渐近混合群体的混合连锁不平衡及其遗传连锁推断

在渐近混合模型中,混合现象发生在每一世代,通过对其混合连锁不平衡的理论分析,发现混合连锁不平衡与两个子群体间的基因频率差成正比。基于这一点,构造了一个对重组率严格单调的函数（△ker=△／（p1-p2）,其中△代表连锁不平衡）,进而据此推断标记基因座与疾病基因座的遗传连锁。应用人类基因组上不连锁的标记基因提供的连锁不平衡信息,基于病人组数据构造了一个准似然比统计量。模拟结果显示,此检验可用于精确的基因定位。文章亦讨论了参数对检验的影响。     

Inferring Admixture Histories of Human Populations Using Linkage Disequilibrium

Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD statistic that can be used to infer mixture proportions as well as dates with fewer constraints on reference populations than previous methods. We define an LD-based three-population test for admixture and identify scenarios in which it can detect admixture events that previous formal tests cannot. We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references. Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations. We implement all of these advances in a software package, ALDER, which we validate in simulations and apply to test for admixture among all populations from the Human Genome Diversity Project (HGDP), highlighting insights into the admixture history of Central African Pygmies, Sardinians, and Japanese.     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

Patterns and Causes of Signed Linkage Disequilibria in Flies and Plants

Most empirical studies of linkage disequilibrium (LD) study its magnitude, ignoring its sign. Here, we examine patterns of signed LD in two population genomic data sets, one from Capsella grandiflora and one from Drosophila melanogaster. We consider how processes such as drift, admixture, Hill–Robertson interference, and epistasis may contribute to these patterns. We report that most types of mutations exhibit positive LD, particularly, if they are predicted to be less deleterious. We show with simulations that this pattern arises easily in a model of admixture or distance-biased mating, and that genome-wide differences across site types are generally expected due to differences in the strength of purifying selection even in the absence of epistasis. We further explore how signed LD decays on a finer scale, showing that loss of function mutations exhibit particularly positive LD across short distances, a pattern consistent with intragenic antagonistic epistasis. Controlling for genomic distance, signed LD in C. grandiflora decays faster within genes, compared with between genes, likely a by-product of frequent recombination in gene promoters known to occur in plant genomes. Finally, we use information from published biological networks to explore whether there is evidence for negative synergistic epistasis between interacting radical missense mutations. In D. melanogaster networks, we find a modest but significant enrichment of negative LD, consistent with the possibility of intranetwork negative synergistic epistasis.     

How Population Growth Affects Linkage Disequilibrium

The “LD curve” relates the linkage disequilibrium (LD) between pairs of nucleotide sites to the distance that separates them along the chromosome. The shape of this curve reflects natural selection, admixture between populations, and the history of population size. This article derives new results about the last of these effects. When a population expands in size, the LD curve grows steeper, and this effect is especially pronounced following a bottleneck in population size. When a population shrinks, the LD curve rises but remains relatively flat. As LD converges toward a new equilibrium, its time path may not be monotonic. Following an episode of growth, for example, it declines to a low value before rising toward the new equilibrium. These changes happen at different rates for different LD statistics. They are especially slow for estimates of σd2, which therefore allow inferences about ancient population history. For the human population of Europe, these results suggest a history of population growth.     

Associative overdominance: Evaluating the effects of inbreeding and linkage disequilibrium

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

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

人类复杂遗传疾病QTL分析方法的理论探讨

利用连锁不平衡理论,人类遗传学家已能把影响人类疾病的质量基因定位在小至1cM区域内,有些基因已被克隆出来。罗泽伟等进一步发展统计分析方法检测及估算分子标记与QTL之间的连锁不平衡系数,从而提出了人类复杂遗传病高解析度基因定位的理论策略。以此为基础,进一步探讨了供试群体在双亲基因频率存在差异时检测QTL和检测QTL互作的方法,给出了有关的理论结果。     

Linkage disequilibrium on chromosome 6 in Australian Holstein-Friesian cattle

We analysed linkage disequilibrium (LD) in Australian Holstein-Friesian cattle by genotyping a sample of 45 bulls for 15 closely-spaced microsatellites on two regions of BTA6 reported to carry important QTL for dairy traits. The order and distance of markers were based on the USDA-MARC linkage map. Frequencies of haplotypes were estimated using the E-M approach and a more computationally-intensive Bayesian approach as implemented in PHASE. LD was then estimated using the Hedrick multiallelic extension of Lewontin normalised coefficient D''. Estimates of D'' from the two approaches were in close agreement (r = 0.91). The mean estimates of D'' for marker pairs with an inter-marker distance of less than 5 cM (n = 13) are 0.57 and 0.51, and for distances more than 20 cM (n = 44) are 0.29 and 0.17, estimated from the E-M and Bayesian approaches, respectively. The Malecot model was fitted for the exponential decline of LD with map distance between markers. The swept radii (the distance at which LD has declined to 1/e (~37%) of its initial value) are 11.6 and 13.7 cM for the above two methods, respectively. The Malecot model was also fitted using map distance in Mb from the bovine integrated map (bovine location database, bLDB) in addition to cM from the MARC map. Overall, the results indicate a high level of LD on chromosome 6 in Australian dairy cattle.     

