Modeling linkage disequilibrium in natural populations: the example of the Soay sheep population of St. Kilda, Scotland

The use of linkage disequilibrium to localize the genes underlying quantitative traits has received considerable attention in the livestock genetics community over the past few years. This has resulted in the investigation of linkage disequilibrium structures of several domestic livestock populations to assess their potential use in fine-mapping efforts. However, the linkage disequilibrium structure of free-living populations has been less well investigated. As the direct evaluation of linkage disequilibrium can be both time consuming and expensive the use of simulations that include as many aspects of population history as possible is advocated as an alternative. A simulation of the linkage disequilibrium structure of the Soay sheep population of St. Kilda, Scotland, is provided as an example. The simulated population showed significant decline of linkage disequilibrium with genetic distance and low levels of background linkage disequilibrium, indicating that the Soay sheep population is a viable resource for linkage disequilibrium fine mapping of quantitative trait loci.     

Disequilibrium Pattern Analysis. I. Theory

We have developed a method, disequilibrium pattern analysis, for examining the disequilibrium distribution of the entire array of two locus multiallelic haplotypes in a population. It is shown that a selected haplotype will produce a distinct pattern of linkage disequilibrium values for all generations while the selection is acting. This pattern will also presumably be maintained for many generations after the selection event, until the disequilibrium pattern is eventually broken down by genetic drift and recombination. Related haplotypes, sharing an allele with a selected haplotype, assume a value of linkage disequilibrium proportional to the frequency of the unshared allele and have a single negative value of the normalized linkage disequilibrium. The analysis assumes zero linkage disequilibrium for all allelic combinations initially. The same basic results continue to apply if the selection involves a new mutant, the occurrence of which creates linkage disequilibrium for some haplotypes. The disequilibrium pattern predicted under selection is robust with respect to the influence of migration and random genetic drift. This method is applicable to population data having linked polymorphic loci including that determined from protein or DNA sequencing.     

Simultaneous detection of linkage disequilibrium and genetic differentiation of subdivided populations

We propose a new method for simultaneously detecting linkage disequilibrium and genetic structure in subdivided populations. Taking subpopulation structure into account with a hierarchical model, we estimate the magnitude of genetic differentiation and linkage disequilibrium in a metapopulation on the basis of geographical samples, rather than decompose a population into a finite number of random-mating subpopulations. We assume that Hardy-Weinberg equilibrium is satisfied in each locality, but do not assume independence between marker loci. Linkage states remain unknown. Genetic differentiation and linkage disequilibrium are expressed as hyperparameters describing the prior distribution of genotypes or haplotypes. We estimate related parameters by maximizing marginal-likelihood functions and detect linkage equilibrium or disequilibrium by the Akaike information criterion. Our empirical Bayesian model analyzes genotype and haplotype frequencies regardless of haploid or diploid data, so it can be applied to most commonly used genetic markers. The performance of our procedure is examined via numerical simulations in comparison with classical procedures. Finally, we analyze isozyme data of ayu, a severely exploited fish species, and single-nucleotide polymorphisms in human ALDH2.     

Analysis of genetic structure in soil populations of Rhizobium leguminosarum recovered from the USA and the UK

Although many studies have shown that animal-associated bacterial species exhibit linkage disequilibrium at chromosomal loci, recent studies indicate that both animal-associated and soil-borne bacterial species can display a nonclonal genetic structure in which alleles at chromosomal loci are in linkage equilibrium. To examine the situation in soil-borne species further, we compared genetic structure in two soil populations of Rhizobium leguminosarum bv. trifolii and two populations of R. leguminosarum bv. viciae from two sites in Oregon, with genetic structure in R. leguminosarum bv. viciae populations recovered from peas grown at a site in Washington, USA, and at a site in Norfolk, UK. A total of 234 chromosomal types (ET) were identified among 682 strains analysed for allelic variation at 13 enzyme-encoding chromosomal loci by multilocus enzyme electrophoresis (MLEE). Chi-square tests for heterogeneity of allele frequencies showed that the populations were not genetically uniform. A comparison of the genetic diversity within combined and individual populations confirmed that the Washington population was the primary cause of genetic differentiation between the populations. Each individual population exhibited linkage disequilibrium, with the magnitude of the disequilibrium being greatest in the Washington population and least in the UK population of R. leguminosarum bv. viciae. Linkage disequilibrium in the UK population was created between two clusters of 9 and 23 ETs, which, individually, were in linkage equilibrium. Strong linkage disequilibrium between the two major clusters of 8 and 12 ETs in the Washington population was caused by the low genetic diversity of the ETs within each cluster relative to the inter-cluster genetic distance. Because neither the magnitude of genetic diversity nor of linkage disequilibrium increased as hierarchical combinations of the six local populations were analysed, we conclude that the populations have not been isolated from each other for sufficient time, nor have they been exposed to enough selective pressure to develop unique multilocus genetic structure.     

