Associative overdominance: Evaluating the effects of inbreeding and linkage disequilibrium

Expressions are obtained for the expected phenotypic values of homozygous and heterozygous genotypes for a neutral marker locus linked to a locus segregating for a recessive deleterious gene. The phenotypic values are functions of the allele frequencies at the marker locus, the inbreeding coefficient and the degree of association of the deleterious gene with the marker alleles. The analysis is extended to more than two alleles at the marker locus. Either linkage disequilibrium or inbreeding alone can produce an apparent superiority of heterozygotes for the marker locus (unless specified otherwise, the terms ‘homozygote’ and ‘heterozygote’ will refer to the marker locus). The effect of linkage disequilibrium on the difference between the heterozygote and homozygote values can be positive (associative overdominance) or negative (associative underdominance), depending on the frequencies of the marker alleles and the degree of their association with the deleterious gene. Inbreeding has always a positive effect. In general, the expected value of a homozygote is a positive function of its allele frequency. When the various homozygous genotypes are combined into one class and the various heterozygous genotypes into another, the phenotypic difference of the two classes is a function of the evenness of the allelic frequency distribution. Inbreeding is a more likely explanation of associative overdominance if the frequency of the deleterious gene is low, but its effect on the character high. Conversely, linkage disequilibrium is more likely if the frequency is high and the effect low. The degrees of association between marker alleles and the deleterious gene can, in principle, be estimated from the observed phenotypic scores and used to calculate expected multi-locus genotype scores. This could provide the basis for statistical tests of the associative overdominance hypothesis as an explanation of observed correlations between multi-locus heterozygosity and phenotypic traits.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

Genetic hitchhiking occurs when alleles at unselected loci are changed in frequency because of an association with alleles at a selected locus. This association may be mediated either by linkage or partial selfing (inbreeding) and can affect the gene frequency and gametic disequilibrium at the neutral loci. Hitchhiking from partial selfing (unlinked loci) occurs more quickly than linkage hitchhiking and generally has a greater effect. In addition, partial-selfing hitchhiking can cause increases or changes in sign in gametic disequilibrium between neutral loci. The effects of the two types of hitchhiking with different levels of dominance, zygotic frequencies and number of selected loci are also examined. The general conditions for linkage and partial-selfing hitchhiking are outlined and the implications of hitchhiking are discussed for marker or electrophoretic loci.     

Review and evaluation of methods correcting for population stratification with a focus on underlying statistical principles

When two or more populations have been separated by geographic or cultural boundaries for many generations, drift, spontaneous mutations, differential selection pressures and other factors may lead to allele frequency differences among populations. If these 'parental' populations subsequently come together and begin inter-mating, disequilibrium among linked markers may span a greater genetic distance than it typically does among populations under panmixia [see glossary]. This extended disequilibrium can make association studies highly effective and more economical than disequilibrium mapping in panmictic populations since less marker loci are needed to detect regions of the genome that harbor phenotype-influencing loci. However, under some circumstances, this process of intermating (as well as other processes) can produce disequilibrium between pairs of unlinked loci and thus create the possibility of confounding or spurious associations due to this population stratification. Accordingly, researchers are advised to employ valid statistical tests for linkage disequilibrium mapping allowing conduct of genetic association studies that control for such confounding. Many recent papers have addressed this need. We provide a comprehensive review of advances made in recent years in correcting for population stratification and then evaluate and synthesize these methods based on statistical principles such as (1) randomization, (2) conditioning on sufficient statistics, and (3) identifying whether the method is based on testing the genotype-phenotype covariance (conditional upon familial information) and/or testing departures of the marginal distribution from the expected genotypic frequencies.     

The effects of deleterious mutations on linked, neutral variation in small populations.

The effects of recessive, deleterious mutations on genetic variation at linked neutral loci can be heterozygosity-decreasing because of reduced effective population sizes or heterozygosity-increasing because of associative overdominance. Here we examine the balance between these effects by simulating individual diploid genotypes in small panmictic populations. The haploid genome consists of one linkage group with 1000 loci that can have deleterious mutations and a neutral marker. Combinations of the following parameters are studied: gametic mutation rate to harmful alleles (U), population size (N), recombination rate (r), selection coefficient (s), and dominance (h). Tight linkage (r 相似文献   

Hla-Sharing, Recurrent Spontaneous Abortion, and the Genetic Hypothesis

A number of studies indicates that there is a high sharing of HLA antigens in couples having recurrent spontaneous abortions. The genetic hypothesis to explain this phenomenon suggests that this fetal loss results from homozygosity of recessive lethal or deleterious alleles in gametic disequilibrium with HLA antigens. Theory predicting the lethality rate is derived when antigens are shared at one, two or three loci, given that the disequilibrium is absolute. In addition, the effects of partial disequilibrium, inbreeding, and segregation distortion on the lethal proportion are examined.     