Linkage disequilibrium in the North American Holstein population

Linkage disequilibrium was estimated using 7119 single nucleotide polymorphism markers across the genome and 200 animals from the North American Holstein cattle population. The analysis of maternally inherited haplotypes revealed strong linkage disequilibrium ( r ²   >   0.8) in genomic regions of ∼50 kb or less. While linkage disequilibrium decays as a function of genomic distance, genomic regions within genes showed greater linkage disequilibrium and greater variation in linkage disequilibrium compared with intergenic regions. Identification of haplotype blocks could characterize the most common haplotypes. Although maximum haplotype block size was over 1 Mb, mean block size was 26–113 kb by various definitions, which was larger than that observed in humans (∼10 kb). Effective population size of the dairy cattle population was estimated from linkage disequilibrium between single nucleotide polymorphism marker pairs in various haplotype ranges. Rapid reduction of effective population size of dairy cattle was inferred from linkage disequilibrium in recent generations. This result implies a loss of genetic diversity because of the high rate of inbreeding and high selection intensity in dairy cattle. The pattern observed in this study indicated linkage disequilibrium in the current dairy cattle population could be exploited to refine mapping resolution. Changes in effective population size during past generations imply a necessity of plans to maintain polymorphism in the Holstein population.     

Linkage Disequilibrium with Linkage Analysis of Multiline Crosses Reveals Different Multiallelic QTL for Hybrid Performance in the Flint and Dent Heterotic Groups of Maize

Multiparental designs combined with dense genotyping of parents have been proposed as a way to increase the diversity and resolution of quantitative trait loci (QTL) mapping studies, using methods combining linkage disequilibrium information with linkage analysis (LDLA). Two new nested association mapping designs adapted to European conditions were derived from the complementary dent and flint heterotic groups of maize (Zea mays L.). Ten biparental dent families (N = 841) and 11 biparental flint families (N = 811) were genotyped with 56,110 single nucleotide polymorphism markers and evaluated as test crosses with the central line of the reciprocal design for biomass yield, plant height, and precocity. Alleles at candidate QTL were defined as (i) parental alleles, (ii) haplotypic identity by descent, and (iii) single-marker groupings. Between five and 16 QTL were detected depending on the model, trait, and genetic group considered. In the flint design, a major QTL (R² = 27%) with pleiotropic effects was detected on chromosome 10, whereas other QTL displayed milder effects (R² < 10%). On average, the LDLA models detected more QTL but generally explained lower percentages of variance, consistent with the fact that most QTL display complex allelic series. Only 15% of the QTL were common to the two designs. A joint analysis of the two designs detected between 15 and 21 QTL for the five traits. Of these, between 27 for silking date and 41% for tasseling date were significant in both groups. Favorable allelic effects detected in both groups open perspectives for improving biomass production.     

The Effect of Linkage Disequilibrium and Family Relationships on the Reliability of Genomic Prediction

Although the concept of genomic selection relies on linkage disequilibrium (LD) between quantitative trait loci and markers, reliability of genomic predictions is strongly influenced by family relationships. In this study, we investigated the effects of LD and family relationships on reliability of genomic predictions and the potential of deterministic formulas to predict reliability using population parameters in populations with complex family structures. Five groups of selection candidates were simulated by taking different information sources from the reference population into account: (1) allele frequencies, (2) LD pattern, (3) haplotypes, (4) haploid chromosomes, and (5) individuals from the reference population, thereby having real family relationships with reference individuals. Reliabilities were predicted using genomic relationships among 529 reference individuals and their relationships with selection candidates and with a deterministic formula where the number of effective chromosome segments (M_e) was estimated based on genomic and additive relationship matrices for each scenario. At a heritability of 0.6, reliabilities based on genomic relationships were 0.002 ± 0.0001 (allele frequencies), 0.022 ± 0.001 (LD pattern), 0.018 ± 0.001 (haplotypes), 0.100 ± 0.008 (haploid chromosomes), and 0.318 ± 0.077 (family relationships). At a heritability of 0.1, relative differences among groups were similar. For all scenarios, reliabilities were similar to predictions with a deterministic formula using estimated M_e. So, reliabilities can be predicted accurately using empirically estimated M_e and level of relationship with reference individuals has a much higher effect on the reliability than linkage disequilibrium per se. Furthermore, accumulated length of shared haplotypes is more important in determining the reliability of genomic prediction than the individual shared haplotype length.     

