Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.     

Estimation of relatedness by DNA fingerprinting

The recent discovery of hypervariable VNTR (variable number of tandem repeat) loci has led to much excitement among population biologists regarding the feasibility of deriving individual estimates of relatedness in field populations by DNA fingerprinting. It is shown that unbiased estimates of relatedness cannot be obtained at the individual level without knowledge of the allelic distributions in both the individuals of interest and the base population unless the proportion of shared marker alleles between unrelated individuals is essentially zero. Since the latter is usually on the order of 0.1-0.5 and since there are enormous practical difficulties in obtaining the former, only an approximate estimator for the relatedness can be given. The bias of this estimator is individual specific and inversely related to the number of marker loci and frequencies of marker alleles. Substantial sampling variance in estimates of relatedness arises from variation in identity by descent within and between loci and, with finite numbers of alleles, from variation in identity in state between genes that are not identical by descent. In the extreme case of 25 assayed loci, each with an effectively infinite number of alleles, the standard error of a relatedness estimate is no less than 14%, 20%, 35%, and 53% of the expectation for full sibs and second-, third-, and fourth-order relationships, respectively. Attempts to ascertain relatedness by means of DNA fingerprinting should proceed with caution.      

Pedigree-Free Estimates of Heritability in the Wild: Promising Prospects for Selfing Populations

Estimating the genetic variance available for traits informs us about a population’s ability to evolve in response to novel selective challenges. In selfing species, theory predicts a loss of genetic diversity that could lead to an evolutionary dead-end, but empirical support remains scarce. Genetic variability in a trait is estimated by correlating the phenotypic resemblance with the proportion of the genome that two relatives share identical by descent (‘realized relatedness’). The latter is traditionally predicted from pedigrees (Φ_A: expected value) but can also be estimated using molecular markers (average number of alleles shared). Nevertheless, evolutionary biologists, unlike animal breeders, remain cautious about using marker-based relatedness coefficients to study complex phenotypic traits in populations. In this paper, we review published results comparing five different pedigree-free methods and use simulations to test individual-based models (hereafter called animal models) using marker-based relatedness coefficients, with a special focus on the influence of mating systems. Our literature review confirms that Ritland’s regression method is unreliable, but suggests that animal models with marker-based estimates of relatedness and genomic selection are promising and that more testing is required. Our simulations show that using molecular markers instead of pedigrees in animal models seriously worsens the estimation of heritability in outcrossing populations, unless a very large number of loci is available. In selfing populations the results are less biased. More generally, populations with high identity disequilibrium (consanguineous or bottlenecked populations) could be propitious for using marker-based animal models, but are also more likely to deviate from the standard assumptions of quantitative genetics models (non-additive variance).     

Frequency dependent selection: I. Rare male phenomenon in D. subobscura dependent on the proportion of Amy genotypes and substrate composition

Analysis of the rare male mating advantage in D. subobscura, as a type of frequency dependent selection on maltose and starch media, was done by applying different statistical approaches (χ², cross-product ratio, variance and regression analysis). They reveal that mating occurs at random when proportions of prospective mates are equal, and that mating success of the males homozygous for Amy-locus genotypes (S/S and F/F) depends on their proportion. Regression analysis showed that the F/F males are sexually more active (have higher vigour) than S/S males. Rare male effect is one-sided and appears in F/F males that partake in more heterogamic matings. Comparison of the number of observed and expected homo- and heterogamic matings shows that homogamic matings are more frequent. Multifactorial analysis of variance shows that the number of matings are different for nine pairs of lines and four possible mating types (S_fS_m, S_fF_m, F_fS_m, F_fF_m). The rare male phenomenon is not dependent on different food composition, but is associated with variations in individual genotypes.     

