Single-crossover recombination and ancestral recombination trees

We consider the Wright–Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the $N \rightarrow \infty $ limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help of a decomposition of the trees into subtrees, we calculate the probabilities of the topologies of the ancestral trees. At the same time, these probabilities lead to a semi-explicit solution of the deterministic single-crossover equation. The latter is a discrete-time dynamical system that emerges from the Wright–Fisher model via a law of large numbers and has been waiting for a solution for many decades.     

Linkage disequilibrium and inference of ancestral recombination in 538 single-nucleotide polymorphism clusters across the human genome

The prospect of using linkage disequilibrium (LD) for fine-scale mapping in humans has attracted considerable attention, and, during the validation of a set of single-nucleotide polymorphisms (SNPs) for linkage analysis, a set of data for 4,833 SNPs in 538 clusters was produced that provides a rich picture of local attributes of LD across the genome. LD estimates may be biased depending on the means by which SNPs are first identified, and a particular problem of ascertainment bias arises when SNPs identified in small heterogeneous panels are subsequently typed in larger population samples. Understanding and correcting ascertainment bias is essential for a useful quantitative assessment of the landscape of LD across the human genome. Heterogeneity in the population recombination rate, rho=4Nr, along the genome reflects how variable the density of markers will have to be for optimal coverage. We find that ascertainment-corrected rho varies along the genome by more than two orders of magnitude, implying great differences in the recombinational history of different portions of our genome. The distribution of rho is unimodal, and we show that this is compatible with a wide range of mixtures of hotspots in a background of variable recombination rate. Although rho is significantly correlated across the three population samples, some regions of the genome exhibit population-specific spikes or troughs in rho that are too large to be explained by sampling. This result is consistent with differences in the genealogical depth of local genomic regions, a finding that has direct bearing on the design and utility of LD mapping and on the National Institutes of Health HapMap project.     

Linkage disequilibrium, selection and recombination at three Loci

Limits to the relationship among linkage disequilibrium, selection and recombination at equilibrium in three-locus, two-allele, deterministic, discrete generation models are determined using linear programming techniques. These results show that the commonly used measures of linkage disequilibrium are not appropriate for a multilocus setting. Additionally, interactions among three loci are important in reducing the strength of selection necessary to maintain a given level of disequilibrium, relative to a two-locus model.     

Subdivision in an ancestral species creates asymmetry in gene trees

We consider gene trees in three species for which the species tree is known. We show that population subdivision in ancestral species can lead to asymmetry in the frequencies of the two gene trees not concordant with the species tree and, if subdivision is extreme, cause the one of the nonconcordant gene trees to be more probable than the concordant gene tree. Although published data for the human-chimp-gorilla clade and for three species of Drosophila show asymmetry consistent with our model, sequencing error could also account for observed patterns. We show that substantial levels of persistent ancestral subdivision are needed to account for the observed levels of asymmetry found in these two studies.     

Linkage disequilibrium and recombination rate estimates in the self-incompatibility region of Arabidopsis lyrata

Genetic diversity is unusually high at loci in the S-locus region of the self-incompatible species of the flowering plant, Arabidopsis lyrata, not just in the S loci themselves, but also at two nearby loci. In a previous study of a single natural population from Iceland, we attributed this elevated polymorphism to linkage disequilibrium (LD) between variants at loci close to the S locus and the S alleles, which are maintained in the population by balancing selection. With the four S-flanking loci whose diversity we previously studied, we could not determine the extent of the region linked to the S loci in which neutral sites are affected. We also could not exclude the possibility of a population bottleneck, or of admixture, as causes of the LD. We have now studied four more distant loci flanking the S-locus region, and more populations, and we analyze the results using a theoretical model of the effect of balancing selection on diversity at linked neutral sites within and between different functional S-allelic classes. In the model, diversity is a function of the number of selectively maintained alleles and the recombination distances from the selectively maintained sites. We use the model to estimate the number of different functional S alleles, their turnover rate, and recombination rates between the S-locus region and other loci. Our estimates suggest that there is a small region of very low recombination surrounding the S-locus region.     

Linkage disequilibrium and DNA markers associated with the gene for cystic fibrosis

R.F.L.P. (Restriction Fragment Length Polymorphism) observed with tightly linked probes to the CF gene allows us to calculate the standardised linkage disequilibrium between CF and these markers. This approach in combination with others strategies permits to situate the gene between D9 and G2. The conditional probabilities observed with these haplotypes modify the classical genetic of CF.     