Consanguinity and the sib-pair method: an approach using identity by descent between and within individuals.

To test for linkage between a trait and a marker, one can consider identical marker alleles in related individuals, for instance, sibs. For recessive diseases, it has been shown that some information may be gained from the identity by descent (IBD) of the two alleles of an affected inbred individual at the marker locus. The aim of this paper is to extend the sib-pair method of linkage analysis to the situation of sib pairs sampled from consanguineous populations. This extension takes maximum advantage of the information provided by both the IBD pattern between sibs and allelic identity within each sib of the pair. This is possible through the use of the condensed identity coefficients. Here, we propose a new test of linkage based on a chi2. We compare the performance of this test with that of the classical chi2 test based on the distribution of sib pairs sharing 0, 1, or 2 alleles IBD. For sib pairs from first-cousin matings, the proposed test can better detect the role of a disease-susceptibility (DS) locus. Its power is shown to be greater than that of the classical test, especially for models where the DS allele may be common and incompletely penetrant; that is to say for situations that may be encountered in multifactorial diseases. A study of the impact of inbreeding on the expected proportions of sib pairs sharing 0, 1, or 2 alleles IBD is also performed here. Ignoring inbreeding, when in fact inbreeding exists, increases the rate of type I errors in tests of linkage.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.     

Methods for high-density admixture mapping of disease genes

Admixture mapping (also known as "mapping by admixture linkage disequilibrium," or MALD) has been proposed as an efficient approach to localizing disease-causing variants that differ in frequency (because of either drift or selection) between two historically separated populations. Near a disease gene, patient populations descended from the recent mixing of two or more ethnic groups should have an increased probability of inheriting the alleles derived from the ethnic group that carries more disease-susceptibility alleles. The central attraction of admixture mapping is that, since gene flow has occurred recently in modern populations (e.g., in African and Hispanic Americans in the past 20 generations), it is expected that admixture-generated linkage disequilibrium should extend for many centimorgans. High-resolution marker sets are now becoming available to test this approach, but progress will require (a). computational methods to infer ancestral origin at each point in the genome and (b). empirical characterization of the general properties of linkage disequilibrium due to admixture. Here we describe statistical methods to estimate the ancestral origin of a locus on the basis of the composite genotypes of linked markers, and we show that this approach accurately estimates states of ancestral origin along the genome. We apply this approach to show that strong admixture linkage disequilibrium extends, on average, for 17 cM in African Americans. Finally, we present power calculations under varying models of disease risk, sample size, and proportions of ancestry. Studying approximately 2500 markers in approximately 2500 patients should provide power to detect many regions contributing to common disease. A particularly important result is that the power of an admixture mapping study to detect a locus will be nearly the same for a wide range of mixture scenarios: the mixture proportion should be 10%-90% from both ancestral populations.     

Sample sizes required to detect linkage disequilibrium between two or three loci.

Estimates of the degree of nonrandom association among genes (linkage disequilibrium) can provide evidence of the role of natural selection in maintaining allozyme polymorphisms in natural populations. This paper outlines the maximum likelihood procedures for such estimates based on gametic or zygotic frequencies at the level of two loci. The analysis is extended to estimating disequilibrium between three loci. In particular, the question of the sampling requirements to detect different intensities of disequilibrium is considered. It is found that relatively large samples are required to detect nonrandom association, unless gene frequencies are intermediate and disequilibrium is relatively intense. This might be one reason why cases of linkage disequilibrium have so far proved to be the exception, rather than the rule, in population studies.     

