Linkage disequilibrium in related breeding lines of chickens

High-density genotyping of single-nucleotide polymorphisms (SNPs) enables detection of quantitative trait loci (QTL) by linkage disequilibrium (LD) mapping using LD between markers and QTL and the subsequent use of this information for marker-assisted selection (MAS). The success of LD mapping and MAS depends on the extent of LD in the populations of interest and the use of associations across populations requires LD between loci to be consistent across populations. To assess the extent and consistency of LD in commercial broiler breeding populations, we used genotype data for 959 and 398 SNPs on chromosomes 1 and 4 on 179-244 individuals from each of nine commercial broiler chicken breeding lines. Results show that LD measured by r(2) extends over shorter distances than reported previously in other livestock breeding populations. The LD at short distance (within 1 cM) tended to be consistent across related populations; correlations of LD measured by r for pairs of lines ranged from 0.17 to 0.94 and closely matched the line relationships based on marker allele frequencies. In conclusion, LD-based correlations are good estimates of line relationships and the relationship between a pair of lines a good predictor of LD consistency between the lines.     

Linkage disequilibrium in Bougainville Island

Linkage disequilibria are estimated for three 2-locus systems in 18 samples from Bougainville Island, Solomon Islands. The systems are haptoglobin, acid phosphatase and MN blood group. The disequilibria are estimated two ways: by maximum likelihood (ML) and by the covariance between the non-alleles. Though seven of the 52 ML estimates are statistically different than zero, none of the covariance estimates are significant. We conclude that because linkage disequilibrium for loosely linked loci is a small quantity and because the sample sizes for most populations studied by anthropologists are small, linkage disequilibrium will not be a useful parameter for the study of natural selection in these populations.     

Linkage disequilibrium in domestic sheep

The last decade has seen a dramatic increase in the number of livestock QTL mapping studies. The next challenge awaiting livestock geneticists is to determine the actual genes responsible for variation of economically important traits. With the advent of high density single nucleotide polymorphism (SNP) maps, it may be possible to fine map genes by exploiting linkage disequilibrium between genes of interest and adjacent markers. However, the extent of linkage disequilibrium (LD) is generally unknown for livestock populations. In this article microsatellite genotype data are used to assess the extent of LD in two populations of domestic sheep. High levels of LD were found to extend for tens of centimorgans and declined as a function of marker distance. However, LD was also frequently observed between unlinked markers. The prospects for LD mapping in livestock appear encouraging provided that type I error can be minimized. Properties of the multiallelic LD coefficient D' were also explored. D' was found to be significantly related to marker heterozygosity, although the relationship did not appear to unduly influence the overall conclusions. Of potentially greater concern was the observation that D' may be skewed when rare alleles are present. It is recommended that the statistical significance of LD is used in conjunction with coefficients such as D' to determine the true extent of LD.     

Linkage disequilibrium and gametophytic self-incompatibility

Summary The approach to linkage equilibrium of a locus linked to the locus determining gametophytic self-incompatibility (S) is considered. For the simplest case of three alleles at the S locus and two at the linked locus it is necessary to consider 3 measures of linkage disequilibrium. These are found to approach their equilibrium value of zero in one of three ways: 1) steadily declining to zero; 2) oscillating as decline proceeds; 3) a combination: 2) followed by 1). Linkage equilibrium may be established before genotype frequencies reach their expectation under random crossing. Earlier studies (Li 1951; Moran 1962) of the approach to S allele equilibrium have been based on the assumption that all types of pollen take part in fertilizations equally frequently. Such an assumption leads to simpler expressions for changes in S gene frequencies but is extremely unrealistic and, in particular, leads to a different rate of approach to equilibrium from the more comprehensive model. It is shown that even in the absence of selection it is not possible to predict the equilibrium gene frequency of a linked locus until S allele equilibrium is reached. This frequency may be either higher or lower than that calculated from a gene count in the starting genotype pool. However, these two gene frequencies may stabilize long before linkage equilibrium is achieved. An examination of selection against one genotype at the linked locus is undertaken. If linkage is complete, lethality can be less effective at reducing the gene frequency than is less intense selection (in only a few generations of selection). Here too linkage equilibrium may be established with selection still effective in bringing about a decline in gene frequency. An examination of the analysis and conclusions of Rasmuson (1980) shows that because these were based on the inadequate formulae previously discussed and exclude phenomena discussed above, they are misleading. The possibility of a gametophytic self-incompatibility system providing a sufficient condition for the sheltering of lethals in the absence of the condition of complete linkage to the S locus (r=0) is shown to be unlikely.     

