The Genetics of DROSOPHILA SUBOBSCURA Populations. IX. Studies on Linkage Disequilibrium in Four Natural Populations

Gametic frequencies were obtained in four natural populations of D. sub-obscura by extracting wild chromosomes and subsequently analyzing them for inversions and allozymes. The genes Lap and Pept-1, both located within the same inversions of chromosome O, were found in striking nonrandom associations with them of the same kind and degree in all populations studied. On the contrary, the gene Acph, also located within the previously mentioned inversions, was found in linkage disequilibrium with them only in two populations and of opposite directions. This is also the case for the genes Est-9 and Hk, both located within chromosome E inversions. While the gene Est-9 was in strong linkage disequilibrium with the inversions, of the same kind and degree in all populations studied, Hk was found to be in linkage equilibrium. Allele frequencies for the 29 genes studied do not show geographical variation except for the genes Lap, Pept-1 and Est-9, the ones found in linkage disequilibria with the geographically varying gene arrangements. Although mechanical or historical explanations for these equilibria cannot be ruled out, these data cannot be explained satisfactorily by the "middle gene explanation," which states that loci displaying such linkage disequilibria are the ones located near the break points of inversions, while the ones displaying linkage equilibria with them are located in the middle of them. There is no evidence for consistent linkage disequilibria between pairs of loci, except for the closely linked genes of the complex locus, Est-9. This would imply, if it is not a peculiarity of the Est-9 complex, that the linkage disequilibria are found only between very closely linked loci or that, for less closely linked genes, the associations are too weak to be detected by the usual samples sizes.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER Xiii. Further Studies on Linkage Disequilibrium

The Raleigh, North Carolina, population of Drosophila melanogaster was examined for linkage disequilibrium in 1974, several years after previous analyses in 1968, 1969, and 1970. alphaglycerol-3-phosphate dehydrogenase-1 (alphaGpdh-1), malate dehydrogenase-1 (Mdh-1), alcohol dehydrogenase (Adh), and hexokinase-C (Hex-C, tentative name, F. M. Johnson, unpublished; position determined by the present authors to be 2-74.5) were assayed for 617 second chromosomes, and esterase-C (Est-C) and octanol dehydrogenase (Odh) were assayed for 526 third chromosomes. In addition, two polymorphic inversions in the second chromosomes [In(2L)t and In(2R)NS] were examined, and the following findings were obtained: (1) No linkage disequilibrium between isozyme genes was detected. Significant linkage disequilibria were found only between the polymorphic inversions and isozyme genes [In(2L)t vs. Adh, and In(2R)NS vs. Hex-C]. Significant disequilibrium was not detected between In(2L)t and alphaGpdh-1, which is included in the inversion, but a tendency toward disequilibrium was consistently found from 1968 to 1974. The frequency of two-strand double crossovers within inversion In(2L)t involving a single crossover on each side of alphaGpdh-1 was estimated to be 0.00022. Thus, the consistent but not significant linkage disequilibrium between the two factors can be explained by recombination after the inversion occurred. (2) Previously existing linkage disequilibrium between Adh and In(2R)NS (the distance is about 30 cM, but the effective recombination value is about 1.75%) was found to have disappeared. (3) No higher-order linkage disequilibrium was detected. (4) Linkage disequilibrium between Odh and Est-C (the distance of which was estimated to be 0.0058 +/- 0.002) could not be detected (chi(2) (df=1) = 0.9).-From the above results, it was concluded that linkage disequilibria among isozyme genes are very rare in D. melanogaster, so that the Franklin-Lewontin model (Franklin and Lewontin 1970) is not applicable to these genes. The linkage disequilibria between some isozyme genes and polymorphic inversions may be explained by founder effect.     