Experimental designs for reliable detection of linkage disequilibrium in unstructured random population association studies

A method is given for design of experiments to detect associations (linkage disequilibrium) in a random population between a marker and a quantitative trait locus (QTL), or gene, with a given strength of evidence, as defined by the Bayes factor. Using a version of the Bayes factor that can be linked to the value of an F-statistic with an existing deterministic power calculation makes it possible to rapidly evaluate a comprehensive range of scenarios, demonstrating the feasibility, or otherwise, of detecting genes of small effect. The Bayes factor is advocated for use in determining optimal strategies for selecting candidate genes for further testing or applications. The prospects for fine-scale mapping of QTL are reevaluated in this framework. We show that large sample sizes are needed to detect small-effect genes with a respectable-sized Bayes factor, and to have good power to detect a QTL allele at low frequency it is necessary to have a marker with similar allele frequency near the gene.     

Genetic microstructure in two Spanish cat populations. II: gametic disequilibrium and spatial autocorrelation

In a previous publication, we described some aspects of the microgenetic structure of two Spanish cat populations (in Barcelona and Alicante). In the present study, the possible existence ofgametic disequilibrium and spatial genetic structure for these populations, at the coat colour pattern and length genes O, A, T D, L, S and W, was analyzed. There was little gametic disequilibrium between pairs of these loci, despite certain pairs that showed significant systematic gametic disequilibrium (a-d and O-S), which appears to show the action of natural selection on domestic cat populations. Nevertheless, we believe that the major cause of the small amount of gametic disequilibrium found was probably a combination of gene drift and gene flow. The results obtained here were clearly in disagreement with those of Hedrick (1985), who concluded that epistatic selection was the cause of the gametic disequilibrium that he found in cat populations. We also found that although Hardy-Weinberg equilibrium could not be demonstrated, the gametic disequilibrium statistics were not affected by this fact, adding credence to the estimates obtained. We found no genetic spatial structure inside the city of Barcelona, as shown by analysis of the spatial autocorrelation of the individual loci, and analysis of the coordinates of the two first axes of a multidimensional scale. However, some gametic disequilibrium statistics showed certain spatial patterns, which leads us to consider the possibility of several evolutionary processes acting upon some of Barcelona's cat colonies.     

Genetic Diversity and Linkage Disequilibrium in Drosophila melanogaster with Different Rates of Development

We have examined eight enzyme polymorphisms in groups of Drosophila melanogaster flies with fast, intermediate and slow development. The allelic frequencies are similar in all three developmental classes, but the distribution of the genotypes among the classes is significantly heterogenous for the three loci on the second chromosome. When the total sample of 300 individuals is examined, significant gametic disequilibrium appears in 3 out of 13 pairs of genes located on the same chromosome and in 4 out of 15 pairs of genes located on different chromosomes. This 25% incidence of disequilibrium between pairs of genes is larger than previously observed in other natural populations (but similar to the incidence observed in laboratory populations). The greater frequency of significant gametic disequilibrium in our study is probably due to the larger number of genomes sampled.-Some models specifically predict that individuals with faster rates of development (i.e., greater fitness) should be more heterozygous (and exhibit more linkage disequilibrium) than individuals with slower development. This hypothesis is not supported by our results.     

Impact of non-ignorable missingness on genetic tests of linkage and/or association using case-parent trios

The transmission/disequilibrium test was introduced to test for linkage disequilibrium between a marker and a putative disease locus using case-parent trios. However, parental genotypes may be incomplete in such a study. When parental information is non-randomly missing, due, for example, to death from the disease under study, the impact on type I error and power under dominant and recessive disease models has been reported. In this paper, we examine non-ignorable missingness by assigning missing values to the genotypes of affected parents. We used unrelated case-parent trios in the Genetic Analysis Workshop 14 simulated data for the Danacaa population. Our computer simulations revealed that the type I error of these tests using incomplete trios was not inflated over the nominal level under either recessive or dominant disease models. However, the power of these tests appears to be inflated over the complete information case due to an excess of heterozygous parents in dyads.     

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.     

Individual Variation in Inbreeding Depression: The Roles of Inbreeding History and Mutation

We use mutation-selection recursion models to evaluate the relative contributions of mutation and inbreeding history to variation among individuals in inbreeding depression and the ability of experiments to detect associations between individual inbreeding depression and mating system genotypes within populations. Poisson mutation to deleterious additive or recessive alleles generally produces far more variation among individuals in inbreeding depression than variation in history of inbreeding, regardless of selfing rate. Moreover, variation in inbreeding depression can be higher in a completely outcrossing or selfing population than in a mixed-mating population. In an initially random mating population, the spread of a dominant selfing modifier with no pleiotropic effects on male outcross success causes a measurable increase in inbreeding depression variation if its selfing rate is large and inbreeding depression is caused by recessive lethals. This increase is observable during a short period as the modifier spreads rapidly to fixation. If the modifier alters selfing rate only slightly, it fails to spread or causes no measurable increase in inbreeding depression variance. These results suggest that genetic associations between mating loci and inbreeding depression loci could be difficult to demonstrate within populations and observable only transiently during rapid evolution to a substantially new selfing rate.     

