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.     

Cost-effective designs for linkage disequilibrium mapping of complex traits

The current development of densely spaced collections of single nucleotide polymorphisms (SNPs) will lead to genomewide association studies for a wide range of diseases in many different populations. Determinations of the appropriate number of SNPs to genotype involve a balancing of power and cost. Several variables are important in these determinations. We show that there are different combinations of sample size and marker density that can be expected to achieve the same power. Within certain bounds, investigators can choose between designs with more subjects and fewer markers or those with more markers and fewer subjects. Which designs are more cost-effective depends on the cost of phenotyping versus the cost of genotyping. We show that, under the assumption of a set cost for genotyping, one can calculate a "threshold cost" for phenotyping; when phenotyping costs per subject are less than this threshold, designs with more subjects will be more cost-effective than designs with more markers. This framework for determining a cost-effective study will aid in the planning of studies, especially if there are choices to be made with respect to phenotyping methods or study populations.     

Evaluation of designs for reference families for livestock linkage mapping experiments

Abstract

The development of dense linkage maps consisting of highly polymorphic loci for livestock species is technically feasible. However, linkage mapping experiments are expensive as they involve many animals and marker typings per animal. To minimize costs of developing linkage maps for livestock species, optimizing designs for mapping studies is necessary. This study provides a general framework for evaluating the efficiency of designs for reference families consisting of two‐ or three‐ generation full‐sib or half‐sib families selected from a segregating population. The influence of number of families, number of offspring per family, family structure (either half‐sib or full‐sib) and marker polymorphism is determined. Evaluation is done for two markers with a recombination rate of .20 and for a marker and a dominant single gene with a recombination rate of .20. Two evaluation criteria are used: expected maximum lod score for detection of linkage and accuracy of an estimated recombination rate defined as probability that the true recombination rate is in an interval around the estimated recombination rate. First, for several designs the contribution of reference families to expected maximum lod score and accuracy is given. Second, the required number of families in a design to obtain a certain value for the evaluation criteria is calculated when number of offspring per family, family structure and marker polymorphism are specified. The required numbers increase when designs are optimized not only for expected maximum lod score but also for accuracy. The required number of animals to map a dominant single gene is very large. Therefore, a set of reference families should be designed for strictly mapping marker loci. Examples illustrate how tabulated results can be generalized to determine the values for a wide range of designs containing two‐ or three‐generation full‐sib or half‐sib families.     

Relative efficiency of the linkage disequilibrium mapping approach in detecting candidate genes for schizophrenia in different European populations

Detection of susceptibility genes in indirect association studies depends not only on the degree of linkage disequilibrium between the disease variant and the SNP marker but also on the difference in their allele frequencies. Little is known about how variations in these parameters may affect the power of indirect association studies among related populations. Toward this goal, we genotyped 40 SNPs at four loci in samples from three European populations, Galician, Greek, and Norwegian. We compared the relative efficiency of all pairs of SNPs in detecting each other in each one of the populations. Our results show that a low percentage of marker SNPs may detect association in some populations but be totally ineffective in others. Therefore, these differences have to be an additional factor to consider when a replication study fails to confirm initial associations, especially if the replication is focused on very few markers.     

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.     

Optimal structure of protocol designs for building genetic linkage maps in livestock

We investigated protocol designs for gene mapping in livestock. The optimization of the population structure was based on the empirical variance of the recombination rate estimator. We concluded that a mixture of half-sib and full-sib families is preferred to half-sib families; a knowledge of parental phases does not improve the quality of the estimation for typical livestock families with five offspring or more; and measurements of the genotype of the mates in half-sib families are not useful. Graphs and algebraic approximations for the practical choice of family size and structure are given.     

Statistical software for gene mapping by admixture linkage disequilibrium

Admixture mapping is a statistical methodology that detects genetic variants in recently admixed populations that are responsible for ethnic differences in disease risk. Three software packages are now available for admixture mapping and we provide a brief overview of the statistical methods and other principal features they implement.     

Markers for mapping by admixture linkage disequilibrium in African American and Hispanic populations

Population linkage disequilibrium occurs as a consequence of mutation, selection, genetic drift, and population substructure produced by admixture of genetically distinct ethnic populations. African American and Hispanic ethnic groups have a history of significant gene flow among parent groups, which can be of value in affecting genome scans for disease-gene discovery in the case-control and transmission/disequilibrium test designs. Disease-gene discovery using mapping by admixture linkage disequilibrium (MALD) requires a map of polymorphic markers that differentiate between the founding populations, along with differences in disease-gene allele frequencies. We describe markers appropriate for MALD mapping by assessing allele frequencies of 744 short tandem repeats (STRs) in African Americans, Hispanics, European Americans, and Asians, by choosing STR markers that have large differences in composite delta, log-likelihood ratios, and/or I*(2) for MALD. Additional markers can be added to this MALD map by utilization of the rapidly growing single-nucleotide-polymorphism databases and the literature, to achieve a 3-10-cM scanning scale. The map will be useful for studies of diseases, including prostate and breast cancer, diabetes, hypertension, and end-stage renal disease, that have large differences in incidence between the founding populations of either Hispanics or African Americans.     