The Genetics of DROSOPHILA SUBOBSCURA Populations. Xiv. Further Data on Linkage Disequilibria

Data coming from one natural population of D. subobscura, that of Crete, are presented in detail and examined for nonrandom associations of genes and gene arrangements. This population and four others previously studied are reanalyzed for the detection of higher than first-order interactions. Only first-order interactions are important and statistically significant, especially those concerning genes and inversions in which these genes are included. The paucity of linkage disequilibria detected is remarkable, and we argue that it does not depend on the methods of study, rather it is genuine. We further argue that most of the disequilibria detected are probably due to mechanisms based on epistatic selection.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xii. Linkage Disequilibrium in a Large Local Population

Seven hundred and three second chromosomes were extracted from a Raleigh, North Carolina population of Drosophila melanogaster in 1970. Additionally, four hundred and eighty-nine third chromosomes were extracted from a large cage population founded from the flies in the 1970 Raleigh collection. The alpha glycerol-3-phosphate dehydrogenase-1, malate dehydrogenase-1, alcohol dehydrogenase, and alpha amylase loci were studied from the second chromosomes, and the esterase-6, esterase-C, and octanol dehydrogenase loci were analyzed from the third chromosomes. Inversions, relative viability and fecundity were studied for both classes of chromosomes. The following significant findings were obtained: (1) All loci examined were polymorphic or had at least two alleles at appreciable frequencies. Analysis of the combined data from this experiment with that of Mukai, Mettler and Chigusa (1971) revealed that the frequencies of the genes in the second chromosomes collected in early August were approximately the same over three years. (2) Linkage disequilibria between and among isozyme genes inter se were not detected except in a few cases which can be considered due to non-random sampling. (3) Linkage disequilibria between isozyme genes and polymorphic inversions were detected when the recombination values between the breakage points of the inversions and the genes in question were small. In only a few cases, were second and third order linkage disequilibria including polymorphic inversions detected. (4) Evidence for either variation among genotypes within loci or cumulative effects of heterozygosity was found for viability and fecundity. As a result of these findings, it was tentatively concluded that although selection might be perceptibly operating on some polymorphic isozyme loci, most of the polymorphic isozyme genes are selectively neutral or near-neutral in the populations studied.     

Genomics of natural populations: Evolutionary forces that establish and maintain gene arrangements in Drosophila pseudoobscura

The evolution of complex traits in heterogeneous environments may shape the order of genes within chromosomes. Drosophila pseudoobscura has a rich gene arrangement polymorphism that allows one to test evolutionary genetic hypotheses about how chromosomal inversions are established in populations. D. pseudoobscura has >30 gene arrangements on a single chromosome that were generated through a series of overlapping inversion mutations with >10 inversions with appreciable frequencies and wide geographic distributions. This study analyses the genomic sequences of 54 strains of Drosophila pseudoobscura that carry one of six different chromosomal arrangements to test whether (i) genetic drift, (ii) hitchhiking with an adaptive allele, (iii) direct effects of inversions to create gene disruptions caused by breakpoints, or (iv) indirect effects of inversions in limiting the formation of recombinant gametes are responsible for the establishment of new gene arrangements. We found that the inversion events do not disrupt the structure of protein coding genes at the breakpoints. Population genetic analyses of 2,669 protein coding genes identified 277 outlier loci harbouring elevated frequencies of arrangement‐specific derived alleles. Significant linkage disequilibrium occurs among distant loci interspersed between regions with low levels of association indicating that distant allelic combinations are held together despite shared polymorphism among arrangements. Outlier genes showing evidence of genetic differentiation between arrangements are enriched for sensory perception and detoxification genes. The data presented here support the indirect effect of inversion hypothesis where chromosomal inversions are favoured because they maintain linked associations among multilocus allelic combinations among different arrangements.     

Gametic associations between inversion and allozyme polymorphisms in Drosophila buzzatii.

