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.     

Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

Mitonuclear linkage disequilibrium in human populations

There is extensive evidence from model systems that disrupting associations between co-adapted mitochondrial and nuclear genotypes can lead to deleterious and even lethal consequences. While it is tempting to extrapolate from these observations and make inferences about the human-health effects of altering mitonuclear associations, the importance of such associations may vary greatly among species, depending on population genetics, demographic history and other factors. Remarkably, despite the extensive study of human population genetics, the statistical associations between nuclear and mitochondrial alleles remain largely uninvestigated. We analysed published population genomic data to test for signatures of historical selection to maintain mitonuclear associations, particularly those involving nuclear genes that encode mitochondrial-localized proteins (N-mt genes). We found that significant mitonuclear linkage disequilibrium (LD) exists throughout the human genome, but these associations were generally weak, which is consistent with the paucity of population genetic structure in humans. Although mitonuclear LD varied among genomic regions (with especially high levels on the X chromosome), N-mt genes were statistically indistinguishable from background levels, suggesting that selection on mitonuclear epistasis has not preferentially maintained associations involving this set of loci at a species-wide level. We discuss these findings in the context of the ongoing debate over mitochondrial replacement therapy.     

Detecting linkage disequilibrium in bacterial populations.

The distribution of the number of pairwise differences calculated from comparisons between n haploid genomes has frequently been used as a starting point for testing the hypothesis of linkage equilibrium. For this purpose the variance of the pairwise differences, VD, is used as a test statistic to evaluate the null hypothesis that all loci are in linkage equilibrium. The problem is to determine the critical value of the distribution of VD. This critical value can be estimated either by Monte Carlo simulation or by assuming that VD is distributed normally and calculating a one-tailed 95% critical value for VD, L, L = EVD + 1.645 sqrt(VarVD), where E(VD) is the expectation of VD, and Var(VD) is the variance of VD. If VD (observed) > L, the null hypothesis of linkage equilibrium is rejected. Using Monte Carlo simulation we show that the formula currently available for Var(VD) is incorrect, especially for genetically highly diverse data. This has implications for hypothesis testing in bacterial populations, which are often genetically highly diverse. For this reason we derive a new, exact formula for Var(VD). The distribution of VD is examined and shown to approach normality as the sample size increases. This makes the new formula a useful tool in the investigation of large data sets, where testing for linkage using Monte Carlo simulation can be very time consuming. Application of the new formula, in conjunction with Monte Carlo simulation, to populations of Bradyrhizobium japonicum, Rhizobium leguminosarum, and Bacillus subtilis reveals linkage disequilibrium where linkage equilibrium has previously been reported.     

Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation-selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients h and s) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates U and ? are unbiased or only slightly upwardly biased, and ? is unbiased for most cases. In highly selfing populations, U and ? are upwardly biased, U is no more than 1.5U and ? is less than 1.1 h, and ? is either unbiased or slightly downwardly biased. With variable mutation effects, U ranges from 0.56 to 0.72U, and s ranges from 1.4 to 1.8s. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.     

Stable linkage disequilibrium without epistasis in subdivided populations

In a large random mating population stable linkage disequilibrium occurs only when there is epistasis. However if a population is divided into a number of subpopulations among which migration occurs, stable linkage disequilibrium in each subpopulation may be produced without epistasis. In the case of two subpopulations a necessary condition for linkage equilibrium in the absence of epistasis is that at least at one of the two loci under consideration the gene frequency must be the same for the two populations. This condition is rather severe and any violation of this will lead to stable linkage disequilibrium. A similar conclusion can be made with more than two populations. In general the presence of linkage disequilibrium does not necessarily imply the existence of epistasis even in equilibrium populations.     

Extensive linkage disequilibrium in small human populations in Eurasia

The extent of linkage disequilibrium (LD) was studied in two small food-gathering populations—Evenki and Saami—and two larger food-producing populations—Finns and Swedes—in northern Eurasia. In total, 50 single-nucleotide polymorphisms (SNPs) from five genes were genotyped using real-time pyrophosphate DNA sequencing, whereas 14 microsatellites were genotyped in two X-chromosomal regions. In addition, hypervariable region I of the mtDNA was sequenced to shed light on the demographic history of the populations. The SNP data, as well as the microsatellite data, reveal extensive levels of LD in Evenki and Saami when compared to Finns and Swedes. mtDNA-sequence variation is compatible with constant population size over time in Evenki and Saami but indicates population expansion in Finns and Swedes. Furthermore, the similarity between Finns and Swedes in SNP allele- and haplotype-frequency distributions indicate that these two populations may share a recent common origin. These findings suggest that populations such as the Evenki and the Saami, rather than the Finns, may be particularly suited for the initial coarse mapping of common complex diseases.     

