Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

Markers linked to vegetative incompatibility (vic) genes and a region of high heterogeneity and reduced recombination near the mating type locus (MAT) in Cryphonectria parasitica

To find markers linked to vegetative incompatibility (vic) genes in the chestnut blight fungus, Cryphonectria parasitica, we constructed a preliminary linkage map. In general, this map is characterized by low levels of polymorphism, as evident from the more than 24 linkage groups observed, compared to seven expected from electrophoretic karyotyping. Nonetheless, we found markers closely linked to two vic genes (vic1 and vic2) making them candidates for positional cloning. Two markers were found to be linked to vic2: one cosegregated with vic2, i.e., it is 0.0 cM from vic2, the other was at a distance of 4.5 cM; a single marker was found 4.0 cM from vic1. The closest markers linked to three other vic genes (vic4, vic6, and vic7) were >15 cM away; additional markers are needed before efficient positional cloning of these three vic genes can be realized. In contrast to the low levels of polymorphism observed across most of the C. parasitica genome, the linkage group containing the MAT locus appears to harbor an extremely high level of RAPD heterogeneity and reduced recombination. Markers within this highly heterogeneous region are in linkage disequilibrium in some natural populations; however, recombination is clearly evident between this region and the MAT locus.     

Lower-than-expected linkage disequilibrium between tightly linked markers in humans suggests a role for gene conversion

Understanding the pattern of linkage disequilibrium (LD) in the human genome is important both for successful implementation of disease-gene mapping approaches and for inferences about human demographic histories. Previous studies have examined LD between loci within single genes or confined genomic regions, which may not be representative of the genome; between loci separated by large distances, where little LD is seen; or in population groups that differ from one study to the next. We measured LD in a large set of locus pairs distributed throughout the genome, with loci within each pair separated by short distances (average 124 bp). Given current models of the history of the human population, nearly all pairs of loci at such short distances would be expected to show complete LD as a consequence of lack of recombination in the short interval. Contrary to this expectation, a significant fraction of pairs showed incomplete LD. A standard model of recombination applied to these data leads to an estimate of effective human population size of 110,000. This estimate is an order of magnitude higher than most estimates based on nucleotide diversity. The most likely explanation of this discrepancy is that gene conversion increases the apparent rate of recombination between nearby loci.     

A method for estimating the mutation,gene conversion and recombination parameters in small multigene families

A simple two-locus gene conversion model is considered to investigate the amounts of DNA variation and linkage disequilibrium in small multigene families. The exact solutions for the expectations and variances of the amounts of variation within and between two loci are obtained. It is shown that gene conversion increases the amount of variation within each locus and decreases the amount of variation between two loci. The expectation and variance of the amount of linkage disequilibrium are also obtained. Gene conversion generates positive linkage disequilibrium and the degree of linkage disequilibrium decreases as the recombination rate is increased. Using the theoretical results, a method for estimating the mutation, gene conversion, and recombination parameters is developed and applied to the data of the Amy multigene family in Drosophila melanogaster. The gene conversion rate is estimated to be approximately 60-165 times higher than the mutation rate for synonymous sites.     

Expected Linkage Disequilibrium for a Neutral Locus Linked to a Chromosomal Arrangement

The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.     

Contrasting evolutionary histories of two introns of the duchenne muscular dystrophy gene, Dmd, in humans