Gametic disequilibria between second chromosome polymorphic arrangements and seven linked allozyme loci were estimated in seven populations of Drosophila buzzatii from Argentina. Significant and consistent associations across populations were detected for Est-1, Est-2, Aldox, and XDH: Phenograms based on Nei's genetic distance showed that chromosomes carrying the 2ST arrangement were more similar to each other, irrespective of the population from which they were extracted, than to chromosomes carrying the derived 2J and 2JZ3.Restriction of recombination in heterokaryotypes seems to be the best explanation for the significant linkage disequilibria between inversions and the loci located inside the rearranged segments, for example, Est-1 and Aldox, or close to the break points, for example, Est-2. However, epistatic interactions between Xdh, which is outside the inversions and not near the break points, and loci tightly linked to the inversions, is the most likely explanation for the association between Xdh and chromosomal arrangements. Some of the associations detected in endemic Argentinean populations are coincident with data obtained in colonizing populations of the Old World and Australia. Thus historical processes that took place in the original area of the species' distribution can account for these linkage disequilibria in colonized populations of D. buzzatii.     

Testing the fisherian mechanism: examining the genetic correlation between male song and female response in waxmoths

Models of indirect (genetic) benefits sexual selection predict linkage disequilibria between genes that influence male traits and female preferences, owing to either non-random mate choice or physical linkage. Such linkage disequilibria, a genetic correlation, can accelerate the evolution of male traits and female preferences to exaggerated levels. But relatively few empirical studies have measured the genetic correlation between male traits and female responses in natural populations, and the findings of those few are mixed: often, genetic correlations are not found. We tested the above prediction in an acoustic pyralid moth, Achroia grisella, in which males attract females with a rhythmic train of sound pulses, and females respond only to song that exceeds a minimum pulse rhythm. Both male song rhythm and female threshold response are repeatable and heritable characters. Because female choice in A. grisella is based largely on male song, and males do not appear to provide direct benefits at mating, genetic correlation between male song rhythm and female response is expected. We studied 2 A. grisella populations, bred them according to a full-sib/half-sib design, split the progeny among 4 different environmental conditions, and measured the male song/female response genetic correlation in each of the 8 resulting groups. While song rhythm and response threshold were generally heritable, we found no evidence of significant genetic correlation between these traits. We suggest that the complexity of the various male song characters, of female response to male song, and of correlations between male song characters and between aspects of female response have mitigated the evolution of strong genetic correlation between song and response. Thus, exaggerated levels of trait development may be tempered.     

Ecological genetic studies in the chromosomal form Mopti ofAnopheles gambiae s.str. in Mali,West Africa

Among the sibling species of the AfrotropicalAnopheles gambiae complex, the nominal taxon (An. gambiae s.str.) is the major malaria vector. Its bionomics suggest a man-dependent speciation process which involves, in West Africa, various incipient species chromosomally recognized by different combinations of 2R paracentric inversions. One of the most recent evolutionary steps of such a speciation process appears to be the chromosomal form Mopti, which is associated with dry season irrigation in arid zones, and is characterized by a remarkable ecological flexibility related to three 2R alternative arrangements, namelybc, u and +, whose expected karyotypes are found in Hardy-Weinberg equilibrium. The study of this chromosomal polymorphism in samples from a 16-locality transect in Mali shows wide variations and highly significant correlation with both temporal and spatial climatic differences. Mosquitoes homokaryotypic for 2Rbc are the actual dry season and arid areas breeders. The regular rise of 2Rbc frequency, up to fixation, during each dry season, corresponds to the South-North clinal increase of the same arrangement along the transect, from about 30% in the humid savanna to near fixation in the South-Saharan zone. This coherent ecological genetics case provides full support to the hypothesis of the adaptive nature of paracentric inversions. Moreover, the very peculiar system of combinations of contiguous 2R inversions, utilized by Mopti as well as by other chromosomal forms ofAn. gambiae, suggests a process of polygenic reorganization based on linkage disequilibria and involving the inversions as driving selection units.     