Distinguishing recombination and intragenic gene conversion by linkage disequilibrium patterns

Deterministic theory suggests that reciprocal recombination and intragenic, interallelic conversion have different effects on the linkage disequilibrium between a pair of genetic markers. Under a model of reciprocal recombination, the decay rate of linkage disequilibrium depends on the distance between the two markers, while under conversion the decay rate is independent of this distance, provided that conversion tracts are short. A population genetic three-locus model provides a function Q of two-locus linkage disequilibria. Viewed as a random variable, Q is the basis for a test of the relative impact of conversion and recombination. This test requires haplotype frequency data of a sufficiently variable three-locus system. One of the few examples currently available is data from the Human Leukocyte Antigen (HLA) class I genes of three Amerindian populations. We find that conversion may have played a dominant role in shaping haplotype patterns over short stretches of DNA, whereas reciprocal recombination may have played a greater role over longer stretches of DNA. However, in order to draw firm conclusions more independent data are necessary.     

Linkage disequilibrium mapping in domestic dog breeds narrows the progressive rod-cone degeneration interval and identifies ancestral disease-transmitting chromosome

Canine progressive rod-cone degeneration (prcd) is a retinal disease previously mapped to a broad, gene-rich centromeric region of canine chromosome 9. As allelic disorders are present in multiple breeds, we used linkage disequilibrium (LD) to narrow the approximately 6.4-Mb interval candidate region. Multiple dog breeds, each representing genetically isolated populations, were typed for SNPs and other polymorphisms identified from BACs. The candidate region was initially localized to a 1.5-Mb zero recombination interval between growth factor receptor-bound protein 2 (GRB2) and SEC14-like 1 (SEC14L). A fine-scale haplotype of the region was developed, which reduced the LD interval to 106 kb and identified a conserved haplotype of 98 polymorphisms present in all prcd-affected chromosomes from 14 different dog breeds. The findings strongly suggest that a common ancestor transmitted the prcd disease allele to many of the modern dog breeds and demonstrate the power of the LD approach in the canine model.     

Linkage disequilibrium, cystic fibrosis, and genetic counseling.

Strong linkage disequilibrium occurs between the cystic fibrosis (CF) locus and polymorphisms detected with the DNA probes XV-2c and KM-19. In a North American population, 86% of CF chromosomes occur with a haplotype which occurs on only 14% of normal chromosomes. An individual homozygous for the highest-risk haplotype has an 81-fold greater probability of carrying a CF allele than does an individual homozygous for the lowest-risk haplotype. The linkage-disequilibrium data can be used for prenatal diagnosis and genetic counseling in CF families. The data are useful in 1-in-4-risk pregnancies when DNA is not available from the propositus and in counseling close relatives of CF families. Serious problems arise with some pregnancies which remain at intermediate risks after analysis, and families are left with difficult decisions. It is not clear that genetic testing for couples at less than 1-in-4 risk is cost-effective or standard care, but use of linkage-disequilibrium data will provide more accurate risk probabilities in a substantial proportion of cases if such testing is carried out. Our results emphasize the need for a specific biological or molecular carrier test. This experience in using linkage-disequilibrium and linkage data in combination for genetic counseling provides a model system for the diagnosis of other disorders.     

Linkage disequilibrium between GABRB3 gene and nonsyndromic familial cleft lip with or without cleft palate