Linkage disequilibrium under genetic hitchhiking in finite populations

The model of genetic hitchhiking predicts a reduction in sequence diversity at a neutral locus closely linked to a beneficial allele. In addition, it has been shown that the same process results in a specific pattern of correlations (linkage disequilibrium) between neutral polymorphisms along the chromosome at the time of fixation of the beneficial allele. During the hitchhiking event, linkage disequilibrium on either side of the beneficial allele is built up whereas it is destroyed across the selected site. We derive explicit formulas for the expectation of the covariance measure D and standardized linkage disequilibrium sigma 2D between a pair of polymorphic sites. For our analysis we use the approximation of a star-like genealogy at the selected site. The resulting expressions are approximately correct in the limit of large selection coefficients. Using simulations we show that the resulting pattern of linkage disequilibrium is quickly-i.e., in <0.1N generations-destroyed after the fixation of the beneficial allele for moderately distant neutral loci, where N is the diploid population size.     

Highly variable patterns of linkage disequilibrium in multiple soybean populations

Prospects for utilizing whole-genome association analysis in autogamous plant populations appear promising due to the reported high levels of linkage disequilibrium (LD). To determine the optimal strategies for implementing association analysis in soybean (Glycine max L. Merr.), we analyzed the structure of LD in three regions of the genome varying in length from 336 to 574 kb. This analysis was conducted in four distinct groups of soybean germplasm: 26 accessions of the wild ancestor of soybean (Glycine soja Seib. et Zucc.); 52 Asian G. max Landraces, the immediate results of domestication from G. soja; 17 Asian Landrace introductions that became the ancestors of North American (N. Am.) cultivars, and 25 Elite Cultivars from N. Am. In G. soja, LD did not extend past 100 kb; however, in the three cultivated G. max groups, LD extended from 90 to 574 kb, likely due to the impacts of domestication and increased self-fertilization. The three genomic regions were highly variable relative to the extent of LD within the three cultivated soybean populations. G. soja appears to be ideal for fine mapping of genes, but due to the highly variable levels of LD in the Landraces and the Elite Cultivars, whole-genome association analysis in soybean may be more difficult than first anticipated.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Measuring the extent of linkage disequilibrium in commercial pig populations

To evaluate the extent of linkage disequilibrium in domestic pigs, we genotyped 33 and 44 unrelated individuals from two commercial populations for 29 and five microsatellite markers located on chromosomes 15 and 2 respectively. A high proportion of marker pairs up to 40 cM apart exhibited significant linkage disequilibrium in both populations. Pair-wise r(2) values averaged between 0.15 and 0.50 (depending on chromosome and population) for markers <1 cM apart and declined to values of 0.05 for more distant syntenic markers. Our results suggest that both populations underwent a bottleneck approximately 20 generations ago, which reduced the effective population size from thousands to <200 animals.     

Comparative losses of quantitative and molecular genetic variation in finite populations of Drosophila melanogaster

Quantitative genetic variation, the main determinant of the ability to evolve, is expected to be lost in small populations, but there are limited data on the effect, and controversy as to whether it is similar to that for near neutral molecular variation. Genetic variation for abdominal and sternopleural bristle numbers and allozyme heterozygosity were estimated in 23 populations of Drosophila melanogaster maintained at effective population sizes of 25, 50, 100, 250 or 500 for 50 generations, as well as in 19 highly inbred populations and the wild outbred base population. Highly significant negative regressions of proportion of initial genetic variation retained on inbreeding due to finite population size were observed for both quantitative characters (b = -0.67 +/- 0.14 and -0.58 +/- 0.11) and allozyme heterozygosity (b = -0.79 +/- 0.10), and the regression coefficients did not differ significantly. Thus, quantitative genetic variation is being lost at a similar rate to molecular genetic variation. However, genetic variation for all traits was lost at rates significantly slower than predicted by neutral theory, most likely due to associative overdominance. Positive, but relatively low correlations were found among the different measures of genetic variation, but their low magnitudes were attributed to large sampling errors, rather than differences in the underlying processes of loss.     