Using the Pareto principle in genome-wide breeding value estimation

Genome-wide breeding value (GWEBV) estimation methods can be classified based on the prior distribution assumptions of marker effects. Genome-wide BLUP methods assume a normal prior distribution for all markers with a constant variance, and are computationally fast. In Bayesian methods, more flexible prior distributions of SNP effects are applied that allow for very large SNP effects although most are small or even zero, but these prior distributions are often also computationally demanding as they rely on Monte Carlo Markov chain sampling. In this study, we adopted the Pareto principle to weight available marker loci, i.e., we consider that x% of the loci explain (100 - x)% of the total genetic variance. Assuming this principle, it is also possible to define the variances of the prior distribution of the ''big'' and ''small'' SNP. The relatively few large SNP explain a large proportion of the genetic variance and the majority of the SNP show small effects and explain a minor proportion of the genetic variance. We name this method MixP, where the prior distribution is a mixture of two normal distributions, i.e. one with a big variance and one with a small variance. Simulation results, using a real Norwegian Red cattle pedigree, show that MixP is at least as accurate as the other methods in all studied cases. This method also reduces the hyper-parameters of the prior distribution from 2 (proportion and variance of SNP with big effects) to 1 (proportion of SNP with big effects), assuming the overall genetic variance is known. The mixture of normal distribution prior made it possible to solve the equations iteratively, which greatly reduced computation loads by two orders of magnitude. In the era of marker density reaching million(s) and whole-genome sequence data, MixP provides a computationally feasible Bayesian method of analysis.     

Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.     

Preferential mating in symmetric multilocus systems: limits for multiallelism and for many Loci

Models in which general forms of preferential mating have been superimposed on the framework of the symmetric heterozygosity selection regime have been examined previously with respect to the existence and local stability of a central polymorphic equilibrium. The results are now extended to produce the limiting form of the stability conditions in two cases: First, where the number of alleles per locus is assumed to be very large; second, where the number of loci affecting the character is very large. It is argued that some type of frequency dependence in the mating pattern must be included, and a particular case is examined in detail. It is shown that multiallelism is ambiguous in its effect on stability, while an increasing number of loci, at least under zero linkage, leads to a simple stability condition which is analogous to the one-locus heterosis principle. Assortative mating appears to be more likely to produce a stable central polymorphism under high levels of allelism than is sexual selection, but is relatively very much weaker than sexual or viability selection if the number of loci involved is large.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Large-scale fungal strain sequencing unravels the molecular diversity in mating loci maintained by long-term balancing selection

Balancing selection, an evolutionary force that retains genetic diversity, has been detected in multiple genes and organisms, such as the sexual mating loci in fungi. However, to quantify the strength of balancing selection and define the mating-related genes require a large number of strains. In tetrapolar basidiomycete fungi, sexual type is determined by two unlinked loci, MATA and MATB. Genes in both loci define mating type identity, control successful mating and completion of the life cycle. These loci are usually highly diverse. Previous studies have speculated, based on culture crosses, that species of the non-model genus Trichaptum (Hymenochaetales, Basidiomycota) possess a tetrapolar mating system, with multiple alleles. Here, we sequenced a hundred and eighty strains of three Trichaptum species. We characterized the chromosomal location of MATA and MATB, the molecular structure of MAT regions and their allelic richness. The sequencing effort was sufficient to molecularly characterize multiple MAT alleles segregating before the speciation event of Trichaptum species. Analyses suggested that long-term balancing selection has generated trans-species polymorphisms. Mating sequences were classified in different allelic classes based on an amino acid identity (AAI) threshold supported by phylogenetics. 17,550 mating types were predicted based on the allelic classes. In vitro crosses allowed us to support the degree of allelic divergence needed for successful mating. Even with the high amount of divergence, key amino acids in functional domains are conserved. We conclude that the genetic diversity of mating loci in Trichaptum is due to long-term balancing selection, with limited recombination and duplication activity. The large number of sequenced strains highlighted the importance of sequencing multiple individuals from different species to detect the mating-related genes, the mechanisms generating diversity and the evolutionary forces maintaining them.     

Pedigree and marker information requirements to monitor genetic variability

There are several measures available to describe the genetic variability of populations. The average inbreeding coefficient of a population based on pedigree information is a frequently chosen option. Due to the developments in molecular genetics it is also possible to calculate inbreeding coefficients based on genetic marker information. A simulation study was carried out involving ten sires and 50 dams. The animals were mated over a period of 20 discrete generations. The population size was kept constant. Different situations with regard to the level of polymorphism and initial allele frequencies and mating scheme (random mating, avoidance of full sib mating, avoidance of full sib and half sib mating) were considered. Pedigree inbreeding coefficients of the last generation using full pedigree or 10, 5 and 2 generations of the pedigree were calculated. Marker inbreeding coefficients based on different sets of microsatellite loci were also investigated. Under random mating, pedigree-inbreeding coefficients are clearly more closely related to true autozygosity (i.e., the actual proportion of loci with alleles identical by descent) than marker-inbreeding coefficients. If mating is not random, the demands on the quality and quantity of pedigree records increase. Greater attention must be paid to the correct parentage of the animals.     

