The Effect of a Selected Locus on Linked Neutral Loci

The effects produced on linked neutral loci as a selected locus evolves towards its equilibrium value are considered. Significant effects on the neutral loci arise if the recombination fraction between the neutral and selected loci is smaller than the order of magnitude of the selective differences at the selected locus. The effect on gene frequencies at the neutral loci, that is, the hitchhiking effect, is determined, as well as the linkage disequilibrium generated by this hitchhiking effect. One of the more important findings is that significant disequilibrium can be generated between two neutral loci by the evolution of a linked selected locus. Consideration is given to the problem of determining how the effect of selection operating in natural populations can be detected, the question of the establishment of inversions in populations, and also to the nonequilibrium properties of populations.     

The hitchhiking effect on linkage disequilibrium between linked neutral loci

We analyzed a three-locus model of genetic hitchhiking with one locus experiencing positive directional selection and two partially linked neutral loci. Following the original hitchhiking approach by Maynard Smith and Haigh, our analysis is purely deterministic. In the first half of the selected phase after a favored mutation has entered the population, hitchhiking may lead to a strong increase of linkage disequilibrium (LD) between the two neutral sites if both are <0.1 s away from the selected site (where s is the selection coefficient). In the second half of the selected phase, the main effect of hitchhiking is to destroy LD. This occurs very quickly (before the end of the selected phase) when the selected site is between both neutral loci. This pattern cannot be attributed to the well-known variation-reducing effect of hitchhiking but is a consequence of secondary hitchhiking effects on the recombinants created in the selected phase. When the selected site is outside the neutral loci (which are, say, <0.1s apart), however, a fast decay of LD is observed only if the selected site is in the immediate neighborhood of one of the neutral sites (i.e., if the recombination rate r between the selected site and one of the neutral sites satisfies r<0.1 s). If the selected site is far away from the neutral sites (say, r > 0.3 s), the decay rate of LD approaches that of neutrality. Averaging over a uniform distribution of initial gamete frequencies shows that the expected LD at the end of the hitchhiking phase is driven toward zero, while the variance is increased when the selected site is well outside the two neutral sites. When the direction of LD is polarized with respect to the more common allele at each neutral site, hitchhiking creates more positive than negative linkage disequilibrium. Thus, hitchhiking may have a distinctively patterned LD-reducing effect, in particular near the target of selection.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

Genetic hitchhiking occurs when alleles at unselected loci are changed in frequency because of an association with alleles at a selected locus. This association may be mediated either by linkage or partial selfing (inbreeding) and can affect the gene frequency and gametic disequilibrium at the neutral loci. Hitchhiking from partial selfing (unlinked loci) occurs more quickly than linkage hitchhiking and generally has a greater effect. In addition, partial-selfing hitchhiking can cause increases or changes in sign in gametic disequilibrium between neutral loci. The effects of the two types of hitchhiking with different levels of dominance, zygotic frequencies and number of selected loci are also examined. The general conditions for linkage and partial-selfing hitchhiking are outlined and the implications of hitchhiking are discussed for marker or electrophoretic loci.     

Linkage disequilibrium under genetic hitchhiking in finite populations

The model of genetic hitchhiking predicts a reduction in sequence diversity at a neutral locus closely linked to a beneficial allele. In addition, it has been shown that the same process results in a specific pattern of correlations (linkage disequilibrium) between neutral polymorphisms along the chromosome at the time of fixation of the beneficial allele. During the hitchhiking event, linkage disequilibrium on either side of the beneficial allele is built up whereas it is destroyed across the selected site. We derive explicit formulas for the expectation of the covariance measure D and standardized linkage disequilibrium sigma 2D between a pair of polymorphic sites. For our analysis we use the approximation of a star-like genealogy at the selected site. The resulting expressions are approximately correct in the limit of large selection coefficients. Using simulations we show that the resulting pattern of linkage disequilibrium is quickly-i.e., in <0.1N generations-destroyed after the fixation of the beneficial allele for moderately distant neutral loci, where N is the diploid population size.     

