Inter-locus interactions: A review of experimental evidence

In quantitative genetics, experiments designed to elucidate the nature of gene action and hence the importance of epistasis, have included analysis of genetic differences among individuals in random mating populations (partitioning of genetic variation, analysis of selection responses), of differences among inbred lines or selected populations (variance components in crosses among lines, chromosome analysis using genetic markers and crossover suppression), of the effects of inbreeding, and of population structure. Evidence in population genetic studies has come from studies of linkage disequilibrium and co-adaptation in natural populations, and of multilocus fitness estimation and linkage disequilibrium and associative overdominance in experimental populations. While it is clear that epistasis does contribute to the genetic variation in some quantitative characters, and in particular reproductive fitness, much of the evidence is equivocal and unsatisfying.     

EPISTASIS AND THE EVOLUTION OF ADDITIVE GENETIC VARIANCE IN POPULATIONS THAT PASS THROUGH A BOTTLENECK

Traditional models of genetic drift predict a linear decrease in additive genetic variance for populations passing through a bottleneck. This perceived lack of heritable variance limits the scope of founder-effect models of speciation. We produced 55 replicate bottleneck populations maintained at two male-female pairs through four generations of inbreeding (average F = 0.39). These populations were formed from an F₂ intercross of the LG/J and SM/J inbred mouse strains. Two contemporaneous control strains maintained with more than 60 mating pairs per generation were formed from this same source population. The average level of within-strain additive genetic variance for adult body weight was compared between the control and experimental lines. Additive genetic variance for adult body weight within experimental bottleneck strains was significantly higher than expected under an additive genetic model This enhancement of additive genetic variance under inbreeding is likely to be due to epistasis, which retards or reverses the loss of additive genetic variance under inbreeding for adult body weight in this population. Therefore, founder-effect speciation processes may not be constrained by a loss of heritable variance due to population bottlenecks.     

An inbreeding model of associative overdominance during a population bottleneck

Associative overdominance, the fitness difference between heterozygotes and homozygotes at a neutral locus, is classically described using two categories of models: linkage disequilibrium in small populations or identity disequilibrium in infinite, partially selfing populations. In both cases, only equilibrium situations have been considered. In the present study, associative overdominance is related to the distribution of individual inbreeding levels (i.e., genomic autozygosity). Our model integrates the effects of physical linkage and variation in inbreeding history among individual pedigrees. Hence, linkage and identity disequilibrium, traditionally presented as alternatives, are summarized within a single framework. This allows studying nonequilibrium situations in which both occur simultaneously. The model is applied to the case of an infinite population undergoing a sustained population bottleneck. The effects of bottleneck size, mating system, marker gene diversity, deleterious genomic mutation parameters, and physical linkage are evaluated. Bottlenecks transiently generate much larger associative overdominance than observed in equilibrium finite populations and represent a plausible explanation of empirical results obtained, for instance, in marine species. Moreover, the main origin of associative overdominance is random variation in individual inbreeding whereas physical linkage has little effect.     

Linkage disequilibrium in the North American Holstein population

Linkage disequilibrium was estimated using 7119 single nucleotide polymorphism markers across the genome and 200 animals from the North American Holstein cattle population. The analysis of maternally inherited haplotypes revealed strong linkage disequilibrium ( r ²   >   0.8) in genomic regions of ∼50 kb or less. While linkage disequilibrium decays as a function of genomic distance, genomic regions within genes showed greater linkage disequilibrium and greater variation in linkage disequilibrium compared with intergenic regions. Identification of haplotype blocks could characterize the most common haplotypes. Although maximum haplotype block size was over 1 Mb, mean block size was 26–113 kb by various definitions, which was larger than that observed in humans (∼10 kb). Effective population size of the dairy cattle population was estimated from linkage disequilibrium between single nucleotide polymorphism marker pairs in various haplotype ranges. Rapid reduction of effective population size of dairy cattle was inferred from linkage disequilibrium in recent generations. This result implies a loss of genetic diversity because of the high rate of inbreeding and high selection intensity in dairy cattle. The pattern observed in this study indicated linkage disequilibrium in the current dairy cattle population could be exploited to refine mapping resolution. Changes in effective population size during past generations imply a necessity of plans to maintain polymorphism in the Holstein population.     