植物基因组中的连锁不平衡

在植物基因组学研究领域, 连锁不平衡(linkage disequilibrium, LD)分析是近年来的一个研究亮点和热点。基于LD的作图方法不仅是新基因发掘的有效途径, 而且也是联系结构基因组学和表型组学的一座桥梁。自2001年基于LD的作图方法在植物中的成功运用至今, 已有大量关于植物基因组中LD结构及LD作图的研究报道。文章系统介绍了LD的基本理论及其在LD作图、单倍型多样性分析、单倍型标签SNP的开发和群体遗传学等研究中的应用, 并就近年来关于LD与群体结构、基因转换和上位效应及G×E互作等方面的研究热点和发展趋势进行了探讨。当前, 世界各国基因争夺大战日趋激烈。中国是基因资源大国, 但还不是基因大国。植物基因组中LD研究热潮的兴起及LD研究的进一步深入, 必将大大推动植物基因组学的快速发展, 特别是加速从作物种质资源中发掘新基因的进程。     

Linkage disequilibrium in wild mice

Crosses between laboratory strains of mice provide a powerful way of detecting quantitative trait loci for complex traits related to human disease. Hundreds of these loci have been detected, but only a small number of the underlying causative genes have been identified. The main difficulty is the extensive linkage disequilibrium (LD) in intercross progeny and the slow process of fine-scale mapping by traditional methods. Recently, new approaches have been introduced, such as association studies with inbred lines and multigenerational crosses. These approaches are very useful for interval reduction, but generally do not provide single-gene resolution because of strong LD extending over one to several megabases. Here, we investigate the genetic structure of a natural population of mice in Arizona to determine its suitability for fine-scale LD mapping and association studies. There are three main findings: (1) Arizona mice have a high level of genetic variation, which includes a large fraction of the sequence variation present in classical strains of laboratory mice; (2) they show clear evidence of local inbreeding but appear to lack stable population structure across the study area; and (3) LD decays with distance at a rate similar to human populations, which is considerably more rapid than in laboratory populations of mice. Strong associations in Arizona mice are limited primarily to markers less than 100 kb apart, which provides the possibility of fine-scale association mapping at the level of one or a few genes. Although other considerations, such as sample size requirements and marker discovery, are serious issues in the implementation of association studies, the genetic variation and LD results indicate that wild mice could provide a useful tool for identifying genes that cause variation in complex traits.     

Linkage disequilibrium and fingerprinting in sugar beet

It has been suggested that map information for molecular markers can be used to strengthen finterprinting analyses. The success of this strategy depends on the distribution of linkage disequilibrium over the genome. Using 451 mapped AFLP markers, we investigated the occurrence of linkage disequilibrium in nine sugar beet breeding lines. A low but significant level of linkage disequilibrium was found for unlinked markers. Only for very tigthly linked (<3 cM) markers was this level substantially higher. This implies that little is gained in utilising the map position of the markers in fingerprinting applications. Received: 25 May 1999 / Accepted: 18 Oktober 1999     

Linkage disequilibrium in the domesticated pig

This study investigated the extent of linkage disequilibrium (LD) in two genomic regions (on chromosomes 4 and 7) in five populations of domesticated pigs. LD was measured with D' and tested for significance with the Fisher exact test. Effects of genetic (linkage) distance, chromosome, population, and their interactions on D' were tested both through a linear model analysis of covariance and by a theoretical nonlinear model. The overall result was that (1) the distance explained most of the variability of D', (2) the effect of chromosome was significant, and (3) the effect of population was significant. The significance of the chromosome effect may have resulted from selection and the significance of the population effect illustrates the effects of population structures and effective population sizes on LD. These results suggest that mapping methods based on LD may be valuable even with only moderately dense marker spacing in pigs.     