Linkage Disequilibrium in Natural Populations of Trypanosoma cruzi (Flagellate), the Agent of Chagas’ Disease1

ABSTRACT. 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 D_IS² < D_ST², and D'_IS² < D'_ST². 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.     

The influence of gene conversion on linkage disequilibrium around a selective sweep

In a 2007 article, McVean studied the effect of recombination on linkage disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep. The results demonstrated that two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. In this article, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep.     

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.     

Local Patterns of Nucleotide Polymorphism Are Highly Variable in the Selfing Species Arabidopsis thaliana

Neighboring genes predictably share similar evolutionary histories to an extent delineated by recombination. This correlation should extend across multiple linked genes in a selfing species such as Arabidopsis thaliana due to its low effective recombination rate. To test this prediction, we performed a molecular population genetics analysis of nucleotide polymorphism and divergence in chromosomal regions surrounding four low-diversity loci. Three of these loci, At1g67140, At3g03700, and TERMINAL FLOWER1 (TFL1), have been previously implicated as targets of selection and we would predict stronger correlations in polymorphism between neighboring loci due to genetic hitchhiking around these loci. The remaining locus, At1g04300, was identified in a study of linkage disequilibrium surrounding the CRYPTOCHROME2 (CRY2) locus. Although we found broad valleys of reduced nucleotide variation around two of our focal genes, At1g67140 and At3g03700, all chromosomal regions exhibited extreme variation in the patterns of polymorphism and evolution between neighboring loci. Although three of our four regions contained potential targets of selection, application of the composite-likelihood-ratio test of selection in conjunction with a goodness-of-fit test supports the selection hypothesis only for the region containing At3g03700. The degree of discordance in evolutionary histories between linked loci within each region generally correlated with estimates of recombination and linkage disequilibrium for that region, with the exception of the region containing At1g04300. We discuss the implications of these data for future population genetics analyses and genomics studies in A. thaliana. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Dynamics of Correlated Genetic Systems. V. Rates of Decay of Linkage Disequilibria in Experimental Populations of DROSOPHILA MELANOGASTER

The dynamic behavior of four-locus gametic frequency distributions was studied in five replicate cage populations of Drosophila melanogaster for up to 50 generations. The joint frequency distributions were resolved into gene frequencies and various disequilibrium measures. In addition, F statistics for marginal single-locus genotypic frequency distributions were followed through time. The gene frequency, disequilibrium and F statistics were obtained for four chromosome 3 enzyme marker loci [isocitrate dehydrogenase (3–27.1), esterase-6 (3–36.8), phosphoglucomutase (3–43.4) and esterase-C (3–49.0)]. The initial structure of the experimental populations featured random mating proportions, and two complementary gametic types with respect to the marker loci, thus assuring complete pairwise linkage disequilibrium among the markers.——The experimental results indicate: (1) the between-replicate variance in gene frequency varied substantially among loci, with isocitrate dehydrogenase showing the greatest between-replicate variance, and esterase-C the least. (2) The F statistics initially were strongly negative but decayed to the neighborhood of zero for all marker loci except esterase-C. The rate at which the F statistics approached zero varied among the marker loci, indicating substantial differences in the distribution of selective effects along the chromosome. The centromeric region, marked by esterase-C, shows the strongest selective effects. (3) The rate of decay of linkage disequilibrium was much faster than expected for pairs of neutral loci, averaging 1.82 times the neutral rate over all replicates and pairs of loci. This acceleration, which was observed for all six pairwise combinations of loci, was interpreted as resulting from the interaction between selection and recombination. Our experimental results are consistent with many investigations of linkage disequilibrium in natural populations of Drosophila melanogaster that show little or no disequilibrium among enzyme loci. (4) A fortuitous contamination of two cages revealed an apparent regulatory interaction between the migrant and nonmigrant chromosomes at the esterase-C locus. The migrant chromosomes were very rapidly absorbed into the recipient populations, despite this interaction. This result suggests that the dynamics of migration in populations may be phenomenologically richer than anticipated by simple theory.     