The malformation of nonsyndromic cleft lip with or without cleft palate (CL/P) is a common congenital disease that affects approximately 1/1000 newborns in Caucasian populations. Genetic studies indicate that CL/P has the characteristics of a complex genetic trait. Linkage analysis and mouse-model knockout studies have suggested several candidate genes mapping in different chromosome regions for CL/P malformation. On these grounds, we have investigated, by linkage disequilibrium (LD) and parametric and nonparametric linkage analyses, five different candidate genes, including those for the beta3 subunit of the gamma-aminobutyric acid receptor (GABRB3), glutamic acid decarboxylase 1 (GAD1), retinoic acid receptor alpha (RARA), transforming growth factor beta3 (TGFB3), and msh ( Drosophila) homeobox homolog 1 (MSX1). Interestingly, a significant LD between GABRB3 and CL/P was obtained ( P-value=0.008 in the allele-wise analysis for multiallelic markers), suggesting that the GABRB3 gene is involved in this congenital disease. This new finding in humans is in agreement with previously reported data obtained with the murine model. Indeed, mouse studies indicate a role for gamma-aminobutyric acid (GABA) and its receptor in normal palate development. Exclusion of the GAD1 gene, which encodes the GABA-producing enzyme, in CL/P pathogenesis was obtained in our study. Moreover, we were unable to confirm the involvement of the MSX1 gene in nonsyndromic CL/P. Modest evidence of LD between marker alleles and CL/P was found at the RARA and TGFB3 loci suggesting a minor role for these genes in our family set of nonsyndromic CL/P.     

Effective population size associated with self-fertilization: lessons from temporal changes in allele frequencies in the selfing annual Medicago truncatula

Despite its significance in evolutionary and conservation biology, few estimates of effective population size (N(e)) are available in plant species. Self-fertilization is expected to affect N(e), through both its effect on homozygosity and population dynamics. Here, we estimated N(e) using temporal variation in allele frequencies for two contrasted populations of the selfing annual Medicago truncatula: a large and continuous population and a subdivided population. Estimated N(e) values were around 5-10% of the population census size suggesting that other factors than selfing must contribute to variation in allele frequencies. Further comparisons between monolocus allelic variation and changes in the multilocus genotypic composition of the populations show that the local dynamics of inbred lines can play an important role in the fluctuations of allele frequencies. Finally, comparing N(e) estimates and levels of genetic variation suggest that H(e) is a poor estimator of the contemporaneous variance effective population size.     

Conservation management of rare and predominantly selfing tropical trees: an example using Hopea bilitonensis (Dipterocarpaceae)

Hopea bilitonensis is an extremely rare and predominantly selfing dipterocarp in Peninsular Malaysia. A comprehensive research was initiated to assess the ecological genetics of H. bilitonensis to elucidate specific ecological and genetic requirements and subsequently to recommend conservation strategies. The objective for conservation of a rare plant such as H. bilitonensis differs from that of a common plant. For common plants, the conservation strategies are to prevent the species from becoming endangered. In contrast, for rare plants, the final race against extinction is being fought. Tropical forests are rich in plant species diversity and obtaining adequate knowledge to set conservation strategies for the majority of these species might be difficult. Thus, it is suggested that for the conservation of tree species, the species can be grouped according to their life history traits. The information generated for a species can then be adapted to species that have similar types of life history traits. We have recently generated the ecological genetics information for a rare and predominantly outcrossed dipterocarp (Shorea lumutensis). This study on H. bilitonensis will provide ecological genetics information for the conservation of rare and predominantly selfing dipterocarps.     

Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination-Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.     

Linkage and recombination between fragile X-linked mental retardation and the factor IX gene

Summary Linkage analysis on a family with fragile X-linked mental retardation was performed using a Taq 1 restriction fragment length polymorphism detected by a cloned human coagulation factor IX cDNA. Two affected brothers in this sibship were found to have different factor IX RFLP alleles, indicating a recombinational event occurred between the two genes. Our data therefore indicate that the gene responsible for fragile X-linked mental retardation is not as tightly linked to the factor IX gene as the previously published data may suggest.     

Cytochrome c: gene structure, homology and ancestral relationships.

In this paper, the author notes the recommended definition of the word "homology" (i.e., indicating an ancestral relationship) and the recommended stipulation that "evidence for homology should be explicitly laid out". The postulated homology for somatic and testes-specific isozymes of cytochrome c is then examined, using recent data obtained from the study of cytochrome c genes. Consideration is also given to some newer findings of molecular biology and possibilities are considered for various types of change in the genome of an organism. Possible roles of introns, pseudogenes and multigene families are considered. The relationship of testes-specific cytochrome c to somatic cytochrome c is carefully considered from data obtained in experimental studies of genes of these two isozymes. If one assumes that these isozymes arose as a consequence of a gene duplication, data from rat and mouse genes indicate that the testes-specific isozyme has incorporated more amino acid changes than the somatic isozyme since the time of their divergence. However, when the 15 amino acid differences (testes-specific vs. somatic isozyme) are considered, there is virtually no similarity in these 15 positions of the testes-specific isozyme with any of the hypothetical ancestral sequences of the somatic isozyme. Nucleotide differences in cytochrome c genes have been evaluated by comparing genes for the two rodent cytochrome c isozymes to cytochrome c genes of fruit flies, chickens and humans. Comparisons of nucleotide substitution rates in genes for the two cytochrome c isozymes in rodents confirm the conclusions from amino acid sequence comparisons; namely, that more rapid nucleotide changes have occurred in the testes-specific cytochrome c gene, than in the somatic cytochrome c gene. Possible explanations for these findings are considered.     