Linkage disequilibrium under recurrent bottlenecks

To model deviations from selectively neutral genetic variation caused by different forms of selection, it is necessary to first understand patterns of neutral variation. Best understood is neutral genetic variation at a single locus. But, as is well known, additional insights can be gained by investigating multiple loci. The resulting patterns reflect the degree of association (linkage) between loci and provide information about the underlying multilocus gene genealogies. The statistical properties of two-locus gene genealogies have been intensively studied for populations of constant size, as well as for simple demographic histories such as exponential population growth and single bottlenecks. By contrast, the combined effect of recombination and sustained demographic fluctuations is poorly understood. Addressing this issue, we study a two-locus Wright-Fisher model of a population subject to recurrent bottlenecks. We derive coalescent approximations for the covariance of the times to the most recent common ancestor at two loci in samples of two chromosomes. This covariance reflects the degree of association and thus linkage disequilibrium between these loci. We find, first, that an effective population-size approximation describes the numerically observed association between two loci provided that recombination occurs either much faster or much more slowly than the population-size fluctuations. Second, when recombination occurs frequently between but rarely within bottlenecks, we observe that the association of gene histories becomes independent of physical distance over a certain range of distances. Third, we show that in this case, a commonly used measure of linkage disequilibrium, σ(2)(d) (closely related to r(2)), fails to capture the long-range association between two loci. The reason is that constituent terms, each reflecting the long-range association, cancel. Fourth, we analyze a limiting case in which the long-range association can be described in terms of a Xi coalescent allowing for simultaneous multiple mergers of ancestral lines.     

Linkage disequilibrium in chromosome A ofDrosophila subobscura

Evidence of strong and consistent association of alleles at theHbdh and6Pgdh loci with the A₂ and A₂₊₆ gene arrangements of the sex chromosome inD. subobscura is presented. Total association between one rare allele ofG6pdh and the rare sex-ratio arrangement A_2+3+5+7 has also been found. Selective or historical factors could explain these linkage disequilibria.     

Linkage disequilibrium ofMHC genes in the chicken

Two loci of the chicken MHC (theB complex) are expressed in erythrocytes,B-F andB-G. The former is homologous to the murineK andD loci and is also expressed in all white blood cells, while the latter is apparently restricted to RBC and is of unknown relationship toH-2 andHLA loci. A recombinant between two congenic, MHC-different strains, CB and CC, has permitted the production of antisera specific for theB-F andB-G alleles of these two strains, and these and other antisera have been used for typing of outbred populations of various chicken breeds.The cross-reactions found with haplotypes other than the donors' are extensive, sometimes even extreme, but it is possible to narrow the specificity of the typing sera by appropriate absorptions. With absorbed sera we have found a linkage disequilibrium which is almost certainly even stronger than that reported in studies of mammalianMHC loci. We have also made observations which suggest that the gametic association of a given set ofB-F andB-G alleles is probably not merely a matter of random crossing-over events.     

Linkage disequilibrium for different scales and applications

Assessing the patterns of linkage disequilibrium (LD) has become an important issue in both evolutionary biology and medical genetics since the rapid accumulation of densely spaced DNA sequence variation data in several organisms. LD deals with the correlation of genetic variation at two or more loci or sites in the genome within a given population. There are a variety of LD measures which range from traditional pairwise LD measures such as D' or r2 to entropy-based multi-locus measures or haplotype-specific approaches. Understanding the evolutionary forces (in particular recombination) that generate the observed variation of LD patterns across genomic regions is addressed by model-based LD analysis. Marker type and its allelic composition also influence the observed LD pattern, microsatellites having a greater power to detect LD in population isolates than SNPs. This review aims to explain basic LD measures and their application properties.     

Linkage disequilibrium with the island model

Linkage disequilibrium between two linked loci was studied for a finite population with a subdivided population structure. Wright's island model was used; extinction and replacement of colonies were also incorporated. Two alleles (A₁ and A₂ at the first locus, and B₁ and B₂ at the second locus) with symmetric mutation rates were assumed, and equilibrium properties of linkage disequilibrium coefficients were analyzed. In terms of analogy with the subdivision of inbreeding coefficient, the variance of linkage disequilibrium is divided into several components: D²_IS (variance of within-colony disequilibrium), D²_ST (variance of correlation of A₁ and B₁ of different gametes of one colony relative to that of the total population), and D²_IT (total variance of disequilibrium). Other subdivisions are D'²_IS (variance of correlation of A₁ and B₁ of one gamete of a colony relative to that of the average gamete of the population) and D'²_ST (variance of the ordinary disequilibrium of the whole population). When migration is limited, the variance becomes large if the correlation of A₁ and B₁ of one colony is taken relative to that of the whole population (D²_ST and D'²_IS). Also, when the rate of extinction-replacement of colonies is high, the whole-population disequilibrium coefficient (D'²_ST) can become fairly large. Observed linkage disequilibria, such as those among markers in the major histocompatibility complex of man and mouse, may well be explained by limited migration, without assuming epistatic natural selection.     