Evidence for adaptation from standing genetic variation on an antimicrobial peptide gene in the mussel Mytilus edulis

Genome scans of population differentiation identify candidate loci for adaptation but provide little information on how selection has influenced the genetic structure of these loci. Following a genome scan, we investigated the nature of the selection responsible for the outlying differentiation observed between populations of the marine mussel Mytilus edulis at a leucine/arginine polymorphism (L31R) in the antimicrobial peptide MGD2. We analysed DNA sequence polymorphisms, allele frequencies and population differentiation of polymorphisms closely linked to L31R, and pairwise and third‐order linkage disequilibria. An outlying level of population differentiation was observed at L31R only, while no departure from panmixia was observed at linked loci surrounding L31R, as in most of the genome. Selection therefore seems to affect L31R directly. Three hypotheses can explain the lack of differentiation in the chromosomal region close to L31R: (i) hitchhiking has occurred but migration and recombination subsequently erased the signal, (ii) selection was weak enough and recombination strong enough to limit the hitchhiking effect to a very small chromosomal region or (iii) selection acted on a pre‐existing polymorphism (i.e. standing variation) at linkage equilibrium with its background. Linkage equilibrium was observed between L31R and linked polymorphisms in every population analysed, as expected under the three hypotheses. However, linkage disequilibrium was observed in some populations between pairs of loci located upstream and downstream to L31R, generating a complex pattern of third‐order linkage disequilibria which is best explained by the hypothesis of selection on a pre‐existing polymorphism. We hypothesise that selection could be either balanced, maintaining alleles at different frequencies depending on the pathogen community encountered locally by mussels, or intermittent, resulting in sporadic fluctuations in allele frequency.     

A microsatellite-based analysis for the detection of selection on BTA1 and BTA20 in northern Eurasian cattle (Bos taurus) populations

Background

Microsatellites surrounding functionally important candidate genes or quantitative trait loci have received attention as proxy measures of polymorphism level at the candidate loci themselves. In cattle, selection for economically important traits is a long-term strategy and it has been reported that microsatellites are linked to these important loci.

Methods

We have investigated the variation of seven microsatellites on BTA1 (Bos taurus autosome 1) and 16 on BTA20, using bovine populations of typical production types and horn status in northern Eurasia. Genetic variability of these loci and linkage disequilibrium among these loci were compared with those of 28 microsatellites on other bovine chromosomes. Four different tests were applied to detect molecular signatures of selection.

Results

No marked difference in locus variability was found between microsatellites on BTA1, BTA20 and the other chromosomes in terms of different diversity indices. Average D'' values of pairwise syntenic markers (0.32 and 0.28 across BTA 1 and BTA20 respectively) were significantly (P < 0.05) higher than for non-syntenic markers (0.15). The Ewens-Watterson test, the Beaumont and Nichol''s modified frequentist test and the Bayesian F_ST-test indicated elevated or decreased genetic differentiation, at SOD1 and AGLA17 markers respectively, deviating significantly (P < 0.05) from neutral expectations. Furthermore, lnRV, lnRH and lnRθ'' statistics were used for the pairwise population comparison tests and were significantly less variable in one population relative to the other, providing additional evidence of selection signatures for two of the 51 loci. Moreover, the three Finnish native populations showed evidence of subpopulation divergence at SOD1 and AGLA17. Our data also indicate significant intergenic linkage disequilibrium around the candidate loci and suggest that hitchhiking selection has played a role in shaping the pattern of observed linkage disequilibrium.

Conclusion

Hitchhiking due to tight linkage with alleles at candidate genes, e.g. the POLL gene, is a possible explanation for this pattern. The potential impact of selective breeding by man on cattle populations is discussed in the context of selection effects. Our results also suggest that a practical approach to detect loci under selection is to simultaneously apply multiple neutrality tests based on different assumptions and estimations.     