Demography,recombination hotspot intensity,and the block structure of linkage disequilibrium

BACKGROUND: Effective gene mapping based on genetic association data will require detailed knowledge of patterns of linkage disequilibrium (LD) in human populations. It has been recently suggested that linkage disequilibrium in humans may be organized in a block-like structure, with islands of high LD separated by regions of rapid breakdown of LD due to recombination hotspots. The experimental data to date, however, are limited, and fundamental questions remain about the implications of recombination rate heterogeneity. Here, we use computer simulations to evaluate how such heterogeneity influences patterns of LD, and we develop formal criteria to assess whether the patterns are functionally block like in the context of association mapping.RESULTS: Our analyses suggest that, even in models of extreme recombination rate heterogeneity, some human populations will have a functionally block-like structure to the pattern of LD, but others will not, depending on their precise demographic histories. In fact, for many models, we find that, following an LD-generating event, populations may move through discrete phases that can be functionally described as pre-block, block, and post-block. An analysis of observed and expected patterns of LD surrounding hotspots within the MHC Class II region confirms these theoretical expectations.CONCLUSIONS: Even if highly punctuated patterns of recombination are the rule, patterns of LD are still likely to show differences among populations and among genomic regions that are of practical importance in the design of genetic association studies. The notion that the average extent of LD is a useful concept for the design of association studies must be abandoned in light of the experimental and theoretical evidence.     

Linkage disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle

When a genetic marker and a quantitative trait locus (QTL) are in linkage disequilibrium (LD) in one population, they may not be in LD in another population or their LD phase may be reversed. The objectives of this study were to compare the extent of LD and the persistence of LD phase across multiple cattle populations. LD measures r and r(2) were calculated for syntenic marker pairs using genomewide single-nucleotide polymorphisms (SNP) that were genotyped in Dutch and Australian Holstein-Friesian (HF) bulls, Australian Angus cattle, and New Zealand Friesian and Jersey cows. Average r(2) was approximately 0.35, 0.25, 0.22, 0.14, and 0.06 at marker distances 10, 20, 40, 100, and 1000 kb, respectively, which indicates that genomic selection within cattle breeds with r(2) >or= 0.20 between adjacent markers would require approximately 50,000 SNPs. The correlation of r values between populations for the same marker pairs was close to 1 for pairs of very close markers (<10 kb) and decreased with increasing marker distance and the extent of divergence between the populations. To find markers that are in LD with QTL across diverged breeds, such as HF, Jersey, and Angus, would require approximately 300,000 markers.     

Linkage disequilibrium analysis identifies an FGFR1 haplotype-tag SNP associated with normal variation in craniofacial shape

Mutations in FGFR1 and TWIST1 have been reported to affect the timing of calvarial suture fusion resulting in craniosynostosis and facial abnormalities. We screened nonpathologic populations for genetic polymorphisms that may associate with normal craniofacial variation. We identified 17 single-nucleotide polymorphisms (SNPs) in FGFR1, 6 of which were novel (g.8591855G-->A, g.8593685G-->A, g.8602303C-->T, g.8602475A-->G (p.Ile293Val), g.8605849C-->T, g.8607868G-->A). No SNPs were found in TWIST1. FGFR1 SNP haplotypes were reconstructed for Caucasian, Asian, Australian Aboriginal, and African American populations. All populations shared two linkage disequilibrium blocks, with one haplotype-tag SNP (htSNP) tagging each block. The htSNP g.8592931G-->C was found to have a significant negative correlation with the cephalic index for all populations (R = -0.187, p = 0.036), with larger correlations in Asians and females. This finding is a starting point in the identification of a set of SNPs that can be genotyped to determine both normal and disease craniofacial phenotypes.