Linkage disequilibrium among modern sugarcane cultivars

Modern sugarcane cultivars are derived from a few interspecific hybrids created early in this century. Linkage disequilibrium was investigated in a population of 59 cultivars representing the most important commercial clones bred in Mauritius as well as a few old cultivars involved in their genealogy. Thirty-eight probes scattered over the sugarcane genome map were used to reveal RFLPs. Forty-two cases of bilocus associations were observed involving a total of 33 loci. Most of them are separated by less than 10 cM. All the corresponding allele couples were found in at least 1 of the originally created cultivars, suggesting that they depict ancient associations. This global disequilibrium is interpreted as the result of the foundation bottleneck related to the first interspecific crosses; the preferential allele associations thus created have been maintained through subsequent crosses when the loci were closely linked. This phenomenon is likely also to apply to genes of agricultural interest. A practical consequence is that markers can be used to track known QTLs in modern breeding materials without the necessity to repeatedly study segregating progenies. This structure gives high value to the correlation between molecular markers and agricultural traits among cultivars. Received: 6 March 1999 / Accepted: 25 March 1999     

Linkage disequilibrium in the human genome and its exploitation

This present review gives an overview on Linkage disequilibrium (LD), its measures and its different utilizations in human genetics studies. In the first part, we provide a detailed and a simplified presentation focusing on the definition of LD, its measures and the major software for its evaluation. Thereafter, we describe and discuss the biological and evolutionary mechanisms which create, remodel, maintain or destroy LD in human population. Consensus has now emerged on the pattern of LD in the genome which has a block-like organization with block of high disequilibrium interrupted by recombination hotspots. However, no standard method exists for the determination of such blocks and, more importantly, for the identification of TagSNP. This would yield inconsistencies between different studies of the same genes, compromising the practical use of TagSNP in association studies. The ACE gene is used to illustrate this. Will it be possible to identify consensus TagSNP that could be used consistently in all populations for testing association of candidate genes in common diseases? What is the part of myth and reality in what is called "individualized medicine"? We conclude that further LD studies are needed to get clear insights into this matter.     

Linkage disequilibrium in synthetic varieties of perennial ryegrass

Synthetic varieties obtained after three to four panmictic generations are variable, not structured and so can be used for association studies. The pattern of linkage disequilibrium (LD) decay determines whether a genome scan or a candidate gene approach can be used for an association study between genotype and phenotype. Our goal was to evaluate the effect of the number of parents used to build the synthetic varieties on the pattern of LD decay. LD was investigated in the gibberelic acid insensitive gene (GAI) region in three synthetic varieties of perennial ryegrass (Lolium perenne L.) chosen for their contrasted number of parents in the initial polycrosses. Results were compared with those obtained from a core collection. STS and SSR markers were used to evaluate variation, structuration and LD in each variety. As expected, the varieties variability increased with the number of parents almost up to the core collection variability. No structuration was observed in the varieties. Significant LDs were observed up to 1.6 Mb in a variety originated from six related parents and not above 174 kb in a variety originated from 336 parents. These results suggest that a candidate gene approach can be used when varieties have a large number of parents and a genome scan approach can be envisaged in specific regions when varieties have a low number of parents. Nevertheless, we strongly recommend to estimate the pattern of LD decay in the population and in the genomic region studied before performing an association study.     

Linkage disequilibrium in laboratory populations of Drosophila nasuta

Summary Natural populations of Drosophila nasuta are polymorphic for many gene arrangements. Two non-overlapping inversions of the third chromosome, III-2 and III-35, are most common and display extreme linkage disequilibrium. Six randomly mating laboratory stocks, each founded by one gravid female heterozygous in coupling for both III-2 and III-35, were observed after 32 generations. Significant linkage disequilibrium was observed in all stocks. Recombinants were found in only two stocks. The absence of effective recombination in some stocks and its presence in others might be due to different genotypic backgrounds. We suggest that natural selection, influencing recombination rates in several ways, and intrachromosomal epistasis between the two inversions were the main factors for the maintenance of linkage disequilibrium in D. nasuta.