Linkage disequilibrium and recent selection at three immunity receptor loci in Drosophila simulans

Immune system genes in a California population sample of Drosophila simulans were shown to bear several hallmarks of the effects of past directional selection. One potential effect of directional selection is an increase in linkage disequilibrium among the polymorphic sites that are linked to the site under selection. In this study, we focus on three D. simulans immunity loci, Hmu, Sr-CI/Sr-CIII, and Tehao, for which the polymorphic sites are in nearly perfect linkage disequilibrium, an unusual finding even with respect to other immunity genes sampled from the same lines. The most likely explanation for this finding is that, at each locus, two divergent alleles have been selected to intermediate frequencies in the recent past. The extent to which the linkage disequilibrium extends to the flanks of each of the immunity genes is minimal, suggesting that the favored mutations actually occurred within the immunity genes themselves. Furthermore, the excess linkage disequilibrium found in the California population is not found in an African D. simulans population sample and may be a result of novel pathogen-mediated selection pressures encountered during establishment of non-African populations.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

RESPONSE TO SELECTION IN PARTIALLY SELF-FERTILIZING POPULATIONS. II. SELECTION ON MULTIPLE TRAITS

The structured linear model (SLM) is generalized to treat selection on multiple, correlated characters. Four different causes of phenotypic correlations are distinguished by the SLM: environmental covariance, identity disequilibrium, pleiotropy, and linkage disequilibrium. Each is characterized by distinct variables because they have different implications for character evolution. Correlations due to identity disequilibrium and linkage disequilibrium depend on both the mating system and the selection regime. As a consequence, they will evolve rapidly under selection. Correlations due to pleiotropy or environmental factors will evolve more slowly and are characterized by parameters that can be estimated from comparisons among relatives. These parameters include several novel “inbreeding covariance components” that emerge from the interaction of inbreeding and genetic dominance. Although data are limited, current estimates suggest that the expression of these components may substantially alter the pattern of multitrait evolution in self-fertilizing populations.     

Amino Acid Covariation in a Functionally Important Human Immunodeficiency Virus Type 1 Protein Region Is Associated With Population Subdivision

The frequently reported amino acid covariation of the highly polymorphic human immunodeficiency virus type 1 (HIV-1) exterior envelope glycoprotein V3 region has been assumed to reflect fitness epistasis between residues. However, nonrandom association of amino acids, or linkage disequilibrium, has many possible causes, including population subdivision. If the amino acids at a set of sequence sites differ in frequencies between subpopulations, then analysis of the whole population may reveal linkage disequilibrium even if it does not exist in any subpopulation. HIV-1 has a complex population structure, and the effects of this structure on linkage disequilibrium were investigated by estimating within- and among-subpopulation components of variance in linkage disequilibrium. The amino acid covariation previously reported is explained by differences in amino acid frequencies among virus subpopulations in different patients and by nonsystematic disequilibrium among patients. Disequilibrium within patients appears to be entirely due to differences in amino acid frequencies among sampling time points and among chemokine coreceptor usage phenotypes of virus particles, but not source tissues. Positive selection explains differences in allele frequencies among time points and phenotypes, indicating that these differences are adaptive rather than due to genetic drift. However, the absence of a correlation between linkage disequilibrium and phenotype suggests that fitness epistasis is an unlikely cause of disequilibrium. Indeed, when population structure is removed by analyzing sequences from a single time point and phenotype, no disequilibrium is detectable within patients. These results caution against interpreting amino acid covariation and coevolution as evidence for fitness epistasis.     

A Linkage Disequilibrium–Based Approach to Selecting Disease-Associated Rare Variants

Rare variants have increasingly been cited as major contributors in the disease etiology of several complex disorders. Recently, several approaches have been proposed for analyzing the association of rare variants with disease. These approaches include collapsing rare variants, summing rare variant test statistics within a particular locus to improve power, and selecting a subset of rare variants for association testing, e.g., the step-up approach. We found that (a) if the variants being pooled are in linkage disequilibrium, the standard step-up method of selecting the best subset of variants results in loss of power compared to a model that pools all rare variants and (b) if the variants are in linkage equilibrium, performing a subset selection using step-based selection methods results in a gain of power of association compared to a model that pools all rare variants. Therefore, we propose an approach to selecting the best subset of variants to include in the model that is based on the linkage disequilibrium pattern among the rare variants. The proposed linkage disequilibrium–based variant selection model is flexible and borrows strength from the model that pools all rare variants when the rare variants are in linkage disequilibrium and from step-based selection methods when the variants are in linkage equilibrium. We performed simulations under three different realistic scenarios based on: (1) the HapMap3 dataset of the DRD2 gene, and CHRNA3/A5/B4 gene cluster (2) the block structure of linkage disequilibrium, and (3) linkage equilibrium. We proposed a permutation-based approach to control the type 1 error rate. The power comparisons after controlling the type 1 error show that the proposed linkage disequilibrium–based subset selection approach is an attractive alternative method for subset selection of rare variants.     