Linkage and Association Between CA Repeat Polymorphism of the TNFR2 Gene and Obesity Phenotypes in Two Independent Caucasian Populations

Previously, our group has reported a suggestive linkage evidence of 1p36 with body mass index (BMI) (LOD = 2.09). The tumor necrosis factor receptor 2 (TNFR2) at 1p36 is an excellent positional and functional candidate gene for obesity. In this study, we have investigated the linkage and association between the TNFR2 gene and obesity phenotypes in two large independent samples, using the quantitative transmission disequilibrium tests (QTDT). The first group was made up of 1 836 individuals from 79 multi-generation pedigrees. The second group was a randomly ascertained set of 636 individuals from 157 US Caucasian nuclear families. Obesity phenotypes tested include BMI, fat mass, and percentage fat mass (PFM). A significant result (P = 0.0056) was observed for linkage with BMI in the sample of the multigenerational pedigrees. Our data support the TNFR2 gene as a quantitative trait locus (QTL) underlying BMI variation in the Caucasian populations.     

Testing an hypothesis of hybrid zone movement for toads in France

Hybrid zone movement may result in substantial unidirectional introgression of selectively neutral material from the local to the advancing species, leaving a genetic footprint. This genetic footprint is represented by a trail of asymmetric tails and displaced cline centres in the wake of the moving hybrid zone. A peak of admixture linkage disequilibrium is predicted to exist ahead of the centre of the moving hybrid zone. We test these predictions of the movement hypothesis in a hybrid zone between common (Bufo bufo) and spined toads (B. spinosus), using 31 nuclear and one mtDNA SNPs along a transect in the northwest of France. Average effective selection in Bufo hybrids is low and clines vary in shape and centre. A weak pattern of asymmetric introgression is inferred from cline discordance of seven nuclear markers. The dominant direction of gene flow is from B. spinosus to B. bufo and is in support of southward movement of the hybrid zone. Conversely, a peak of admixture linkage disequilibrium north of the hybrid zone suggests northward movement. These contrasting results can be explained by reproductive isolation of the B. spinosus and B. bufo gene pools at the southern (B. spinosus) side of the hybrid zone. The joint occurrence of asymmetric introgression and admixture linkage disequilibrium can also be explained by the combination of low dispersal and random genetic drift due to low effective population sizes.     

Constructing a linkage–linkage disequilibrium map using dominant-segregating markers

The relationship between linkage disequilibrium (LD) and recombination fraction can be used to infer the pattern of genetic variation and evolutionary process in humans and other systems. We described a computational framework to construct a linkage–LD map from commonly used biallelic, single-nucleotide polymorphism (SNP) markers for outcrossing plants by which the decline of LD is visualized with genetic distance. The framework was derived from an open-pollinated (OP) design composed of plants randomly sampled from a natural population and seeds from each sampled plant, enabling simultaneous estimation of the LD in the natural population and recombination fraction due to allelic co-segregation during meiosis. We modified the framework to infer evolutionary pasts of natural populations using those marker types that are segregating in a dominant manner, given their role in creating and maintaining population genetic diversity. A sophisticated two-level EM algorithm was implemented to estimate and retrieve the missing information of segregation characterized by dominant-segregating markers such as single methylation polymorphisms. The model was applied to study the relationship between linkage and LD for a non-model outcrossing species, a gymnosperm species, Torreya grandis, naturally distributed in mountains of the southeastern China. The linkage–LD map constructed from various types of molecular markers opens a powerful gateway for studying the history of plant evolution.     