Tests for a Disease-susceptibility Locus allowing for an Inbreeding Coefficient (F)

We begin by discussing the false positive test results that arise because of cryptic relatedness and population substructure when testing a disease susceptibility locus. We extend and evaluate the Hardy-Weinberg disequilibrium (HWD) method, allowing for an inbreeding coefficient (F) in a similar way that Devlin and Roeder (1999) allowed for inbreeding in a case-control study. Then we compare the HWD measure and the common direct measure of linkage disequilibrium, both when there is no population substructure (F = 0) and when there is population substructure (F not = 0), for a single marker. The HWD test statistic gives rise to false positives caused by population stratification. These false positives can be controlled by adjusting the test statistic for the amount of variance inflation caused by the inbreeding coefficient (F). The power loss for the HWD test that arises when controlling for population structure is much less than that which arises for the common direct measure of linkage disequilibrium. However, in the multiplicative model, the HWD test has virtually no power even when allowing for non-zero F.     

The variance in inbreeding depression and the recovery of fitness in bottlenecked populations

Theoretical analyses of inbreeding suggest that following an increased degree of inbreeding there may be a temporary recovery of fitness, because of selection either within or among inbred lineages. This is possible because selection can act more efficiently to remove deleterious alleles given the greater homozygosity of such populations. If common, recovery of fitness following inbreeding may be important for understanding some evolutionary processes and for management strategies of remnant populations, yet empirical evidence for such recovery in animals is scant. Here we describe the effects of single-pair population bottlenecks on a measure of fitness in Drosophila melanogaster. We compared a large number of families from each of 52 inbred lines with many families from the outbred population from which the inbred lineages were derived. Measures were made at the third and the 20th generations after the bottleneck. In both generations there was, on average, substantial inbreeding depression together with a highly significant variance among the inbred lines in the amount of fitness reduction. The average fitness of inbred lines was correlated across generations. Our data provide evidence for the possibility of recovery of fitness at two levels, because (i) the average fitness reduction in the F20 generation was significantly less than in the F3 generation, which implies that selection within lines has occurred, and (ii) the large variance in inbreeding depression among inbred lines implies that selection among them is possible. The high variance in inbreeding depression among replicate lines implies that modes of evolution which require a low level of inbreeding depression can function at least in a fraction of inbred populations within a species and that results from studies with low levels of replication should be treated with caution.     

Variance of Neutral Genetic Variances within and between Populations for a Quantitative Character

The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.     

THE DISTRIBUTION AMONG POPULATIONS IN PHENOTYPIC VARIANCE WITH INBREEDING

The effects of inbreeding on the phenotypic variance within populations were measured in a set of 30 bottlenecked lines derived from a single source population of Drosophila melanogaster. Inbred lines had significant variance among lines in the amount of phenotypic variance within lines, for thorax length, and sternopleural bristle scores. When significance levels were corrected on an experimentwide basis, no line had significant increases in phenotypic variance for sternopleural bristle counts, although two lines had significant increases in thorax length variance. These results demonstrate that inbred lines cannot be treated as necessarily more uniform than outbred lines and that results on changes in variance due to inbreeding should be treated with caution unless there has been sufficient replication. These results also demonstrate the validity of an important assumption of models of evolution by variance-mediated mechanisms, such as the variance-induced peak-shift model.     

Efficiency of selection, as measured by single nucleotide polymorphism variation, is dependent on inbreeding rate in Drosophila melanogaster

It is often hypothesized that slow inbreeding causes less inbreeding depression than fast inbreeding at the same absolute level of inbreeding. Possible explanations for this phenomenon include the more efficient purging of deleterious alleles and more efficient selection for heterozygote individuals during slow, when compared with fast, inbreeding. We studied the impact of inbreeding rate on the loss of heterozygosity and on morphological traits in Drosophila melanogaster. We analysed five noninbred control lines, 10 fast inbred lines and 10 slow inbred lines; the inbred lines all had an expected inbreeding coefficient of approximately 0.25. Forty single nucleotide polymorphisms in DNA coding regions were genotyped, and we measured the size and shape of wings and counted the number of sternopleural bristles on the genotyped individuals. We found a significantly higher level of genetic variation in the slow inbred lines than in the fast inbred lines. This higher genetic variation was resulting from a large contribution from a few loci and a smaller effect from several loci. We attributed the increased heterozygosity in the slow inbred lines to the favouring of heterozygous individuals over homozygous individuals by natural selection, either by associative over‐dominance or balancing selection, or a combination of both. Furthermore, we found a significant polynomial correlation between genetic variance and wing size and shape in the fast inbred lines. This was caused by a greater number of homozygous individuals among the fast inbred lines with small, narrow wings, which indicated inbreeding depression. Our results demonstrated that the same amount of inbreeding can have different effects on genetic variance depending on the inbreeding rate, with slow inbreeding leading to higher genetic variance than fast inbreeding. These results increase our understanding of the genetic basis of the common observation that slow inbred lines express less inbreeding depression than fast inbred lines. In addition, this has more general implications for the importance of selection in maintaining genetic variation.     

