20 that were predicted to be under negative selection from 278, indicating that positive selection of amino acids occurs at a greater frequency within the antigen recognition sites.     

动物的性选择

有性生殖为个体之间设置了一个冲突和竞争的环境,因为雌雄个体都希望最大限度地把自己的基因传递给后代。性选择保证了动物的繁殖成功。性选择可以分为性别内选择和性别间选择。性别内选择促使动物格斗器官或其他有利于在格斗中获胜的一些特征得到发展;性别间选择促使用来吸引异性的一些特征得到发展。雌性动物的配偶选择或与所选择的特征协同进化,或可以从选择中得到直接的利益。     

'Social heterosis' as a process that maintains genetic variation--a comment

In the 'mating pool' mode of reproduction, offspring genotypes at each generation are taken randomly from a common population and subdivided into groups where individuals representing a finite sample from the pooled distribution reproduce proportional to their fitness. Assuming that genetically diverse groups contribute more offspring, a recent article by Nonacs & Kapheim [J. Evol. Biol. 20 (2007) 2253] shows that allelic diversity can be easily maintained and proposes the process of 'social heterosis' as a potentially powerful mechanism that accounts for a significant amount of genetic variation. Contrary to their suggestions, I show here that there is a reduced efficiency of selection and an increased probability of fixation of segregating alleles when many loci are simultaneously undergoing social heterosis even if independence of action of the different loci and linkage equilibrium are assumed. The critical issue is that linkage disequilibria are generated by the sampling process of creating small groups and interfere with selection.     

Selection with Partial Selfing. I. Mass Selection

The expected responses to mass selection carried out before or after reproduction in a population whose members all have a fixed probability of self pollination (s) are formulated using covariances of relatives and their component quadratic functions for a model with arbitrary additive and dominance effects. The response measured in the first generation offspring after selection (immediate gain) can differ from that retained when the population has regained equilibrium (permanent gain). The population mean behaves in a predictable manner during the return to equilibrium, and its value at any time can be predicted from earlier generations. The permanent gain from selection after reproduction is always (1 + s)/2 times as large as that from selection before reproduction, but the relationship of the immediate gains depends on the genetic model assumed. Numerical analysis applied to a model with two alleles per locus and varying allele frequencies, dominance ratios and numbers of loci showed that the proportion of the immediate gain retained at equilibrium was reduced with the large inbreeding depression associated with increasing dominance levels and numbers of loci and was generally lower for selection after reproduction than before. In the absence of information as to the magnitude of genetic variances and inbreeding depression in species reproducing by partial selfing, the importance of this phenomenon is unknown.     

Natural selection on MHC IIβ in parapatric lake and stream stickleback: Balancing,divergent, both or neither?

Major histocompatibility complex (MHC) genes encode proteins that play a central role in vertebrates' adaptive immunity to parasites. MHC loci are among the most polymorphic in vertebrates' genomes, inspiring many studies to identify evolutionary processes driving MHC polymorphism within populations and divergence between populations. Leading hypotheses include balancing selection favouring rare alleles within populations, and spatially divergent selection. These hypotheses do not always produce diagnosably distinct predictions, causing many studies of MHC to yield inconsistent or ambiguous results. We suggest a novel strategy to distinguish balancing vs. divergent selection on MHC, taking advantage of natural admixture between parapatric populations. With divergent selection, individuals with immigrant alleles will be more infected and less fit because they are susceptible to novel parasites in their new habitat. With balancing selection, individuals with locally rare immigrant alleles will be more fit (less infected). We tested these contrasting predictions using three‐spine stickleback from three replicate pairs of parapatric lake and stream habitats. We found numerous positive and negative associations between particular MHC IIβ alleles and particular parasite taxa. A few allele–parasite comparisons supported balancing selection, and others supported divergent selection between habitats. But, there was no overall tendency for fish with immigrant MHC alleles to be more or less heavily infected. Instead, locally rare MHC alleles (not necessarily immigrants) were associated with heavier infections. Our results illustrate the complex relationship between MHC IIβ allelic variation and spatially varying multispecies parasite communities: different hypotheses may be concurrently true for different allele–parasite combinations.     