Replication and refinement of a quantitative trait locus influencing milk protein percentage on ovine chromosome 3

A previous genome scan that was conducted in Spanish Churra sheep identified a significant quantitative trait locus (QTL) for milk protein percentage (PP) on chromosome 3 (OAR3), between markers KD103 and OARVH34. The aim of this study was to replicate these results and to refine the mapped position of this QTL. To accomplish this goal, we analysed 14 new half‐sib families of Spanish Churra sheep including 1661 ewes from 29 different flocks. These animals were genotyped for 21 microsatellite markers mapping to OAR3. In addition to a classical linkage analysis (LA), a combined linkage disequilibrium and linkage analysis (LDLA) was performed with the aim of enhancing the resolution of the QTL mapping. The LA that was performed in this sheep population identified the presence of a highly significant QTL for PP near marker KD103 (P_c < 0.001; P_exp < 0.001). The phenotypic variance that was owing to the QTL was 2.74%. Two segregating families for the target QTL were identified in this population with QTL effect estimates of 0.47 and 0.95 SD. The LDLA identified the same QTL as the previous analyses with a high level of statistical significance (P = 9.184 E‐11) and narrowed the confidence interval (CI) to a 13 cM region. These results confirm the segregation of the previously identified OAR3 QTL that influences PP in Spanish Churra sheep. Future research will aim to increase the marker density across the refined CI and to analyse the corresponding candidate genes to identify the allelic variant or variants that underlie this genetic effect.     

Sexual and parental antagonism shape genomic architecture

Populations with two sexes are vulnerable to a pair of genetic conflicts: sexual antagonism that can arise when alleles have opposing fitness effects on females and males; and parental antagonism that arises when alleles have opposing fitness effects when maternally and paternally inherited. This paper extends previous theoretical work that found stable linkage disequilibrium (LD) between sexually antagonistic loci. We find that LD is also generated between parentally antagonistic loci, and between sexually and parentally antagonistic loci, without any requirement of epistasis. We contend that the LD in these models arises from the admixture of gene pools subject to different selective histories. We also find that polymorphism maintained by parental antagonism at one locus expands the opportunity for polymorphism at a linked locus experiencing parental or sexual antagonism. Taken together, our results predict the chromosomal clustering of loci that segregate for sexually and parentally antagonistic alleles. Thus, genetic conflict may play a role in the evolution of genomic architecture.     

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.     

Mixed linear model association mapping for low chloride accumulation rate in oriental-type tobacco (Nicotiana tabaccum L.) germplasm

Chloride is an essential micronutrient in tobacco (Nicotiana tabaccum L.) cultivation. However, large amounts of it have many adverse effects on burning quality of tobacco leaves. The objective of this study was to evaluate the genetic variability among 70 oriental-type tobacco genotypes and determine the genomic regions associated with chloride accumulation rate using mixed linear model (MLM) procedure. A total number of 66 alleles were detected by 26 simple sequence repeat (SSR) loci with an average of 2.53 alleles per locus. A model-based Bayesian approach subdivided 70 tobacco genotypes into the three subgroups. Almost 5.85% of the 325 marker pairs showed a significant level of linkage disequilibrium (P ≤ 0.01). Using MLM procedure, 1 SSR locus (pt30027) from linkage group 13 was identified to be associated with the gene(s) controlling low chloride accumulation in oriental tobacco genotypes. Identified markers could be of great interest in marker-assisted selection in tobacco breeding programs.     

Sequence Diversity and Linkage Disequilibrium within the Merozoite Surface Protein-1 (Msp-1) Locus of Plasmodium falciparum: A Longitudinal Study in Brazil

ABSTRACT. The merozoite surface protein‐1 (MSP‐1) is a major vaccine candidate for the asexual blood stage of malaria. We examined both the extent of sequence diversity in block 17, the 3′end of Msp‐1 gene coding for a 19‐kDa polypeptide (MSP‐1₁₉) putatively involved in red blood cell binding, and the patterns of linkage disequilibrium between polymorphic sites throughout the Msp‐1 locus. The parasite population sample consisted of Plasmodium falciparum isolates collected between 1985 and 1998 in Rondônia. an area of hypoendemic malaria transmission in the southwestern Brazilian Amazon. Results were summarized as follows. (I) Seven block‐17 sequence variants or haplotypes were found among 130 isolates, including two new haplotypes (novel combinations of previously reported amino acid replacements), here named Brazil‐1 (E‐TSR‐F) and Brazil‐2 (Q‐TSR‐F). (2) As previously shown for other Msp‐1 polymorphisms, frequencies of block‐17 haplotypes displayed significant temporal variation. (3) Extensive linkage disequilibrium was demonstrated between neighboring dimorphic sites within block 17, as well as between polymorphisms at the 5′and 3′ends of Msp‐1 (map distance range: 3.83–4.99 kb). (4) The overall patterns of linkage disequilibrium within Msp‐1 remained stable over a period of nearly one decade, and examples of possible ‘epidemic’ expansion of parasites carrying particular Msp‐1 alleles were found in the 1980s and 1990s. These results are discussed in relation to the population biology of P. falciparum and the development of malaria vaccines based on MSP‐1.