Genetic Variation and Differentiation among Populations of Chum Salmon Oncorhynchus ketaWalbaum from Southern Russian Far East

Allozyme variation of populations of chum salmon Oncorhynchus ketafrom southern Russian Far East was examined. Of 55 loci screened, 31 were polymorphic. Within-population variation accounted for most of the allele diversity; F _STaveraged over loci was 0.052. Linkage disequilibrium was found in less than 5% of locus pairs in the chum population examined. Analysis of within- and among-population variance components of linkage disequilibrium using D-statistics (Ohta, 1982) showed that most genetic variation was distributed among populations.     

Background selection and population differentiation

A general analytical formula is derived, which predicts the effects of background selection on population differentiation at a neutral locus as a result of its linkage with selected loci of deleterious mutations. The theory is based on the assumptions of random mating, multiplicative fitness, and weak selection in hermaphrodite plants in the island model of population structure. The analytical results show that Fst at the neutral locus increases as a result of the effects of background selection, regardless of the dependence or independence among linked background selective loci. The increment in Fst is closely related to the magnitude of linkage disequilibria between the neutral locus and selected loci, and can be estimated by the ratio of Fst with background selection to Fst without background selection minus one. The steady-state linkage disequilibrium between a neutral locus and a selected locus in subpopulations, primarily attained by gene flow, decreases with the recombination rate, and can be enhanced when there are dependence among linked selected loci. Monte Carlo computer simulations with two- and three-locus models show that the analytical formulae perform well under general conditions. Application of the present theory may aid in analyzing the genome-wide mapping of the effect of background selection in terms of Fst.     

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.     

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.     

Evolution at the tip and base of the X chromosome in an African population of Drosophila melanogaster

Hitchhiking effects of advantageous mutations have been invoked to explain reduced polymorphism in regions of low crossing-over in Drosophila. Besides reducing DNA heterozygosity, hitchhiking effects should produce strong linkage disequilibrium and a frequency spectrum skewed toward an excess of rare polymorphisms (compared to the neutral expectation). We measured DNA polymorphism in a Zimbabwe population of D. melanogaster at three loci, yellow, achaete, and suppressor of forked, located in regions of reduced crossing-over. Similar to previously published surveys of these genomic regions in other populations, we observed low levels of nucleotide variability. However, the frequency spectrum was compatible with a neutral model, and there was abundant evidence for recombination in the history of the yellow and ac genes. Thus, some aspects of the data cannot be accounted for by a simple hitchhiking model. An alternative hypothesis, background selection, might be compatible with the observed patterns of linkage disequilibrium and the frequency spectrum. However, this model cannot account for the observed reduction in nucleotide heterozygosity. Thus, there is currently no satisfactory theoretical model for the data from the tip and base of the X chromosome in D. melanogaster.      

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.     

Three-Locus Systems Impose Additional Constraints on Pairwise Disequilibria

Combinations of allele frequencies and pairwise linkage disequilibrium terms, each of which is permissible at the two-locus level, may not always be permissible at the three-locus level. These additional constraints on the possible maximum and minimum values for the pairwise disequilibrium terms are formally determined and numerically analyzed. In some cases, the three-locus constraints on a pairwise disequilibrium (D) may be equivalent to the usual two-locus constraints, while in others, the positive or negative range may be restricted. This can result in situations where the allowable values of D are limited to only positive or only negative values up to the extreme case where there is only a single admissible value. No additional restrictions are placed on pairwise disequilibrium values when four loci are considered, other than those imposed by the three-way combinations containing the two loci of interest. A new measure of normalized pairwise linkage disequilibrium, allowing for the three-locus constraints, is defined and illustrated by an application to data from the human histocompatibility antigen (HLA) system. An analogous normalized three-way disequilibrium measure is also formulated.