Field estimates of parentage reveal sexually antagonistic selection on body size in a population of Anolis lizards

Sexual dimorphism evolves when selection favors different phenotypic optima between the sexes. Such sexually antagonistic selection creates intralocus sexual conflict when traits are genetically correlated between the sexes and have sex‐specific optima. Brown anoles are highly sexually dimorphic: Males are on average 30% longer than females and 150% heavier in our study population. Viability selection on body size is known to be sexually antagonistic, and directional selection favors large male size whereas stabilizing selection constrains females to remain small. We build on previous studies of viability selection by measuring sexually antagonistic selection using reproductive components of fitness over three generations in a natural population of brown anoles. We estimated the number of offspring produced by an individual that survived to sexual maturity (termed RS^V), a measure of individual fitness that includes aspects of both individual reproductive success and offspring survival. We found directional selection on male body size, consistent with previous studies of viability selection. However, selection on female body size varied among years, and included periods of positive directional selection, quadratic stabilizing selection, and no selection. Selection acts differently in the sexes based on both survival and reproduction and sexual conflict appears to be a persistent force in this species.     

The interpretation of selection coefficients

Evolutionary biologists have an array of powerful theoretical techniques that can accurately predict changes in the genetic composition of populations. Changes in gene frequencies and genetic associations between loci can be tracked as they respond to a wide variety of evolutionary forces. However, it is often less clear how to decompose these various forces into components that accurately reflect the underlying biology. Here, we present several issues that arise in the definition and interpretation of selection and selection coefficients, focusing on insights gained through the examination of selection coefficients in multilocus notation. Using this notation, we discuss how its flexibility—which allows different biological units to be identified as targets of selection—is reflected in the interpretation of the coefficients that the notation generates. In many situations, it can be difficult to agree on whether loci can be considered to be under “direct” versus “indirect” selection, or to quantify this selection. We present arguments for what the terms direct and indirect selection might best encompass, considering a range of issues, from viability and sexual selection to kin selection. We show how multilocus notation can discriminate between direct and indirect selection, and describe when it can do so.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

A test for deviation from island-model population structure

The neutral island model forms the basis for several estimation models that relate patterns of genetic structure to microevolutionary processes. Estimates of gene flow are often based on this model and may be biased when the model's assumptions are violated. An appropriate test for violations is to compare FST scores for individual loci to a null distribution based on the average FST taken over multiple loci. A parametric bootstrap method is described here based on Wright's beta-distribution to generate null distributions of FST for each locus. These null distributions account for error introduced by sampling populations, individuals and loci, and also biological sources of error, including variable alleles/locus and inbreeding. Confidence limits can be obtained directly from these distributions. Significant deviations from the island model may be the result of selection, deviations from the island model's migration pattern, nonequilibrium conditions, or other deviations from island-model assumptions. Only strong biases are likely to be detected because of the inherently large sampling variation of FST. Nevertheless, a coefficient, Nb, describing bias in the spread of the beta-distribution in units comparable to the gene flow parameter, Nm, can be obtained for each locus. In samples from populations of the butterfly Coenonympha tullia, the loci Idh-1, Mdh-1, Pgi and Pgm showed significantly lower FST than expected.     

THE COADAPTATION OF PARENTAL AND OFFSPRING CHARACTERS

Parents often have important influences on their offspring's traits and/or fitness (i.e., maternal or paternal effects). When offspring fitness is determined by the joint influences of offspring and parental traits, selection may favor particular combinations that generate high offspring fitness. We show that this epistasis for fitness between the parental and offspring genotypes can result in the evolution of their joint distribution, generating genetic correlations between the parental and offspring characters. This phenomenon can be viewed as a coadaptive process in which offspring genotypes evolve to function with the parentally provided environment and, in turn, the genes for this environment become associated with specific offspring genes adapted to it. To illustrate this point, we present two scenarios in which selection on offspring alone alters the correlation between a maternal and an offspring character. We use a quantitative genetic maternal effect model combined with a simple quadratic model of fitness to examine changes in the linkage disequilibrium between the maternal and offspring genotypes. In the first scenario, stabilizing selection on a maternally affected offspring character results in a genetic correlation that is opposite in sign to the maternal effect. In the second scenario, directional selection on an offspring trait that shows a nonadditive maternal effect can result in selection for positive covariances between the traits. This form of selection also results in increased genetic variation in maternal and offspring characters, and may, in the extreme case, promote host-race formation or speciation. This model provides a possible evolutionary explanation for the ubiquity of large genetic correlations between maternal and offspring traits, and suggests that this pattern of coinheritance may reflect functional relationships between these characters (i.e., functional integration).     

ARE GREENBEARDS INTRAGENOMIC OUTLAWS?