Nucleotide variation of the duplicated amylase genes in Drosophila kikkawai

We examined levels and patterns of the nucleotide polymorphism of the Amylase genes with a head-to-head duplication in Drosophila kikkawai. The levels of variation in D. kikkawai were comparable to those in Drosophila melanogaster. Tajima's test, Fu and Li's test, HKA test, and MK test did not show significant departure from neutrality. We found an excess of replacement changes in the within-locus class, representing polymorphism in one of the duplicated genes, compared with the between-locus class, representing polymorphism shared between the duplicated genes. Most replacement changes in the within-locus class were singletons. These results suggest that most replacement changes are deleterious. A contrasting evolutionary pattern, involving concerted evolution in the coding regions but differential evolution in the 5'-flanking regions, was observed. However, unlike the duplicated Amy genes of D. melanogaster, the coding regions of the duplicated genes in D. kikkawai tended to diverge. Using Ohta's model of the small multigene family, we found that recombination (interchromosomal equal crossing-over) rate was one order higher than gene conversion (unequal crossing-over) rate, resulting in a considerable but incomplete homogenization of the duplicated coding regions. Linkage disequilibria were found in the intron as well as within and around the regulatory cis-element sequences of one of the duplicated genes (Amy1). The possible causes of these linkage disequilibria were discussed.     

Disequilibrium among several linked neutral genes in finite population I. Mean changes in disequilibrium

Formulae are developed for computing changes in expected values in a finite population of linkage disequilibrium among neutral genes from more than two loci, although the exact analysis is taken up to only six loci. An essentially haploid model is used. As with two loci, the three-locus disequilibrium declines exponentially at all generations, but for m > 3 loci a matrix has to be constructed to give joint changes in the m-locus disequilibrium and products of disequilibria with fewer loci, for example of two m/2-locus disequilibria. The asymptotic rates of change in multilocus disequilibria depend on the arrangement of genes on the chromosome as well as its total length, but the initial rate of breakdown of disequilibrium from a line cross base is less dependent on the arrangement. With equally spaced loci the asymptotic rate of breakdown of m locus disequilibrium is roughly proportional to m. Although mutation and interference are excluded from the main analysis, it is shown how they can be incorporated.     

The Genetics of DROSOPHILA SUBOBSCURA Populations. Xvii. Further Genic Heterogeneity within Electromorphs by Urea Denaturation and the Effect of the Increased Genic Variability on Linkage Disequilibrium Studies

Urea denaturation of allozymes was used to provide finer resolution of allelic states within classes of different electrophoretic mobility. This method gives perfectly repeatable results. About 170 isogenic strains for the O chromosome of Drosophila subobscura, derived from two natural populations, were constructed. Their gene arrangements were studied, as well as eight polymorphic genes located on the O chromosome (Est-5, Odh, Ao, ME, Xdh, Lap, Pept-1 and Acph). Crosses performed indicate that differences in urea sensitivity are genetically controlled by the same genes that control electrophoretic mobility. Twice as many alleles have been detected in comparison to the usual electrophoretic method. However, the effective number of alleles did not increase considerably.Studies of linkage disequilibria, by taking into account the finer resolution of allelic states, gave results nearly identical with those obtained in studies where the usual electrophoretic method was used. Although the power of the test is diminished, the absence of genic associations seems to indicate that there are no hidden linkage disequilibria in electrophoretic studies (because of consolidation effects of real alleles into few electromorph classes). The paucity of linkage disequilibria would indicate that there are no epistatic interactions such as those suggested in the model of Franklin and Lewontin (1970).     

Genic VERSUS Chromosomal Variation in Natural Populations of DROSOPHILA SUBOBSCURA

Gametic frequencies in one mainland and one island population of D. subobscura were obtained by means of extracting wild chromosomes and subsequently analyzing them for inversions and allozymes. The high degree of cytological heterogeneity which characterizes these populations is not reflected in the genetic data. Two cases of non-random association were observed among eighteen pair-wise comparisons involving gene alleles and inversions to which the locus is linked. In both cases exchange of alleles at the locus is completely suppressed by the inversions. Four cases of linkage disequilibrium were detected among eighteen pairs of loci; two of them could best be explained as transient associations generated by random drift. The results suggest that disequilibria among enzyme loci are not widespread in natural populations—Populations with a lower degree of chromosomal variation are genetically as variable as populations with a higher degree of chromosomal variation. This observation does not support the hypothesis that selection in marginal homokaryotypic populations is for specialized homozygous genotypes.     

