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.     

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malate dehydrogenase-1 (Mdh-1), alcohol dehydrogenase (Adh), and hexokinase-C (Hex-C, tentative name, F. M. Johnson, unpublished; position determined by the present authors to be 2-74.5) were assayed for 617 second chromosomes, and esterase-C (Est-C) and octanol dehydrogenase (Odh) were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.     

Linkage Disequilibrium in Natural Populations of DROSOPHILA MELANOGASTER. Seasonal Variation

Linkage disequilibrium among ten polymorphic allozyme loci and polymorphic inversions on chromosomes 2 and 3 in a natural population of Drosophila melanogaster was examined early and late in the annual season. Similar to previous studies, little linkage disequilibrium was observed among allozymes. The two significant cases that were observed in the first sample behaved in a contradictory way. One declined much more rapidly than expected due simply to recombination; the other declined slowly as expected. There was little change in allozyme or inversion frequencies during the season.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xi. Genetic Variability in a Local Population

Six hundred and ninety-one second chromosomes were extracted from a Raleigh, North Carolina population, and the following experimental results were obtained: (1) Salivary gland chromosomes of all lines were observed and the number of inversion-carrying chromosomes was 130, among which 76 carried In(2R)NS, 36 carried In(2L)t, 4 carried In(2L)t and In(2R)NS, and 14 carried different kinds of rare inversions. (2) Viabilities of homozygotes and heterozygotes were examined. The frequency of lethal-carrying chromosomes was 275/691 (or 0.398):70/130 (or 0.538) in inversion-carrying chromosomes and 205/561 (or 0.365) in inversion-free chromosomes. The former is significantly higher than the latter. The average homozygote viability was 0.4342 including lethal lines and 0.7163 excluding those, the average heterozygote viability being 1.0000. The detrimental load to lethal load ratio (D:L ratio) was 0.334/0.501 = 0.67. The average viability of lethal heterozygotes was less than that of lethal-free heterozygotes, significantly in inversion-free individuals but not significantly so in inversion-carrying individuals. Inversion heterozygotes seem to have slightly better viability than the inversion-free heterozygotes on the average, but not significantly so. (3) The average degree of dominance of viability polygenes was estimated to be 0.293 +/- 0.071 for all heterozygotes whose component chromosomes had better viabilities than 0.6 of the average heterozygote viability, 0.177 +/- 0.077 for inversion-free heterozygotes and 0.489 +/- 0.082 for inversion heterozygotes. (4) Mutation rates of viability polygenes and lethal genes were estimated on the basis of genetic loads and average degrees of dominance of lethal genes and viability polygenes. Estimates were very close to those obtained by direct estimation. (5) Possible overdominance and epistasis were detected, but the magnitude must be very small. (6) The effective size of the population was estimated to be much greater than 10,000 by using the allelism rate of lethal-carrying chromosomes (0.0040) and their frequency.-On the basis of these findings and the comparison with the predicted result (Mukai and Maruyama 1971), the mechanisms of the maintenance of genetic variability in the population are discussed.     

A Study of Linkage Disequilibrium in Populations of DROSOPHILA MELANOGASTER

This paper presents the results of a study of linkage disequilibrium between five polymorphic enzyme genes located on chromosome 3 of D. melanogaster. Three sets of chromosomes were examined: two represented samples from successive years of the same natural population, and one came from a large laboratory population. Out of the thirty possible tests for linkage disequilibrium between pairs of loci, two were significant at the 5% level and two at the 1% level. This result cannot reasonably be ascribed to chance alone. The pairs of loci that had a significant correlation in one sample had higher than average correlations in the other samples (though not necessarily in the same direction); this effect was highly significant statistically. There was no tendency for the high correlations to be associated with tightness of linkage between the loci concerned. All five loci were involved in at least one significant effect. It was concluded that these results are difficult to explain on the neutral allele theory of protein polymorphism, but are consistent with the concept of selective control of allele frequencies.     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xvii. a Population Carrying Genetic Variability Explicable by the Classical Hypothesis

About 400 second chromosomes were extracted from the Aomori population, a northernmost population of D. melanogaster on Honshu in Japan, and the following experimental results were obtained. (1) The frequency of lethal chromosomes was 0.23. (2) The effective size of the population was estimated to be about 3000, from the allelism rate of lethal chromosomes and their frequency. (3) The detrimental and lethal loads for viability were 0.243 and 0.242, respectively, and the D/L ratio became 1.00. (4) The average degree of dominance for mildly deleterious genes was estimated to be 0.178 ± 0.056. (5) Additive (σ²_A) and dominance (σ²_D) variances of viability were estimated to be 0.00276 ± 0.00090 and 0.00011 ± 0.00014, respectively. (6) There was no significant difference in environmental variances between homozygotes and heterozygotes. Using these estimates, we discuss the maintenance mechanisms of genetic variability of viability in the population. The mutation-selection balance explained these experimental results.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xviii. Clinal and Uniform Genetic Variation over Populations