Greenbeard genes identify copies of themselves in other individuals and cause their bearer to behave nepotistically toward those individuals. Hence, they can be favored by kin selection, irrespective of the degree of genealogical relationship between social partners. Although greenbeards were initially developed as a thought experiment, a number of recent discoveries of greenbeard alleles in real populations have led to a resurgence of interest in their evolutionary dynamics and consequences. One issue over which there has been disagreement is whether greenbeards lead to intragenomic conflict. Here, to clarify the "outlaw" status of greenbeards, we develop population genetic models that formally examine selection of greenbeard phenotypes under the control of different loci. We find that, in many cases, greenbeards are not outlaws because selection for or against the greenbeard phenotype is the same across all loci. In contrast, when social interactions are between genealogical kin, we find that greenbeards can be outlaws because different genes can be selected in different directions. Hence, the outlaw status of greenbeard genes crucially depends upon the particular biological details. We also clarify whether greenbeards are favored due to direct or indirect fitness effects and address the relationship of the greenbeard effect to sexual antagonism and reciprocity.     

Selection against accumulating mutations in niche-preference genes can drive speciation

Our current understanding of sympatric speciation is that it occurs primarily through disruptive selection on ecological genes driven by competition, followed by reproductive isolation through reinforcement-like selection against inferior intermediates/heterozygotes. Our evolutionary model of selection on resource recognition and preference traits suggests a new mechanism for sympatric speciation. We find speciation can occur in three phases. First a polymorphism of functionally different phenotypes is established through evolution of specialization. On the gene level, regulatory functions have evolved in which some alleles are conditionally switched off (i.e. are silent). These alleles accumulate harmful mutations that potentially may be expressed in offspring through recombination. Second mating associated with resource preference invades because harmful mutations in parents are not expressed in the offspring when mating assortatively, thereby dividing the population into two pre-zygotically isolated resource-specialist lineages. Third, silent alleles that evolved in phase one now accumulate deleterious mutations over the following generations in a Bateson-Dobzhansky-Muller fashion, establishing a post-zygotic barrier to hybridization.     

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.     

Genetic correlation and response to selection in simulated populations

Summary Effects of truncation selection of a primary trait upon genetic correlation with a secondary trait were examined over 30 generations in genetic populations simulated by computer. Populations were 24 males and 24 females mated randomly with replacement; number of offspring was determined by intensity of selection. Each trait was controlled by 48 loci segregating independently, effects were equal at every locus, and gene frequency was arbitrarily set at 0.5 at each locus in the initial generation. All combinations of three genetic correlations, three intensities of selection, and three environmental variances were simulated. Gene action was additive. Genetic correlation was set by number of loci which affected both traits and was measured each generation as the product-moment correlation of genotypic values and estimated by two methods of combining phenotypic covariances between parent and offspring.Genetic correlations in each offspring generation remained consistently near initial correlations for all environmental variances when fraction of offspring saved as parents was as large as one-half. When the fraction of offspring saved was as small as one-fifth, genetic correlations decreased but most rapidly with heritability high and after the 15th generation of selection. Truncation selection caused genetic correlation to decrease in those offspring selected to become parents of the next generation. Amount of reduction depended on heritability of the selected trait rather than on degree of truncation selection. Estimates of genetic correlation from phenotypic covariances between parent and offspring fluctuated markedly from real correlations in the small populations simulated.Michigan Agricultural Experiment Station Journal Article 4836. Part of North Central Regional Project NC-2.     

Opposites attract? Mate choice for parasite evasion and the evolutionary stability of sex

If sex is naturally selected as a way to combat parasites, then sexual selection for disease resistance might increase the overall strength of selection for outcrossing. In the present study, we compared how two forms of mate choice affect the evolutionary stability of outcrossing in simultaneous hermaphrodites. In the first form, individuals preferred to mate with uninfected individuals (condition-dependent choice). In the second form, individuals preferred to mate with individuals that shared the least number of alleles in common at disease-resistance loci. The comparisons were made using individual-based computer simulations in which we varied parasite virulence, parasite transmission rate, and the rate of deleterious mutation at 500 viability loci. We found that alleles controlling both forms of mate choice spread when rare, but their effects on the evolutionary stability of sex were markedly different. Surprisingly, condition-dependent choice for uninfected mates had little effect on the evolutionary stability of sexual reproduction. In contrast, active choice for mates having different alleles at disease-resistance loci had a pronounced positive effect, especially under low rates of deleterious mutation. Based on these results, we suggest that mate choice that increases the genetic diversity of offspring can spread when rare in a randomly mating population, and, as an indirect consequence, increase the range of conditions under which sexual reproduction is evolutionarily stable.