DMLE+: Bayesian linkage disequilibrium gene mapping

SUMMARY: The program DMLE+ allows Bayesian inference of the location of a gene carrying a mutation influencing a discrete trait (such as a disease) and/or other parameters of interest (such as mutation age) based on the observed linkage disequilibrium at multiple genetic markers. DMLE+ uses either individual marker genotypes, or haplotypes, integrates over uncertain population allele frequencies, and can incorporate prior information about gene location from an annotated human genome sequence. AVAILABILITY: DMLE+ is available in both Windows GUI and portable UNIX command line versions at http://dmle.org.     

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.     

Methods for linkage disequilibrium mapping in crops

Linkage disequilibrium (LD) mapping in plants detects and locates quantitative trait loci (QTL) by the strength of the correlation between a trait and a marker. It offers greater precision in QTL location than family-based linkage analysis and should therefore lead to more efficient marker-assisted selection, facilitate gene discovery and help to meet the challenge of connecting sequence diversity with heritable phenotypic differences. Unlike family-based linkage analysis, LD mapping does not require family or pedigree information and can be applied to a range of experimental and non-experimental populations. However, care must be taken during analysis to control for the increased rate of false positive results arising from population structure and variety interrelationships. In this review, we discuss how suitable the recently developed alternative methods of LD mapping are for crops.     

Tests of candidate genes in breed cross populations for QTL mapping in livestock

In recent years, several F₂ crosses between outbred lines of livestock have been developed to identify quantitative trait loci (QTL). These populations are valuable for further genetic analysis, including positional candidate gene loci (CGL). Analysis of CGL in F₂ populations is, however, hindered by extensive between-breed linkage disequilibrium (LD). The objectives here were to develop and evaluate three tests for CGL in simulated F₂ breed-cross populations. 1) A standard association test, based on the fixed effect of CGL genotype. This test was significant for CGL at considerable distances from the QTL. 2) A marker-assisted association test, based on a test at the CGL of the fixed effect of CGL genotype in a breed-cross QTL interval mapping model. This removed the impact of between-breed LD, but was not powerful in detecting CGL closely linked to the QTL, unless the CGL was the QTL. 3) An F-drop test, comparing F ratios for a QTL at the CGL with and without the CGL included as fixed effect. It had low power to distinguish close from distant CGL. Power to distinguish two CGL within 10 cM from the QTL was limited and little improved by including QTL effects associated with markers to remove between-breed LD, although the power was greater when one of the CGL was the causative mutation. Therefore, while we conclude that candidate gene tests in QTL mapping populations must be interpreted with caution, we now have a clearer picture of the value of candidate gene tests in these populations.     

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.     

Characterizing linkage disequilibrium in pig populations

Knowledge of the extent and range of linkage disequilibrium (LD), defined as non-random association of alleles at two or more loci, in animal populations is extremely valuable in localizing genes affecting quantitative traits, identifying chromosomal regions under selection, studying population history, and characterizing/managing genetic resources and diversity. Two commonly used LD measures, r(2) and D', and their permutation based adjustments, were evaluated using genotypes of more than 6,000 pigs from six commercial lines (two terminal sire lines and four maternal lines) at ~4,500 autosomal SNPs (single nucleotide polymorphisms). The results indicated that permutation only partially removed the dependency of D' on allele frequency and that r(2) is a considerably more robust LD measure. The maximum r(2) was derived as a function of allele frequency. Using the same genotype dataset, the extent of LD in these pig populations was estimated for all possible syntenic SNP pairs using r(2) and the ratio of r(2) over its theoretical maximum. As expected, the extent of LD highest for SNP pairs was found in tightest linkage and decreased as their map distance increased. The level of LD found in these pig populations appears to be lower than previously implied in several other studies using microsatellite genotype data. For all pairs of SNPs approximately 3 centiMorgan (cM) apart, the average r(2) was equal to 0.1. Based on the average population-wise LD found in these six commercial pig lines, we recommend a spacing of 0.1 to 1 cM for a whole genome association study in pig populations.     