It has been reported in the previous papers of this series that in the eastern United States and Japan there is a north-to-south cline of additive genetic variance of viability and that the amount of the additive genetic variance in the northern population can be explained by mutation-selection balance. To determine whether or not the difference in the genetic variation in northern and southern populations can be explained by the differences in mutation rate and/or effective population size, numerical calculations were made using population genetic parameters. In addition, the average heterozygosities of the northern and southern populations at ten of 19 polymorphic structural loci surveyed were estimated in relation to the cline of additive genetic variance of viability, and the following findings were obtained. (1) The changes in mutation rate and population size cannot simultaneously explain the difference in additive genetic variance and inbreeding decline between the northern and southern populations. Thus, the operation of some kind of balancing selection, most likely diversifying selection, was suggested to explain the observed excess of additive genetic variance. (2) Estimates of the average heterozygosities of the southern population were not significantly different from those of the northern population. Thus, it was strongly suggested that the excess of additive genetic variance in the southern population cannot be caused by structural loci, but by factors outside the structural loci, and that protein polymorphisms are selectively neutral or nearly neutral.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xix. Genotype-Environment Interaction in Viability

To investigate whether or not an excess of additive genetic variance for viability detected in southern natural populations of Drosophila melanogaster was created by diversifying selection, genotype-environment interaction was tested as follows. (1) Two karyotype chromosomes were used: 61 second chromosomes with the standard karyotype and 63 second chromosomes carrying In(2L)t. Their homozygote viabilities were larger than 50% of the average viability of random heterozygotes. (2) The effects of two factors (culture media and yeasts) were examined at three levels (the culture media: tomato, corn and banana; and the yeasts: sake, brewer's and baker's). The results of 16 three by three factorial experiments by the Cy method in the same karyotype groups for relative viabilities of homozygotes and heterozygotes elucidated the following findings: (1) there was no significant difference between the two karyotype groups, (2) the variance components of genotype-environment interaction were highly significant, (3) the variance component of heterozygotes was significantly smaller than that of homozygotes. From the experimental findings and previous results, diversifying selection in natural populations acting on viability polygenes to increase the additive genetic variance was suggested. The relation of the present result to protein polymorphism is also discussed.     

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. Xvi. Excess of Additive Genetic Variance of Viability

About 500 second and 500 third chromosomes were extracted, using the marked inversion technique, from the Orlando-Lake Placid, Florida, population. From the experiments using these chromosomes, the following findings were obtained: (1) The frequencies of lethal-carrying chromosomes were 0.37 in the second and 0.55 in the third chromosomes. (2) The size of the population was estimated to be effectively infinite, on the basis of the allelism rate of lethal-carrying chromosomes. (3) The detrimental and lethal loads for viability were, respectively, 0.40 and 0.45 for the second and 0.52 and 0.78 for the third chromosomes. Consequently, the detrimental to lethal load ratio is 0.90 for the second and 0.67 for the third chromosomes. (4) Lethal genes were shown to be deleterious when heterozygous. (5) The average degree of dominance for mildly deleterious genes (viability polygenes) was estimated to be nearly 0.5, although the confidence interval is large. (6) Additive (sigma( 2) (A)) and dominance (sigma(2) ( D)) variances of viability were estimated by using a partial diallel cross method. The results were (see PDF) and (see PDF) for the second chromosomes. (7) Environmental variances of viability were estimated. The result indicates that the heterozygotes are more homeostatic than the homozygotes. The most striking finding is that the additive variance is larger than expected on the classical hypothesis from the detrimental load. Several possible explanations for the discrepancy are offered. The most likely cause, we suggest, is genotype-environment interaction (diversifying selection) acting on viability polygenes. Overdominance is inconsistent with the low dominance variance, and frequency-dependent selection also appears unlikely as an explanation.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER. Xv. Nature of Developmental Homeostasis for Viability

Developmental homeostasis of relative viability was examined for homozygotes and heterozygotes using second chromosomes from two populations of Drosophila melanogaster. One was a chromosome population in which spontaneous mutations were allowed to accumulate since it was begun with a single near-normal second chromosome. The second was a natural population approximately at equilibrium. For the estimation of relative viability, the Cy method was employed (Wallace 1956), and environmental variance between simultaneously replicated cultures was used as the index of developmental homeostasis. A new method was used in the estimation of sampling variance for relative viability that was employed for the calculation of environmental variance (error variance between simultaneously replicated cultures - sampling variance). The following findings were obtained.: (1) The difference in environmental variance between homozygotes and heterozygotes could not be seen when a chromosome population with variation due to new mutations was tested. (2) When a chromosome group isolated from an approximate equilibrium population was examined, heterozygotes manifested a smaller environmental variance than the homozygotes if their relative viabilities were approximately the same. (3) There was a slight negative correlation between viability and environmental variance, although opposite results were found when the viabilities of individuals were high, especially when overdominance (coupling overdominance, Mukai 1969 a, b) was manifest. On the basis of these findings, it was concluded that developmental homeostasis was a product of natural selection, and its mechanism was discussed.     

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.