Genetic structure and linkage disequilibrium in landrace populations of barley in Sardinia

Multilocus digenic linkage disequilibria (LD) and their population structure were investigated in eleven landrace populations of barley (Hordeum vulgare ssp. vulgare L.) in Sardinia, using 134 dominant simple-sequence amplified polymorphism markers. The analysis of molecular variance for these markers indicated that the populations were partially differentiated (F(ST) = 0.18), and clustered into three geographic areas. Consistent with this population pattern, STRUCTURE analysis allocated individuals from a bulk of all populations into four genetic groups, and these groups also showed geographic patterns. In agreement with other molecular studies in barley, the general level of LD was low (13% of locus pairs, with P < 0.01) in the bulk of 337 lines, and decayed steeply with map distance between markers. The partitioning of multilocus associations into various components indicated that genetic drift and founder effects played a major role in determining the overall genetic makeup of the diversity in these landrace populations, but that epistatic homogenising or diversifying selection was also present. Notably, the variance of the disequilibrium component was relatively high, which implies caution in the pooling of barley lines for association studies. Finally, we compared the analyses of multilocus structure in barley landrace populations with parallel analyses in both composite crosses of barley on the one hand and in natural populations of wild barley on the other. Neither of these serves as suitable mimics of landraces in barley, which require their own study. Overall, the results suggest that these populations can be exploited for LD mapping if population structure is controlled.     

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.     

Geographic components of linkage disequilibrium in natural populations of Escherichia coli

Geographic variation in the genetic structure of natural enteric populations of Escherichia coli was assessed at both the single-locus and dilocus levels from allozyme genotypes at 12 enzyme loci in 178 cell lines isolated from human hosts in Sweden, Iowa, and Tonga. Although there was significant heterogeneity in allele frequencies at six of the 12 loci, geographic variation accounted for only 2.0% of the total genetic diversity (HT = 0.518). Ohta's D-statistics were used to partition the total variance of dilocus linkage disequilibrium into within-population and between-population components. The observed total variance in disequilibrium (0.0339), averaged over 66 locus-pairs, was significantly greater than would be expected (0.0103) if alleles were randomly associated in an unstructured total population; and both within-locality and between-locality components made substantial contributions to the total variance. Half the locus-pairs exhibited the specific dual relationship among components expected when random factors are generating disequilibrium, but 20% of the locus-pairs showed the opposite relationship, reflecting systematic allele associations. The magnitude of dilocus disequilibrium apparently is unrelated to the chromosomal distance between loci. This and other evidence indicates that substitutive recombination rates in natural populations are sufficiently low to permit indirect periodic selection to play a prominent role in generating multilocus genetic structure.      

Evolution of linkage disequilibrium of the founders in exponentially growing populations

Evolution of linkage disequilibrium of the founders in exponentially growing populations was studied using a time-inhomogeneous It? process model. The model is an extension of the diffusion approximation of the Wright-Fisher model. As a measure of linkage disequilibrium, the squared standard linkage deviation, which is defined by a ratio of the moments, was considered. A system of ordinary differential equations that these moments obey was obtained. This system can be solved numerically. By simulations, it was shown that the squared standard linkage deviation gives a good approximation of the expectation of the squared correlation coefficient of gamete frequencies. In addition, a perturbative solution was obtained when the growth rate is not large. By using the perturbation, an asymptotic formula for the squared standard linkage deviation after a large number of generations was obtained. According to the formula, the squared standard linkage deviation tends to be 1/(4Nc), where N is the current size of the population and c is the recombination fraction between two loci. It is dependent on neither the initial effective size, the growth rate, nor the mutation rate. In exponentially growing populations, linkage disequilibrium will be asymptotically the same as that in a constant size population, the effective size of which is the current effective size.     

A sib-pair regression model of linkage disequilibrium for quantitative traits

A multiple-regression model is described for the detection of linkage disequilibrium in quantitative trait loci. The model is developed for application to large numbers of single nucleotide polymorphism (SNP) markers genotyped on small nuclear families. Parental data are not required by the method, although it provides a direct means to test quantitative trait locus-marker allele association and to determine whether any such association is attributable to linkage disequilibrium or population admixture. Analytical expectations for the regression coefficients are derived, allowing direct interpretation of the parameter estimates. Simulation studies indicate a substantial improvement in power over classical linkage studies of sibling pairs and show the effects of population admixture on the model outcomes.