Multipoint analysis of human quantitative genetic variation.

A unique method of partitioning human quantitative genetic variation into effects due to specific chromosomal regions is presented. This method is based on estimating the proportion of genetic material, R, shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, on the basis of their marker genotypes at a set of marker loci spanning the region. The mean and variance of the distribution of R conditional on IBD status and recombination pattern between two marker loci are derived as a function of the distance between the two loci. The distribution of the estimates of R is exemplified using data on 22 loci on chromosome 7. A method of using the estimated R values and observed values of a quantitative trait in a set of sibships to estimate the proportion of total genetic variance explained by loci in the region of interest is presented. Monte Carlo simulation techniques are used to show that this method is more powerful than existing methods of quantitative linkage analysis based on sib pairs. It is also shown through simulation studies that the proposed method is sensitive to genetic variation arising from both a single locus of large effect as well as from several loosely linked loci of moderate phenotypic effect.     

Extent of height variability explained by known height-associated genetic variants in an isolated population of the Adriatic coast of Croatia

Background

Human height is a classical example of a polygenic quantitative trait. Recent large-scale genome-wide association studies (GWAS) have identified more than 200 height-associated loci, though these variants explain only 2∼10% of overall variability of normal height. The objective of this study was to investigate the variance explained by these loci in a relatively isolated population of European descent with limited admixture and homogeneous genetic background from the Adriatic coast of Croatia.

Methodology/Principal Findings

In a sample of 1304 individuals from the island population of Hvar, Croatia, we performed genome-wide SNP typing and assessed the variance explained by genetic scores constructed from different panels of height-associated SNPs extracted from five published studies. The combined information of the 180 SNPs reported by Lango Allen el al. explained 7.94% of phenotypic variation in our sample. Genetic scores based on 20∼50 SNPs reported by the remaining individual GWA studies explained 3∼5% of height variance. These percentages of variance explained were within ranges comparable to the original studies and heterogeneity tests did not detect significant differences in effect size estimates between our study and the original reports, if the estimates were obtained from populations of European descent.

Conclusions/Significance

We have evaluated the portability of height-associated loci and the overall fitting of estimated effect sizes reported in large cohorts to an isolated population. We found proportions of explained height variability were comparable to multiple reference GWAS in cohorts of European descent. These results indicate similar genetic architecture and comparable effect sizes of height loci among populations of European descent.     

Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

Insemination efficiency of two alternative male mating tactics in the guppy Poecilia reticulata

In this study we compared the insemination efficiency of two alternative mating tactics (courtship and sneak mating) in the guppy Poecilia reticulata by quantifying the number of sperm delivered during a copulation. During a single copulation, guppies delivered between zero and 92% of the sperm available, as determined by mechanically stripping the males'' sperm reserve at rest. The absolute number of sperm delivered after courtship was three times larger than that delivered through sneak mating; nonetheless, the variance was large with both tactics and the two distributions largely overlapped. The number of sperm available at rest increased with male size. With both tactics, the number of sperm delivered was positively correlated with the sperm available. Contrary to courtship copulations, in sneak copulations there was no correlation between the number of sperm delivered and male size. However, once the data were standardized for sperm reserve, small males delivered a larger proportion of their available sperm during sneak copulation. The rate of sexual acts (sigmoid and thrust rate) before copulation was not correlated with the number of sperm available. After the occurrence of a copulation in both the courtship and sneak copulation groups, the sexual activity of the male decreased in proportion to the amount of sperm he previously inseminated.     

Effect of linkage on the control of inbreeding in selection programmes

Selection and mating methods for controlling inbreeding in selection programmes are based on relationships obtained from pedigrees. The efficiency of these methods has always been tested by studies using genetic models of independent loci. However, under linkage the rate of inbreeding obtained from pedigrees can be different from the probability of identity by descent of genes. We simulated a quantitative trait under artificial selection controlled by a large number of genes spread on genome regions of different sizes. A method to control inbreeding based on minimising the average coancestry of selected individuals with a restriction in the loss of selection response, and a mating procedure to control inbreeding were applied. These methods, that use coancestry relationships, were not effective in controlling inbreeding when the genome sizes were smaller than five morgans or so. However, for larger genome sizes the methods were sufficiently efficient. For very tight linkage, methods that utilise molecular information from markers should be used. We finally discuss the effects of the selection of individual major genes on the neutral variability of adjacent genome regions.     