Heterozygosity–fitness correlations and their relevance to studies on inbreeding depression in threatened species

The majority of reported multilocus heterozygosity–fitness correlations (HFCs) are from large, outbred populations, and their relevance to studies on inbreeding depression in threatened populations is often stressed. The results of such HFC studies conducted on outbred populations may be of limited application to threatened population management, however, as bottlenecked populations exhibit increased incidence of inbreeding, increased linkage disequilibrium, reduced genetic diversity and possible effects of historical inbreeding such as purging. These differences may affect both our ability to detect inbreeding depression in threatened species, and our interpretation of the underlying mechanisms for observed heterozygosity–fitness relationships. The study of HFCs in outbred populations is of interest in itself, but the results may not translate directly to threatened populations that have undergone severe bottlenecks.     

Glossina swynnertoni (Diptera: Glossinidae): effective population size and breeding structure estimated by mitochondrial diversity

Nucleotide diversity was examined at mitochondrial COI and r16S2 loci in eight Glossina swynnertoni Austen collections from northern Tanzania and from a culture maintained by the International Atomic Energy Agency. Eighteen composite haplotypes were observed among 149 flies, two of which were common to all samples and 10 were private. Mean haplotype diversity was 0.59 and nucleotide diversity was 0.0013. There were excess singular haplotypes and mutation-drift disequilibrium suggesting that populations had experienced an earlier bottleneck and subsequent expansion. Factorial correspondence analysis showed that haplotype frequencies varied much more temporally (G ST=0.18) than spatially (G ST=0.04). The estimate of effective population size N e in Tarangire was a harmonic mean approximately 50 reproductive flies averaged over approximately 47 generations. The mean rate of gene flow was estimated to be approximately 5+/-1 reproducing females per generation but inflated because of mutation-drift disequilibrium arising from likely earlier bottlenecks.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

The imprecision of heterozygosity-fitness correlations hinders the detection of inbreeding and inbreeding depression in a threatened species

In nonpedigreed wild populations, inbreeding depression is often quantified through the use of heterozygosity-fitness correlations (HFCs), based on molecular estimates of relatedness. Although such correlations are typically interpreted as evidence of inbreeding depression, by assuming that the marker heterozygosity is a proxy for genome-wide heterozygosity, theory predicts that these relationships should be difficult to detect. Until now, the vast majority of empirical research in this area has been performed on generally outbred, nonbottlenecked populations, but differences in population genetic processes may limit extrapolation of results to threatened populations. Here, we present an analysis of HFCs, and their implications for the interpretation of inbreeding, in a free-ranging pedigreed population of a bottlenecked species: the endangered takahe (Porphyrio hochstetteri). Pedigree-based inbreeding depression has already been detected in this species. Using 23 microsatellite loci, we observed only weak evidence of the expected relationship between multilocus heterozygosity and fitness at individual life-history stages (such as survival to hatching and fledging), and parameter estimates were imprecise (had high error). Furthermore, our molecular data set could not accurately predict the inbreeding status of individuals (as 'inbred' or 'outbred', determined from pedigrees), nor could we show that the observed HFCs were the result of genome-wide identity disequilibrium. These results may be attributed to high variance in heterozygosity within inbreeding classes. This study is an empirical example from a free-ranging endangered species, suggesting that even relatively large numbers (>20) of microsatellites may give poor precision for estimating individual genome-wide heterozygosity. We argue that pedigree methods remain the most effective method of quantifying inbreeding in wild populations, particularly those that have gone through severe bottlenecks.     

Effects of genetic drift on variance components under a general model of epistasis

We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.     

A Building Block Model for Quantitative Genetics

We introduce a quantitative genetic model for multiple alleles which permits the parameterization of the degree, D, of dominance of favorable or unfavorable alleles. We assume gene effects to be random from some distribution and independent of the D's. We then fit the usual least-squares population genetic model of additive and dominance effects in an infinite equilibrium population to determine the five genetic components--additive variance sigma 2 a, dominance variance sigma 2 d, variance of homozygous dominance effects d2, covariance of additive and homozygous dominance effects d1, and the square of the inbreeding depression h--required to treat finite populations and large populations that have been through a bottleneck or in which there is inbreeding. The effects of dominance can be summarized as functions of the average, D, and the variance, sigma 2 D. An important distinction arises between symmetrical and nonsymmetrical distributions of gene effects. With symmetrical distributions d1 = -d2/2 which is always negative, and the contribution of dominance to sigma 2 a is equal to d2/2. With nonsymmetrical distributions there is an additional contribution H to sigma 2 a and -H/2 to d1, the sign of H being determined by D and the skew of the distribution. Some numerical evaluations are presented for the normal and exponential distributions of gene effects, illustrating the effects of the number of alleles and of the variation in allelic frequencies. Random additive by additive (a*a) epistatic effects contribute to sigma 2 a and to the a*a variance, sigma 2/aa, the relative contributions depending on the number of alleles and the variation in allelic frequencies.(ABSTRACT TRUNCATED AT 250 WORDS)     