Identification of a psoriasis susceptibility candidate gene by linkage disequilibrium mapping with a localized single nucleotide polymorphism map

Psoriasis is a chronic inflammatory disease of the skin with both genetic and environmental risk factors. Here we describe the creation of a single-nucleotide polymorphism (SNP) map spanning 900-1200 kb of chromosome 3q21, which had been previously recognized as containing a psoriasis susceptibility locus, PSORS5. We genotyped 644 individuals, from 195 Swedish psoriatic families, for 19 polymorphisms. Linkage disequilibrium (LD) between marker and disease was assessed using the transmission/disequilibrium test (TDT). In the TDT analysis, alleles of three of these SNPs showed significant association with disease (P<0.05). A 160-kb interval encompassing these three SNPs was sequenced, and a coding sequence consisting of 13 exons was identified. The predicted protein shares 30-40% homology with the family of cation/chloride cotransporters. A five-marker haplotype spanning the 3' half of this gene is associated with psoriasis to a P value of 3.8<10(-5). We have called this gene SLC12A8, coding for a member of the solute carrier family 12 proteins. It belongs to a class of genes that were previously unrecognized as playing a role in psoriasis pathogenesis.     

Markers for ornamental traits in Phalaenopsis orchids: population structure, linkage disequilibrium and association mapping

Although Phalaenopsis orchids are among the most economically important potted plants, little is known about either the genetic diversity among varieties or the genetic complexity of key ornamental traits. Therefore, we analysed the genetic diversity of a broad collection of Phalaenopsis varieties and selected wild species by means of molecular markers. The marker data were used to obtain genetic distances, estimates of the degree of linkage disequilibrium and population structure for the genotypes under study. With a total of 492 markers, the genotypes clustered according to their horticultural classification (for example, old hybrids vs. more recent hybrids) but not according to their origin, indicating extensive exchange of germplasm among breeders. Linkage disequilibrium was found to decrease relatively slowly, most likely due to the small number of generations that have occurred since the first hybrids were generated. Based on the most likely estimates for the population structure (ranging from 10 to 12 subpopulations), associations between ornamental traits like flower size, flower colour, flower type, flower texture, stem length and leaf shape were calculated. These results can now serve as starting points for detailed analyses of the genetic architecture of these traits.     

Map-based molecular diversity, linkage disequilibrium and association mapping of fruit traits in melon

Melon has tremendous fruit diversity, the product of complex interactions of consumer preferences in different countries and a wide range of agro-climatic zones. Understanding footprints of divergence underlying formation of various morphotypes is important for developing sustainable and high-quality melons. Basic understanding of population structure and linkage disequilibrium (LD) is limited in melon and has lagged behind other crops. Characterization of population structure and LD are essential for carrying out association mapping of quantitative trait loci (QTL) underlying various complex traits. Mapped single-locus microsatellite markers are known to be very valuable for resolving the population structure and 268 such markers were used in the current study to resolve population structure and LD pattern using 87 accessions of melons belonging to Eastern European, Euro-North American and Asian types. A mixed linear model was implemented to detect QTL for various fruit traits. Various levels of QTL with high to moderate stringency were detected for fruit shape, fruit weight, soluble solids, and rind pressure and a majority of them was found to be in agreement with the previously published data, indicating that association mapping can be very useful for melon molecular breeding. Minor discrepancies in the position, strength and the variation explained by the QTL present between the methods of association and recombinant mapping approaches can be bridged if more melon groups and larger sets of accessions are involved in future studies, combined with high-throughput marker panels.     

Optimized group sequential study designs for tests of genetic linkage and association in complex diseases

The study of genetic linkage or association in complex traits requires large sample sizes, as the expected effect sizes are small and extremely low significance levels need to be adopted. One possible way to reduce the numbers of phenotypings and genotypings is the use of a sequential study design. Here, average sample sizes are decreased by conducting interim analyses with the possibility to stop the investigation early if the result is significant. We applied optimized group sequential study designs to the analysis of genetic linkage (one-sided mean test) and association (two-sided transmission/disequilibrium test). For designs with two and three stages at overall significance levels of.05 and.0001 and a power of.8, we calculated necessary sample sizes, time points, and critical boundaries for interim and final analyses. Monte Carlo simulation analyses were performed to confirm the validity of the asymptotic approximation. Furthermore, we calculated average sample sizes required under the null and alternative hypotheses in the different study designs. It was shown that the application of a group sequential design led to a maximal increase in sample size of 8% under the null hypothesis, compared with the fixed-sample design. This was contrasted by savings of up to 20% in average sample sizes under the alternative hypothesis, depending on the applied design. These savings affect the amounts of genotyping and phenotyping required for a study and therefore lead to a significant decrease in cost and time.     

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.