Disequilibrium Pattern Analysis. I. Theory

We have developed a method, disequilibrium pattern analysis, for examining the disequilibrium distribution of the entire array of two locus multiallelic haplotypes in a population. It is shown that a selected haplotype will produce a distinct pattern of linkage disequilibrium values for all generations while the selection is acting. This pattern will also presumably be maintained for many generations after the selection event, until the disequilibrium pattern is eventually broken down by genetic drift and recombination. Related haplotypes, sharing an allele with a selected haplotype, assume a value of linkage disequilibrium proportional to the frequency of the unshared allele and have a single negative value of the normalized linkage disequilibrium. The analysis assumes zero linkage disequilibrium for all allelic combinations initially. The same basic results continue to apply if the selection involves a new mutant, the occurrence of which creates linkage disequilibrium for some haplotypes. The disequilibrium pattern predicted under selection is robust with respect to the influence of migration and random genetic drift. This method is applicable to population data having linked polymorphic loci including that determined from protein or DNA sequencing.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Selection and genetic drift of polymorphisms within the merozoite surface protein-1 gene of Plasmodium falciparum

Intragenic recombination in the merozoite surface protein-1 gene (Msp-1) of Plasmodium falciparum is a major mechanism for allelic variation among natural parasite populations. The frequency of recombination depends on the intensity of transmission in the vector mosquito. In the present study, linkage disequilibrium between polymorphic 'loci' in the 5'- and 3'-regions of Msp-1 was examined in parasite populations from Brazilian Amazon and southern Vietnam and compared with that in a Thai population previously reported. The R2 test identified clusters of linkage disequilibria between the 5'- and 3'-regions, which are different among the three populations. However, the overall strength of linkage disequilibria was stronger in Brazil, a hypoendemic area, than in Vietnam and Thailand, mesoendemic areas, suggesting that linkage disequilibrium in Msp-1 inversely correlates with the intensity of transmission. To investigate possible mechanisms for linkage disequilibrium in Msp-1, we applied the Fst index, which measures the inter-population variance in allele frequency, to 'loci' in Msp-1 among the three populations. The Fst test identified two distinct regions with respect to inter-population allele frequency in Msp-1: one for highly divergent 'loci' in the 5'-region and the other for non-divergent 'loci' in the 3'-region. These results suggest that genetic drift is not the sole mechanism for linkage disequilibrium, but selection operates on 'loci' in the 3'-region in hypo- and mesoendemic areas of malaria.     

Exome-based linkage disequilibrium maps of individual genes: functional clustering and relationship to disease

Exome sequencing identifies thousands of DNA variants and a proportion of these are involved in disease. Genotypes derived from exome sequences provide particularly high-resolution coverage enabling study of the linkage disequilibrium structure of individual genes. The extent and strength of linkage disequilibrium reflects the combined influences of mutation, recombination, selection and population history. By constructing linkage disequilibrium maps of individual genes, we show that genes containing OMIM-listed disease variants are significantly under-represented amongst genes with complete or very strong linkage disequilibrium (P = 0.0004). In contrast, genes with disease variants are significantly over-represented amongst genes with levels of linkage disequilibrium close to the average for genes not known to contain disease variants (P = 0.0038). Functional clustering reveals, amongst genes with particularly strong linkage disequilibrium, significant enrichment of essential biological functions (e.g. phosphorylation, cell division, cellular transport and metabolic processes). Strong linkage disequilibrium, corresponding to reduced haplotype diversity, may reflect selection in utero against deleterious mutations which have profound impact on the function of essential genes. Genes with very weak linkage disequilibrium show enrichment of functions requiring greater allelic diversity (e.g. sensory perception and immune response). This category is not enriched for genes containing disease variation. In contrast, there is significant enrichment of genes containing disease variants amongst genes with more average levels of linkage disequilibrium. Mutations in these genes may less likely lead to in utero lethality and be subject to less intense selection.     

On Models of Quantitative Genetic Variability: A Stabilizing Selection-Balance Model

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.     

Sample sizes required to detect linkage disequilibrium between two or three loci.