Inbreeding depression in male gametic performance

One key objective in evolutionary ecology is to understand the magnitude of inbreeding depression expressed across sex‐specific components of fitness. One major component of male fitness is fertilization success, which depends on male gametic performance (sperm and pollen performance in animals and plants, respectively). Inbreeding depression in male gametic performance could create sex‐specific inbreeding depression in fitness, increase the benefit of inbreeding avoidance and reduce the efficacy of artificial insemination and pollination. However, there has been no assessment of the degree to which inbreeding generally depresses male gametic performance and hence post‐copulatory or post‐pollination fertilization success. Because inbreeding depression is understood to be a property of diploid entities, it is not clear what degree of inbreeding depression in haploid gametic performance should be expected. Here, we first summarize how inbreeding depression in male gametic performance could potentially arise through gene expression in associated diploid cells and/or reduced genetic diversity among haploid gametes. We then review published studies that estimate the magnitude of inbreeding depression in traits measuring components of sperm or pollen quantity, quality and competitiveness. Across 51 published studies covering 183 study traits, the grand mean inbreeding load was approximately one haploid lethal equivalent, suggesting that inbreeding depresses male gametic performance across diverse systems and traits. However, there was an almost complete lack of explicit estimates from wild populations. Future studies should quantify inbreeding depression in systematic sets of gametic traits under naturally competitive and noncompetitive conditions and quantify the degree to which gamete phenotypes and performance reflect haploid vs. diploid gene expression.     

A Systematic Approach to Mapping Recessive Disease Genes in Individuals from Outbred Populations

The identification of recessive disease-causing genes by homozygosity mapping is often restricted by lack of suitable consanguineous families. To overcome these limitations, we apply homozygosity mapping to single affected individuals from outbred populations. In 72 individuals of 54 kindred ascertained worldwide with known homozygous mutations in 13 different recessive disease genes, we performed total genome homozygosity mapping using 250,000 SNP arrays. Likelihood ratio Z-scores (ZLR) were plotted across the genome to detect ZLR peaks that reflect segments of homozygosity by descent, which may harbor the mutated gene. In 93% of cases, the causative gene was positioned within a consistent ZLR peak of homozygosity. The number of peaks reflected the degree of inbreeding. We demonstrate that disease-causing homozygous mutations can be detected in single cases from outbred populations within a single ZLR peak of homozygosity as short as 2 Mb, containing an average of only 16 candidate genes. As many specialty clinics have access to cohorts of individuals from outbred populations, and as our approach will result in smaller genetic candidate regions, the new strategy of homozygosity mapping in single outbred individuals will strongly accelerate the discovery of novel recessive disease genes.     

Theoretical value of estimates of general combining ability in the autotetraploid crop

Summary The means of half-sib progenies have been indicated as selection criteria for intra-population improvement while the average of the means of full-sib progenies in diallel analyses have been proposed as predictors, in part, of the means of untested synthetic varieties. When these measures based on progeny means are expressed as deviations from a defined greater population of crosses, they are often termed the general combining ability (GCA). In this study the GCA estimates or a facsimile were theoretically investigated for the one locus, digene, autotetraploid model to verify the genetic basis and its value for selection and prediction in the presence of a naturally occurring phenomena of autopolyploids called gametic disequilibrium with three types of non-additive inheritance. Two breeding objectives were envisioned, the selection of best parents with recurrent selection based on GCA in the continued development of elite populations and the prediction of advanced generation synthetic variety performance. The first generation means of progenies with a potential bias due to gametic disequilibrium were compared to GCA estimation of same progenies in the absence of gametic disequilibrium. The results indicated that testcrossing plants to a population without gametic disequilibrium could be used for selection of best parents. The gametic disequilibrium in the cross may increase or depress selection response dependent on the array of genotypes which happen to be evaluated, on the type of genic action at the locus, and on the frequency of the desirable allele in the testor population. The GCA estimates for prediction of synthetic performance were potentially biased by gametic disequilibrium. An assumption of pollination by the same array of gametes was made for all plants, but obviously was unrealistic for GCA estimation with partial diallels, or with no selfing, and in other situations. The GCA estimate was shown to be an unreliable predictor of synthetic variety performance. When it was assumed that different plants were pollinated by different arrays of gametes, a more realistic situation, no genetic interpretation of GCA values was possible even with purely additive gene action at the locus.Cooperative investigation of the Alfalfa Production Research Unit, United States Department of Agriculture, Agricultural Research Service, and the Nevada Agricultural Experiment Station, Reno, Nevada     