Genetic coadaptation in the chromosomal polymorphism of Drosophila subobscura II. Changes of gametic disequilibrium in experimental populations

Experimental populations were examined for temporal changes of gametic disequilibria between allozyme loci (Lap and Pept-1) and gene arrangements of the O chromosome of Drosophila subobscura (O _st and O ₃₊₄₊₇) under several environmental conditions. In the foundation of the experimental populations a genetic perturbation was carried out in order to test the relevance of the current hypotheses used to explain the allozyme-inversion associations observed in natural populations. Differential changes of gametic disequilibria were detected over generations under the different environmental conditions. Mere mechanical or stochastic factors cannot explain the results and natural selection is probably the major agent generating the detected gametic associations. The observations are interpreted as a proof of coadaptation of D. subobscura inversions.     

Disequilibrium among several linked neutral genes in finite population. II. Variances and covariances of disequilibria

A method is derived for computing the variances and covariances of linkage disequilibria between neutral genes in finite populations, which is based on a linear transformation of results given previously for the mean values of disequilibria. The formulae obtained are limited to moments of sixth order or less, such as the variance of the three-locus disequilibrium. It is shown that there is no covariance between any pair of disequilibria in populations starting equilibrium. The pattern of change with time in variance of the three-locus disequilibrium from populations initially in equilibrium is similar to that for two loci, except that the highest values are achieved rather earlier and are smaller.     

A sequential coalescent algorithm for chromosomal inversions

Chromosomal inversions are common in natural populations and are believed to be involved in many important evolutionary phenomena, including speciation, the evolution of sex chromosomes and local adaptation. While recent advances in sequencing and genotyping methods are leading to rapidly increasing amounts of genome-wide sequence data that reveal interesting patterns of genetic variation within inverted regions, efficient simulation methods to study these patterns are largely missing. In this work, we extend the sequential Markovian coalescent, an approximation to the coalescent with recombination, to include the effects of polymorphic inversions on patterns of recombination. Results show that our algorithm is fast, memory-efficient and accurate, making it feasible to simulate large inversions in large populations for the first time. The SMC algorithm enables studies of patterns of genetic variation (for example, linkage disequilibria) and tests of hypotheses (using simulation-based approaches) that were previously intractable.     

Edaphic microsatellite DNA divergence in wild emmer wheat, Triticum dicoccoides, at a microsite: Tabigha, Israel

Twenty eight microsatellite markers were used to analyze genetic divergence in tandem dinucleotide repeated DNA regions between two edaphic subpopulations of Triticum dicoccoides growing on the contrasting terra rossa and basalt soilsfrom a microsite at Tabigha, north of the Sea of Galilee, Israel. The terra rossa soil niche was drier and more stressful than the basalt throughout the growing season (November to May). Significant microsatellite divergence in allele distribution, repeat length, genetic diversity, and linkage disequilibria were found between emmer wheat from the two soil types over two short transects of 100 m each. Soil-specific and -unique alleles and linkage disequilibria were observed in the terra rossa and basalt subpopulations. A permutation test showed that the effects of random genetic drift were very low for the significant genetic diversity at microsatellite loci between the two subpopulations, suggesting that an adaptive molecular pattern derived by edaphic selection may act upon variation of the microsatellites. Received: 4 February 2000 / Accepted: 31 March 2000<@head-com-p1a.lf>Communicated by H.F. Linskens     

Gene Conversion, Linkage, and the Evolution of Repeated Genes Dispersed among Multiple Chromosomes