Linkage disequilibrium--understanding the evolutionary past and mapping the medical future

Linkage disequilibrium--the nonrandom association of alleles at different loci--is a sensitive indicator of the population genetic forces that structure a genome. Because of the explosive growth of methods for assessing genetic variation at a fine scale, evolutionary biologists and human geneticists are increasingly exploiting linkage disequilibrium in order to understand past evolutionary and demographic events, to map genes that are associated with quantitative characters and inherited diseases, and to understand the joint evolution of linked sets of genes. This article introduces linkage disequilibrium, reviews the population genetic processes that affect it and describes some of its uses. At present, linkage disequilibrium is used much more extensively in the study of humans than in non-humans, but that is changing as technological advances make extensive genomic studies feasible in other species.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

Assignment of the locus for a new lethal neonatal metabolic syndrome to 2q33-37.

A new neonatal syndrome characterized by intrauterine growth retardation, lactic acidosis, aminoaciduria, liver hemosiderosis, and early death was recently described. The pathogenesis of this disease is unknown. The mode of inheritance is autosomal recessive, and so far only 17 cases have been reported in 12 Finnish families. Here we report the assignment of the locus for this new disease to a restricted region on chromosome 2q33-37. We mapped the disease locus in a family material insufficient for traditional linkage analysis by using linkage disequilibrium, a possibility available in genetic isolates such as Finland. The primary screening of the genome was performed with samples from nine affected individuals in five families. In the next step, conventional linkage analysis was performed in eight families, with a total of 12 affected infants, and finally the locus assignment was proved by demonstrating linkage disequilibrium to the regional markers in 20 disease chromosomes. Linkage analysis restricted the disease locus to a 3-cM region between markers D2S164 and D2S2359, and linkage disequilibrium with the ancestral haplotype restricted the disease locus further to the immediate vicinity of marker D2S2250.     

Development and characterisation of microsatellite markers for the medicinal plant Scutellaria baicalensis (Lamiaceae)

Scutellaria baicalensis is a popular medicinal plant that is on the verge of extinction due to uncontrolled harvesting, habitat destruction and deterioration of its ecosystem. We isolated and characterised 21 microsatellite loci in this species. Ninety-four individuals from six populations were used to test the polymorphism of the microsatellite loci. The number of alleles per locus ranged from 1 to 13, with a mean of 7.2. Observed and expected heterozygosities varied from 0.000 to 1.000 and 0.000 to 0.938, respectively. Among these new microsatellite markers, only two loci showed significant deviation from Hardy–Weinberg equilibrium. No locus pairs showed significant linkage disequilibrium. The 21 primer pairs were tested in other Scutellaria species. Most of these primer pairs worked successfully, except for Scut18. These new microsatellite markers could be applied to investigate the genetic diversity and population genetic structure of S. baicalensis and its closely related species.     

Modeling haplotype block variation using Markov chains

Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity.     

Linkage disequilibrium in natural populations of Trypanosoma cruzi (flagellate), the agent of Chagas' disease

We have studied linkage disequilibrium in natural populations of Trypanosoma cruzi, the agent of Chagas' disease, by analyzing (i) a set of 524 stocks from the whole geographical range of the parasite, characterized at four gene loci coding for enzymes; (ii) a subsample of 121 stocks characterized at 12 enzyme loci; and (iii) a subset of 386 stocks from six locations in Bolivia, characterized by four enzyme loci. Our results show that the linkage disequilibrium reaches the maximum possible value, given the observed allelic frequencies, for almost all the locus pairs. This result is most consistent with the hypothesis that genetic recombination is absent or very rare in T. cruzi natural populations. Partition of the linkage disequilibrium variance for the six Bolivian populations shows that both inter- and intrapopulation components are substantial and that the relationships among the components are D2IS less than D2ST, and D'2IS less than D'2ST. These inequalities are interpreted as the result of an interplay between genetic drift, rare or absent mating, and clonal selection in generating linkage disequilibrium in T. cruzi populations.     

Normative genetic profiles of RAAS pathway gene polymorphisms in North Indian and South Indian populations

Population-based genetic association studies, popularly known as case-control studies, have continued to be the most preferred method for deciphering the genetic basis of various complex diseases, even in the post-human genome sequencing era. However, interpopulation differences in allele, genotype, and haplotype frequencies and linkage disequilibrium patterns lead to inconsistent results in candidate gene association studies. Therefore, for any meaningful disease association study, knowledge of the normative genetic background of the baseline population is a prerequisite. In addition, such genetic variation data also provide a ready-made menu of allele frequencies and linkage disequilibrium patterns of various polymorphisms in specific candidate genes in a particular population, which is a useful reference for further genetic association studies. Such genetic variation data are lacking for the Indian population, which represents about one-sixth of the world's population. In the present study we have reported the allele, genotype, and haplotype frequencies, Hardy-Weinberg equilibrium status, and linkage disequilibrium patterns of 12 polymorphisms in six candidate genes from the renin-angiotensin-aldosterone system among Indians. Because of their different history of origin, the Indian population is broadly divided into two subpopulations: North Indians (Caucasian Europeans) and South Indians (Dravidians). Considering this well-documented difference in gene pools, we have presented a comparative account of the normative genetic data of North Indian and South Indian populations with at least four individuals of urban and suburban origin from each of the representative states of northern and southern India.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Decomposing multilocus linkage disequilibrium