Estimates of the degree of nonrandom association among genes (linkage disequilibrium) can provide evidence of the role of natural selection in maintaining allozyme polymorphisms in natural populations. This paper outlines the maximum likelihood procedures for such estimates based on gametic or zygotic frequencies at the level of two loci. The analysis is extended to estimating disequilibrium between three loci. In particular, the question of the sampling requirements to detect different intensities of disequilibrium is considered. It is found that relatively large samples are required to detect nonrandom association, unless gene frequencies are intermediate and disequilibrium is relatively intense. This might be one reason why cases of linkage disequilibrium have so far proved to be the exception, rather than the rule, in population studies.     

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.     

Gene Flow and Selection in a Two-Locus System

A model of gene flow and selection in two linked loci is analyzed. The problems considered are the effects of linkage on the clines in frequencies at the two loci and the role of gene flow in producing linkage disequilibrium between the loci. Also, the possible significance of linkage as a mechanism for permitting a population of "track" spatial changes in the environment is considered. The results are that when the recombination fraction between the loci is of the same order of magnitude as the selection coefficients or smaller, then linkage is important in determining the gene frequencies and a substantial amount of linkage disequilibrium is present in the cline. Depending on the spatial pattern of selection on the two loci, linkage can either decrease or increase a population's response to local selection.     

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.     

Nucleotide variability at G6pd and the signature of malarial selection in humans

Glucose-6-phosphate dehydrogenase (G6PD) deficiency is the most common enzymopathy in humans. Deficiency alleles for this X-linked disorder are geographically correlated with historical patterns of malaria, and the most common deficiency allele in Africa (G6PD A-) has been shown to confer some resistance to malaria in both hemizygous males and heterozygous females. We studied DNA sequence variation in 5.1 kb of G6pd from 47 individuals representing a worldwide sample to examine the impact of selection on patterns of human nucleotide diversity and to infer the evolutionary history of the G6PD A- allele. We also sequenced 3.7 kb of a neighboring locus, L1cam, from the same set of individuals to study the effect of selection on patterns of linkage disequilibrium. Despite strong clinical evidence for malarial selection maintaining G6PD deficiency alleles in human populations, the overall level of nucleotide heterozygosity at G6pd is typical of other genes on the X chromosome. However, the signature of selection is evident in the absence of genetic variation among A- alleles from different parts of Africa and in the unusually high levels of linkage disequilibrium over a considerable distance of the X chromosome. In spite of a long-term association between Plasmodium falciparum and the ancestors of modern humans, patterns of nucleotide variability and linkage disequilibrium suggest that the A- allele arose in Africa only within the last 10,000 years and spread due to selection.     

Linkage disequilibrium in natural populations of Trypanosoma cruzi (flagellate), the agent of Chagas' disease

We have studied linkage disequilibrium in natural populations of Trypanosoma cruzi, the agent of Chagas' disease, by analyzing (i) a set of 524 stocks from the whole geographical range of the parasite, characterized at four gene loci coding for enzymes; (ii) a subsample of 121 stocks characterized at 12 enzyme loci; and (iii) a subset of 386 stocks from six locations in Bolivia, characterized by four enzyme loci. Our results show that the linkage disequilibrium reaches the maximum possible value, given the observed allelic frequencies, for almost all the locus pairs. This result is most consistent with the hypothesis that genetic recombination is absent or very rare in T. cruzi natural populations. Partition of the linkage disequilibrium variance for the six Bolivian populations shows that both inter- and intrapopulation components are substantial and that the relationships among the components are D2IS less than D2ST, and D'2IS less than D'2ST. These inequalities are interpreted as the result of an interplay between genetic drift, rare or absent mating, and clonal selection in generating linkage disequilibrium in T. cruzi populations.     

On the utility of linkage disequilibrium as a statistic for identifying targets of positive selection in nonequilibrium populations

A critically important challenge in empirical population genetics is distinguishing neutral nonequilibrium processes from selective forces that produce similar patterns of variation. We here examine the extent to which linkage disequilibrium (i.e., nonrandom associations between markers) improves this discrimination. We show that patterns of linkage disequilibrium recently proposed to be unique to hitchhiking models are replicated under nonequilibrium neutral models. We also demonstrate that jointly considering spatial patterns of association among variants alongside the site-frequency spectrum is nonetheless of value. Through a comparison of models of equilibrium neutrality, nonequilibrium neutrality, equilibrium hitchhiking, nonequilibrium hitchhiking, and recurrent hitchhiking, we evaluate a linkage disequilibrium (LD) statistic (omega(max)) that appears to have power to identify regions recently shaped by positive selection. Most notably, for demographic parameters relevant to non-African populations of Drosophila melanogaster, we demonstrate that selected loci are distinguishable from neutral loci using this statistic.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.