The Duchenne muscular dystrophy (Dmd) locus lies in a region of the X chromosome that experiences a high rate of recombination and is thus expected to be relatively unaffected by the effects of selection on nearby genes. To provide a picture of nucleotide variability at a high-recombination locus in humans, we sequenced 5. 4 kb from two introns of Dmd in a worldwide sample of 41 alleles from Africa, Asia, Europe, and the Americas. These same regions were also sequenced in one common chimpanzee and one orangutan. Dramatically different patterns of genetic variation were observed at these two introns, which are separated by >500 kb of DNA. Nucleotide diversity at intron 44 pi = 0.141% was more than four times higher than nucleotide diversity at intron 7 pi = 0.034% despite similar levels of divergence for these two regions. Intron 7 exhibited significant linkage disequilibrium extending over 10 kb and also showed a significant excess of rare polymorphisms. In contrast, intron 44 exhibited little linkage disequilibrium and no skew in the frequency distribution of segregating sites. Intron 7 was much more variable in Africa than in other continents, while intron 44 displayed similar levels of variability in different geographic regions. Comparison of intraspecific polymorphism to interspecific divergence using the HKA test revealed a significant reduction in variability at intron 7 relative to intron 44, and this effect was most pronounced in the non-African samples. These results are best explained by positive directional selection acting at or near intron 7 and demonstrate that even genes in regions of high recombination may be influenced by selection at linked sites.     

Linkage disequilibria between pairs of loci within a highly polymorphic region of chromosome 2Q.

A recently described region on chromosome 2q contains seven restriction fragment length polymorphisms (RFLPs) revealed by single-copy probes isolated from a 20-kilobase (kb) segment of a single cosmid insert. Analysis of six of these loci demonstrates modest amounts of linkage disequilibrium. This reflects the presence of a substantial number of different haplotypes in this chromosome region and indicates that the region could be used as one highly polymorphic locus. No consistent relationship is found between the amount of linkage disequilibrium and the physical distance between pairs of loci. For seven of the 10 pairs of diallelic loci studied, the observed disequilibrium can be attributed primarily to the absence of the minor haplotype from the population. These results suggest that, for small regions of the genome, factors such as mutation, genetic drift, and population admixture may have effects that outweight those of recombination. In addition, results are reviewed which show that estimates of linkage disequilibrium coefficients for tightly linked loci are very imprecise. Thus, the inference of gene order from linkage disequilibrium values must be regarded with caution.     

Disequilibrium in Two-Locus Mutation-Selection Balance Models

Equilibrium behavior of two-locus mutation-selection balance models is analyzed using perturbation techniques. The classical result of Haldane for one locus is shown to carry over to two loci, if fitnesses are replaced by marginal fitnesses. If the fitness of the double heterozygote is smaller than would be produced by a multiplicative model, as in additive or quantitative fitness models, the disequilibrium is negative--an excess of gametes with one rare allele. In this case the disequilibrium can be as large as one-half its maximum value possible, if the recombination rate is small, not greater than the strength of selection. If the fitness of the double heterozygote is larger than would be produced by a multiplicative model, the disequilibrium is positive, and is very small relative to its maximum value possible, even if the recombination rate is zero.     

Protein variation in Adh and Adh-related in Drosophila pseudoobscura. Linkage disequilibrium between single nucleotide polymorphisms and protein alleles

A 3.5-kb segment of the alcohol dehydrogenase (Adh) region that includes the Adh and Adh-related genes was sequenced in 139 Drosophila pseudoobscura strains collected from 13 populations. The Adh gene encodes four protein alleles and rejects a neutral model of protein evolution with the McDonald-Kreitman test, although the number of segregating synonymous sites is too high to conclude that adaptive selection has operated. The Adh-related gene encodes 18 protein haplotypes and fails to reject an equilibrium neutral model. The populations fail to show significant geographic differentiation of the Adh-related haplotypes. Eight of 404 single nucleotide polymorphisms (SNPs) in the Adh region were in significant linkage disequilibrium with three ADHR protein alleles. Coalescent simulations with and without recombination were used to derive the expected levels of significant linkage disequilibrium between SNPs and 18 protein haplotypes. Maximum levels of linkage disequilibrium are expected for protein alleles at moderate frequencies. In coalescent models without recombination, linkage disequilibrium decays between SNPs and high frequency haplotypes because common alleles mutate to haplotypes that are rare or that reach moderate frequency. The implication of this study is that linkage disequilibrium mapping has the highest probability of success with disease-causing alleles at frequencies of 10%.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

Linkage analysis of "necessary" disease loci versus "susceptibility" loci.