We present a mathematically precise formulation of total linkage disequilibrium between multiple loci as the deviation from probabilistic independence and provide explicit formulas for all higher-order terms of linkage disequilibrium, thereby combining J. Dausset et al.'s 1978 definition of linkage disequilibrium with H. Geiringer's 1944 approach. We recursively decompose higher-order linkage disequilibrium terms into lower-order ones. Our greatest simplification comes from defining linkage disequilibrium at a single locus as allele frequency at that locus. At each level, decomposition of linkage disequilibrium is mathematically equivalent to number theoretic compositions of positive integers; i.e., we have converted a genetic decomposition into a mathematical decomposition.     

Genetic diversity and linkage disequilibrium in the Polynesian population of Niue Island

Isolated populations that recently have been derived from small homogeneous groups of founders should have low genetic diversity and high levels of linkage disequilibrium and should be ideal for mapping ancestral polymorphisms that influence complex genetic disease susceptibility. Populations that fulfill these criteria have been difficult to identify. We have been looking for Polynesian populations with these characteristics, because Polynesians have high rates of complex genetic diseases. In Niue Islanders all ancestral female (mitochondrial HSVI sequence) and 90.4% of ancestral male (Y-chromosome haplogroup) lineages are of Southeast Asian origin. The frequency of European Y-chromosome haplogroups is 7.2%. The diversities of mitochondrial HSV1 sequences (h = 0.18 +/- 0.05) and Y-chromosome haplo-groups (h = 0.18 +/- 0.05) are lower than values published for any other population. Ten autosomal microsatellites spaced over 5.8 cM show low allele numbers in Niue Islanders relative to Europeans (55 vs. 88 total alleles, respectively) and a modest reduction in heterozygous loci (0.71 +/- 0.02 vs. 0.78 +/- 0.02, p = 0.04). The higher linkage disequilibrium (d2) between these loci in Niue Islanders relative to Europeans (p = 0.001) is negatively correlated (r = -0.47, p = 0.01) with genetic distance. In summary, Niue Islanders are genetically isolated and have a homogeneous Southeast Asian ancestry. They have reduced autosomal genetic diversity and high levels of linkage disequilibrium that are consistent with the influence of genetic drift mechanisms, such as a founder effect or bottlenecks. High-powered linkage disequilibrium studies designed to map ancestral polymorphisms that influence complex genetic disease susceptibility may be feasible in this population.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

The direction of linkage disequilibrium: a new measure based on the ancestral-derived status of segregating alleles

A new measure of directional linkage disequilibrium is developed for detecting epistatic selection on interacting genes. Simulations show that by orienting the direction of linkage disequilibrium on the basis of the ancestral-derived status of alleles, the new measure indeed improves the power to detect a positive fitness interaction between two new mutations.     

The genetic basis of female mate preferences

We review the evidence for genetic variation in female and male mate preferences. Genetic differences between species and partially isolated races show that preferences can evolve and were genetically variable in the past. Within populations there is good evidence of genetic variation, both of discrete genetic effects (8 cases) and quantitative genetic effects (17 cases), from a diverse range of taxa. We also review evidence for the presence of genetic covariance between mate preferences and sexual traits in the other sex. The 11 studies go a long way to validating the theoretical prediction of positive genetic covariance. The few negative results are best explained by a lack of appropriate experimental design. One unresolved question is whether genetic covariance is due to linkage disequilibrium between unlinked genes or physical linkage. Some evidence points to linkage disequilibrium but this is not yet conclusive.     

Study on genetic coadaptability of wild quail populations in China

Genetic coadaptability of wild Japanese quail, wild Common quail and Domestic quail populations in China was studied using 7 microsatellite DNA markers and Monte Carlo method to test genetic disequilibrium. The molecular effects of genetic coadaptability were analyzed through a new statistical model of neutral site. The results showed that genetic coadaptability dominated the genetic disequilibrium of the three quail populations, and totally 16.67%, 9.66% and 10.05% of non-allelic combinations were in the genetic disequilibrium in wild Japanese quail, wild Common quail and Domestic quail populations, respectively. Genetic coadaptability existed at almost all the tested sites. In the molecular point of view, genetic coadaptability plays an important role of keeping lots of polymorphisms in natural populations. Therefore, it is another key factor to the genetic disequilibrium in the population except for linkage. The results enrich the conceptions and connotations of genetic disequilibrium, and help us know more about genetic coadaptability and its effects, and lay a foundation of evaluation and protection of wild quail genetic resources in China.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Study on genetic coadaptability of wild quail populations in China

Genetic coadaptability, developed from the process of evolution, is one of the properties of gene pool as well as gene frequency of each locus. It was explained in detail by Nei[1] in 1973. He proposed that during evolutionary process, non-allelic genes o…