The evolution of the probabilities of genetic identity within and between the loci of a multigene family dispersed among multiple chromosomes is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, but the same for every chromosome; the dependence of the probabilities of identity on the location on each chromosome is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. Under the assumption of loose linkage (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), explicit approximations are obtained for the equilibrium values of the probabilities of identity and of the linkage of disequilibria. The probabilities of identity are of order one [i.e., O(1)] and do not depend on location; the linkage disequilibria are of O(epsilon) and, within each chromosome, depend on location through the crossover rates. It is demonstrated also that the ultimate rate and pattern of convergence to equilibrium are close to that of a much simpler, location-independent model. If intrachromosomal conversion is absent, the above results hold even without the assumption of loose linkage. In all cases, the relative errors are of O(epsilon). Even if the conversion rate between genes on nonhomologous chromosomes is considerably less than between genes on the same chromosome or homologous chromosomes, the probabilities of identity between the former genes are still almost as high as those between the latter, and the rate of convergence is still not much less than with equal conversion rates. If the crossover rates are much less than 1/2, then most of the linkage disequilibrium is due to intrachromosomal conversion. If linkage is loose, the reduction of the linkage disequilibria to O(epsilon) requires only O(-ln epsilon) generations.     

Linkage Disequilibrium in Natural Populations of DROSOPHILA MELANOGASTER

Two large, stable populations (Texas and Japan) of Drosophila melanogaster were surveyed at 21 allozyme loci on the second and third chromosomes and for chromosomal gene arrangements on those two chromosomes. Over 220 independent gametes were sampled from each population. The types and frequencies of the surveyed genetic variation are similar to those observed previously and suggest only slight differentiation among geographically distant populations. Linkage disequilibrium among linked allozymes loci is only slightly, if at all, detectable with these sample sizes. Linkage disequilibrium between linked inversions and allozymes loci is common especially when located in the same arm. These disequilibria appear to be in the same direction for most comparisons in the two population samples. This result is interpreted as evidence of similar selective environments (ecological and genetic) in the two populations. It is also noted that the direction of these linkage disequilibria appears to be oriented with respect to the gene frequencies at the component loci.     

Polymorphic inversion and esterase loci complex on chromosome 2 of Drosophila buzzatii. II. Spatial variation

The potential influence of linked inversions on allele frequency variation at the Est-1 and Est-2 loci among Australian populations of D. buzzatii was determined by statistical analyses allele and inversion gametic frequencies. Most of the significant spatial and climatic associations found for all Est-1 allele frequencies, and for one allele only of Est-2 (Est-2c+), were accounted for by their linkage disequilibria with the inversions, which covaried with environmental variables. Consistent with this result, the spatial and climatic associations for conditional Est-1 and Est-2 allele frequencies tended to be different from those for the respective unadjusted allele frequencies. In one important respect, the results for Est-1 and Est-2 were not altered by inversions. For both unadjusted and conditional Est-1 allele frequencies, few climatic associations remain after correcting for geographic location, whereas for both unadjusted and conditional Est-2 allele frequencies, climatic associations remain after correcting for geographic location. Thus, apparent selection affecting allele frequencies at the Est-2 locus is not accounted for by linked inversions.     

Evidence for Linkage Disequilibrium Maintained by Selection in Two Natural Populations of DROSOPHILA SUBOBSCURA

One island and one mainland population of Drosophila subobscura were found polymorphic at the XDH (xanthine dehydrogenase) and the AO (aldehyde oxidase) loci. It was observed that one allele at the XDH locus, which has a low frequency in both populations, is nonrandomly associated with the alleles at the AO locus. Two lines of evidence support the thesis that this linkage disequilibrium is due to epistasis rather than random drift: (1) D or r, measures of the disequilibrium, have the same sign and magnitude in both populations. (2) The linkage disequilibrium is not due to inversions. Inversions segregating on the chromosome carrying XDH and AO have been separated into two classes, between which exchange of alleles at the two loci is suppressed. Linkage disequilibrium for XDH and AO was observed within each class. In the absence of any exchange of alleles, these disequilibria must have arisen and been maintained independently. The suggestion is made that the epistatic disequilibrium results from the close structural and physiological relationship which exists between the two enzymes.