The association of some diseases with specific alleles of certain genetic markers has been difficult to explain. Several explanations have been proposed for the phenomenon of association, e.g. the existence of multiple, interacting genes (epistasis) or a disease locus in linkage disequilibrium with the marker locus. One might suppose that when marker data from families with associated diseases are analyzed for linkage, the existence of the association would assure that linkage will be found, and found at a tight recombination fraction. In fact, however, linkage analyses of some diseases associated with HLA, as well as diseases associated with alleles at other loci located throughout the genome, show significant evidence against linkage, and others show loose linkage, to the puzzlement of many researchers. In part, the puzzlement arises because linkage analysis is ideal for looking for loci that are necessary, even if not sufficient, for disease expression but may be much less useful for finding loci that are neither necessary nor sufficient for disease expression (so-called susceptibility loci). This work explores what happens when one looks for linkage to susceptibility loci. A susceptibility locus in this case means that the allele increases risk but is neither necessary nor sufficient for disease expression. It might be either an allele at the marker locus itself that is increasing susceptibility or an allele at a locus in linkage disequilibrium with the marker. This work uses computer simulation to examine how linkage analyses behave when confronted with data from such a model.(ABSTRACT TRUNCATED AT 250 WORDS)     

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。     

Linkage disequilibrium under skewed offspring distribution among individuals in a population

Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size. The correlations depend on the rates of recombination and random drift and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events. Since a prediction of linkage disequilibrium can be written in terms of correlations in coalescence times, it follows that the prediction of linkage disequilibrium is a function not only of the rate of recombination but also of the reproduction parameters. Low linkage disequilibrium is predicted if the offspring of a single individual frequently replace almost the entire population. However, high linkage disequilibrium can be predicted if the offspring of a single individual replace an intermediate fraction of the population. In some cases the model reproduces the standard Wright-Fisher predictions. Contrary to common intuition, high linkage disequilibrium can be predicted despite frequent recombination, and low linkage disequilibrium under infrequent recombination. Simulations support the analytical results but show that the variance of linkage disequilibrium is very large.     

A genome-wide departure from the standard neutral model in natural populations of Drosophila

We analyze nucleotide polymorphism data for a large number of loci in areas of normal to high recombination in Drosophila melanogaster and D. simulans (24 and 16 loci, respectively). We find a genome-wide, systematic departure from the neutral expectation for a panmictic population at equilibrium in natural populations of both species. The distribution of sequence-based estimates of 2Nc across loci is inconsistent with the assumptions of the standard neutral theory, given the observed levels of nucleotide diversity and accepted values for recombination and mutation rates. Under these assumptions, most estimates of 2Nc are severalfold too low; in other words, both species exhibit greater intralocus linkage disequilibrium than expected. Variation in recombination or mutation rates is not sufficient to account for the excess of linkage disequilibrium. While an equilibrium island model does not seem to account for the data, more complicated forms of population structure may. A proper test of alternative demographic models will require loci to be sampled in a more consistent fashion.     

The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

Hitchhiking and recombination in birds: evidence from Mhc-linked and unlinked loci in Red-winged Blackbirds (Agelaius phoeniceus)

Hitchhiking phenomena and genetic recombination have important consequences for a variety of fields for which birds are model species, yet we know virtually nothing about naturally occurring rates of recombination or the extent of linkage disequilibrium in birds. We took advantage of a previously sequenced cosmid clone from Red-winged Blackbirds (Agelaius phoeniceus) bearing a highly polymorphic Mhc class II gene, Agph-DABI, to measure the extent of linkage disequilibrium across approximately 40 kb of genomic DNA and to determine whether non-coding nucleotide diversity was elevated as a result of physical proximity to a target of balancing selection. Application of coalescent theory predicts that the hitchhiking effect is enhanced by the larger effective population size of blackbirds compared with humans, despite the presumably higher rates of recombination in birds. We surveyed sequence polymorphism at three Mhc-linked loci occurring 1.5-40 kb away from Agph-DAB1 and found that nucleotide diversity was indistinguishable from that found at three presumably unlinked, non-coding introns (beta-actin intron 2, beta-fibrinogen intron 7 and rhodopsin intron 2). Linkage disequilibrium as measured by Lewontin's D' was found only across a few hundred base pairs within any given locus, and was not detectable among any Mhc-linked loci. Estimated rates of the per site recombination rate p derived from three different analytical methods suggest that the amounts of recombination in blackbirds are up to two orders of magnitude higher than in humans, a discrepancy that cannot be explained entirely by the higher effective population size of blackbirds relative to humans. In addition, the ratio of the number of estimated recombination events per mutation frequently exceeds 1, as in Drosophila, again much higher than estimates in humans. Although the confidence limits of the blackbird estimates themselves span an order of magnitude, these data suggest that in blackbirds the hitchhiking effect for this region is negligible and may imply that the per site per individual recombination rate is high, resembling those of Drosophila more than those of humans.     