Descent measures for two loci with some applications

For any four genes, two at each of two loci, in a population, a 15 component descent measure has been introduced. These components are the probabilities of the 15 possible arrangements on a set of initial gametes of those genes of which the four of interest are copies. Since identity by descent of genes is equivalent to their being copies of a single gene on an initial gamete, descent measures have inbreeding coefficients as special cases. The individual descent measure, defined for four genes on two uniting gametes can be evaluated for any pedigree by means of an algorithm developed here. If initial gametic frequencies are specified, descent measures allow genotypic frequencies and disequilibria functions at one and two loci to be found. The procedures are illustrated for selfing and for sib mating. Several applications of the descent measures are discussed.     

Loss of genetic diversity in isolated populations of an alpine endemic Pilosella alpicola subsp. ullepitschii: effect of long-term vicariance or long-distance dispersal?

Pilosella alpicola subsp. ullepitschii (Asteraceae) is a strictly allogamous, diploid Carpathian endemic. Its distribution range comprises two areas separated by about 600 km. While in the Western Carpathians (Slovakia and Poland) the taxon occurs in numerous sites, only four localities of man-made origin are known from the Eastern and Southern Carpathians (Romania). We used allozyme markers to test two likely possible scenarios for the origin of this disjunction: long distance dispersal and vicariance. Our data indicate a significant loss of genetic diversity in the isolated Eastern and Southern Carpathian populations in following genetic parameters (averaged per region): percentage of polymorphic loci (38.9% found in the Eastern and Southern Carpathians versus 58.3% in the Western Carpathians), allelic richness (1.4 vs. 1.6), expected heterozygosity (0.134 vs. 0.235), mean number of distinguishable multilocus genotypes (4.3 vs. 10.6) and proportion of distinguishable multilocus genotypes (0.34 vs. 0.68). Higher proportion of homozygous loci found in the Eastern and Southern Carpathian populations might indicate a higher rate of inbreeding due to non-random mating. We assume that these genetically depauperate populations have experienced a very strong genetic bottleneck, probably due to a founder effect. Although our data suggest that the long-distance dispersal model is most likely, more discriminate genetic markers should be used to test this further.     

A method for estimating the effective number of loci affecting a quantitative character

A likelihood method is introduced that jointly estimates the number of loci and the additive effect of alleles that account for the genetic variance of a normally distributed quantitative character in a randomly mating population. The method assumes that measurements of the character are available from one or both parents and an arbitrary number of full siblings. The method uses the fact, first recognized by Karl Pearson in 1904, that the variance of a character among offspring depends on both the parental phenotypes and on the number of loci. Simulations show that the method performs well provided that data from a sufficient number of families (on the order of thousands) are available. This method assumes that the loci are in Hardy–Weinberg and linkage equilibrium but does not assume anything about the linkage relationships. It performs equally well if all loci are on the same non-recombining chromosome provided they are in linkage equilibrium. The method can be adapted to take account of loci already identified as being associated with the character of interest. In that case, the method estimates the number of loci not already known to affect the character. The method applied to measurements of crown–rump length in 281 family trios in a captive colony of African green monkeys (Chlorocebus aethiopus sabaeus) estimates the number of loci to be 112 and the additive effect to be 0.26 cm. A parametric bootstrap analysis shows that a rough confidence interval has a lower bound of 14 loci.     

The variance of sample heterozygosity

The variance of sample heterozygosity, averaged over several loci, is studied in a variety of situations. The variance depends on the sampling implicit in the mating system as well as on that explicit in the loci scored and individuals sampled. There are also effects of allelic distributions over loci and of linkage or linkage disequilibrium between pairs of loci. Results are obtained for populations in drift and mutation balance, for infinite populations undergoing mixed self and random mating, and for finite monoecious populations with or without selfing. For unlinked loci in drift/mutation balance, variances appear to be lessened more by increasing the number of loci scored than by increasing the number of individuals sampled. For infinite populations under the mixed self and random mating system, however, the reverse is true. Methods for estimating the variance of sample heterozygosity are discussed, with attention being paid to unbalanced data where not all loci are scored in all individuals.