Dynamics of Correlated Genetic Systems. V. Rates of Decay of Linkage Disequilibria in Experimental Populations of DROSOPHILA MELANOGASTER

The dynamic behavior of four-locus gametic frequency distributions was studied in five replicate cage populations of Drosophila melanogaster for up to 50 generations. The joint frequency distributions were resolved into gene frequencies and various disequilibrium measures. In addition, F statistics for marginal single-locus genotypic frequency distributions were followed through time. The gene frequency, disequilibrium and F statistics were obtained for four chromosome 3 enzyme marker loci [isocitrate dehydrogenase (3–27.1), esterase-6 (3–36.8), phosphoglucomutase (3–43.4) and esterase-C (3–49.0)]. The initial structure of the experimental populations featured random mating proportions, and two complementary gametic types with respect to the marker loci, thus assuring complete pairwise linkage disequilibrium among the markers.——The experimental results indicate: (1) the between-replicate variance in gene frequency varied substantially among loci, with isocitrate dehydrogenase showing the greatest between-replicate variance, and esterase-C the least. (2) The F statistics initially were strongly negative but decayed to the neighborhood of zero for all marker loci except esterase-C. The rate at which the F statistics approached zero varied among the marker loci, indicating substantial differences in the distribution of selective effects along the chromosome. The centromeric region, marked by esterase-C, shows the strongest selective effects. (3) The rate of decay of linkage disequilibrium was much faster than expected for pairs of neutral loci, averaging 1.82 times the neutral rate over all replicates and pairs of loci. This acceleration, which was observed for all six pairwise combinations of loci, was interpreted as resulting from the interaction between selection and recombination. Our experimental results are consistent with many investigations of linkage disequilibrium in natural populations of Drosophila melanogaster that show little or no disequilibrium among enzyme loci. (4) A fortuitous contamination of two cages revealed an apparent regulatory interaction between the migrant and nonmigrant chromosomes at the esterase-C locus. The migrant chromosomes were very rapidly absorbed into the recipient populations, despite this interaction. This result suggests that the dynamics of migration in populations may be phenomenologically richer than anticipated by simple theory.     

THE DETECTION OF GAMETIC DISEQUILIBRIUM BETWEEN ALLOZYME LOCI IN NATURAL POPULATIONS OF DROSOPHILA

The capacity of the usual tests (chi-square and related tests) to detect gametic disequilibrium between allozyme loci in natural populations of Drosophila has been investigated. We analyzed a large collection of previously reported gametic samples from natural populations involving a variety of loosely linked allozyme loci located along the O chromosome of Drosophila subobscura and the second chromosome of D. melanogaster. It is found that the statistical power of the individual tests to detect the sample disequilibria between allozyme loci is remarkably low, being the average (over pairs of loci) of power estimates close to 0.20 in both species. Moreover, the average minimum disequilibrium (D‘_min) that would be required to reject (90% probability) the hypothesis of gametic equilibrium is higher than 0.50 given the observed degree of polymorphism and sample sizes used. This means that statistically significant associations between allozyme loci would rarely be detected by single-sample tests even when much disequilibrium is present in natural populations of Drosophila. However, an alternative approach based on the analysis of disquilibrium for large sets of gametic samples, combining probabilities from single independent tests and assessing significance by a bootstrap procedure, reveals that most of the locus pairs within segment I and II of the O chromosome of D. subobscura and left arm of the second chromosome of D. melanogaster present significant nonrandom associations. Within these chromosomal sections, the observed average absolute value of disquilibrium (D‘) between loci is around 0.25 (under the more conservative estimation). Also, a positive relationship between the magnitude of disequilibrium and linkage was detected. These findings suggest that weak or moderate values of disequilibrium between loosely linked allozyme loci are more frequent in natural populations of Drosophila than is currently believed.