The dynamics of interlocus associations in the three-locus hitchhiking model

The hitchhiking effects of a selected locus upon the dynamics of the pairwise association,D _nn between two neutral loci is examined analytically for the special case where at least one of the neutral loci is in linkage equilibrium with the selected locus. The results apply approximately whenever the product of the pairwise associations between the selected locus and each neutral locus is negligible with respect to the three-way linkage disequilibrium. It is shown that precisely four broad classes of trajectories are possible, whether the selected locus is between (nsn) or to one side (snn) of the neutral loci, and whatever the mode of selection operating.D _nn may: (1) decay rapidly to zero, at a rate faster in each generation than that expected for two isolated neutral loci; (2) monotonically decay to zero at a rate which is slower in every generation than under the usual neutral regime; (3) increase initially and/or in intermediate periods before eventually slowly decaying to zero; or (4) exhibit type 1 behavior in the first segment of the trajectory and either type 2 or 3 behavior in the subsequent generations, with the transition marked by a change in sign. The nature of a given trajectory is largely determined by the direction of gene frequency change at the selected locus, and the initial signs of bothD _nn and the three-way linkage disequilibrium.The single most important consequence of these results is that there is no simple relation between the amount of pairwise association between two neutral markers and the recombination fraction between them. Several factors influencing the magnitude of the hitchhiking effect are also examined. It is shown that, all else being equal, the greater the three-way linkage disequilibrium, the greater the departure ofD _nn from the expected neutral dynamic. Increased recombination among the loci reduces the hitchhiking effect onD _nn . The dependence of the behavior upon the exact position of the selected locus is also determined both within and betweennsn andsnn chromosomal systems. An interesting discovery is that given equivalentnsn andsnn systems, with each having the same recombination between their two neutral loci,D _nn will deviate more from the standard neutral dynamic in thesnn system if its selected locus is sufficiently tightly linked to the neutral loci.     

FROM CLONAL TO SEXUAL HYBRIDS: GENETIC RECOMBINATION VIA TRIPLOIDS IN ALL-HYBRID POPULATIONS OF WATER FROGS

Speciation via interspecific hybrids is very rare in animals, as compared to plants. Whereas most plants overcome the problem of meiosis between different chromosome sets by tetraploidization, animal hybrids often escape hybrid sterility by clonal reproduction. This comes at the expense of genetic diversity and the ability to purge deleterious mutations. However, here we show that all-hybrid populations of diploid (LR) and triploid (LLR and LRR) water frogs ( Pelophylax esculentus ) have secondarily acquired sexual reproduction. First, in a crossing experiment analyzed with microsatellite markers, triploid hybrids of both sexes and genotypes (LLR and LRR) recombined their homospecific genomes. Second, the great majority of natural populations investigated had low multilocus linkage disequilibrium, indicating a high recombination rate. As predicted from mating system models, the L genome had constant, low levels of linkage disequilibrium, whereas linkage disequilibrium in the R genome showed a significant reduction with increasing proportion of recombining triploids. This direct evidence of sexual reproduction in P. esculentus calls for a change of the conventional view of hybridogens as clonally reproducing diploids. Rather, hybridogens can be independent sexually reproducing units with an evolutionary potential.