中国美利奴羊MHC-DRB1 exon2单倍型构建及与布鲁氏菌病易感性关联分析

为研究中国美利奴羊MHC-DRB1基因exon2单倍型与布鲁氏菌易感性的关联性,本实验采用PCR直接测序法对40例布鲁氏菌血清检测阳性和阴性个体MHC-DRB1 exon2的单核苷酸多态性(SNPs)进行检测,而后运用SHEsis在线软件对筛选的SNPs构建单倍型并进行单倍型关联分析.结果显示,在270 bp的序列内共检测到41个SNPs,经Hardy-Weinberg平衡检测筛选出符合条件的SNPs有29个,连锁不平衡发现9个连锁不平衡域,而且每个block中的SNPs两两之间存在强连锁不平衡.单倍型分析显示,由于连锁不平衡存在,仅构建9种单倍型,其中只有Hap8和Hap9两种单倍型在病例-对照组中比较差异有统计学意义(P0.05).     

Protein variation in Adh and Adh-related in Drosophila pseudoobscura. Linkage disequilibrium between single nucleotide polymorphisms and protein alleles

A 3.5-kb segment of the alcohol dehydrogenase (Adh) region that includes the Adh and Adh-related genes was sequenced in 139 Drosophila pseudoobscura strains collected from 13 populations. The Adh gene encodes four protein alleles and rejects a neutral model of protein evolution with the McDonald-Kreitman test, although the number of segregating synonymous sites is too high to conclude that adaptive selection has operated. The Adh-related gene encodes 18 protein haplotypes and fails to reject an equilibrium neutral model. The populations fail to show significant geographic differentiation of the Adh-related haplotypes. Eight of 404 single nucleotide polymorphisms (SNPs) in the Adh region were in significant linkage disequilibrium with three ADHR protein alleles. Coalescent simulations with and without recombination were used to derive the expected levels of significant linkage disequilibrium between SNPs and 18 protein haplotypes. Maximum levels of linkage disequilibrium are expected for protein alleles at moderate frequencies. In coalescent models without recombination, linkage disequilibrium decays between SNPs and high frequency haplotypes because common alleles mutate to haplotypes that are rare or that reach moderate frequency. The implication of this study is that linkage disequilibrium mapping has the highest probability of success with disease-causing alleles at frequencies of 10%.     

Bottleneck Effects on Genetic Variance for Courtship Repertoire

Bottleneck effects on evolutionary potential in mating behavior were addressed through assays of additive genetic variances and resulting phenotypic responses to drift in the courtship repertoires of six two-pair founder-flush lines and two control populations of the housefly. A simulation addressed the complication that an estimate of the genetic variance for a courtship trait (e.g., male performance vigor or the female requirement for copulation) must involve assays against the background behavior of the mating partners. The additive ``environmental' effect of the mating partner's phenotype simply dilutes the net parent-offspring covariance for a trait. However, if there is an interaction with this ``environmental' component, negative parent-offspring covariances can result under conditions of high incompatibility between the population's distributions for male performance and female choice requirements, despite high levels of genetic variance. All six bottlenecked lines exhibited significant differentiation from the controls in at least one measure of the parent-offspring covariance for male performance or female choice (estimated by 50 parent-son and 50 parent-daughter covariances for 10 courtship traits per line) which translated to significant phenotypic drift. However, the average effect across traits or across lines did not yield a significant net increase in genetic variance due to bottlenecks. Concerted phenotypic differentiation due to the founder-flush event provided indirect evidence of directional dominance in a subset of traits. Furthermore, indirect evidence of genotype-environment interactions (potentially producing genotype-genotype effects) was found in the negative parent-offspring covariances predicted by the male-female interaction simulation and by the association of the magnitude of phenotypic drift with the absolute value of the parent-offspring covariance. Hence, nonadditive genetic effects on mating behavior may be important in structuring genetic variance for courtship, although most of the increases in genetic variance would be expected to reflect inbreeding depression with relatively rare situations representing the facilitation of speciation by bottlenecks.     

A test of quantitative genetic theory using Drosophila- effects of inbreeding and rate of inbreeding on heritabilities and variance components

Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding - inbred to the same absolute level - and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.