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.     

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 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.     

The Genetic Variance for Viability and Its Components in a Local Population of DROSOPHILA MELANOGASTER

Two hundred and ninety second chromosomes extracted from a natural population of Drosophila melanogaster were analyzed to estimate the genetic variance of viability and its components by means of a partial diallel cross (Design II of Comstock and Robinson 1952). The additive and dominance variances are estimated to be 0.009 and 0.0012. Using the dominance variance and the inbreeding depression, the effective number of overdominant loci contributing to the variance in viability is estimated to be very small, a dozen or less. Either the actual number of loci is small, or the distribution of viabilities is strongly skewed with a large majority of very weakly selected loci. The additive variance in viability appears to be too large to be accounted for by recurrent harmful mutants or by overdominant loci at equilibrium with various genetic parameters estimated independently. The excess might be due to frequency-dependent selection, to negative correlations between viability and fertility, or possibly to the presence of a mutator. The selection for viability and fertility, or possibly to the presence of a mutator. The selection for viability at the average polymorphic locus must be very slight, of the order of 10(-3) or less.     

The Genetics of DROSOPHILA SUBOBSCURA Populations. V. a Study of Linkage Disequilibrium in Natural Populations between Genes and Inversions of the E Chromosome

The genetics of Hk and Est-9 complex gene have been studied in Drosophila subobscura. While Hk alleles mendelize normally, Est-9 is a complex locus consisting of several very closely linked genes with active and silent alleles. Both genes are located on chromosome E; a detailed genetic map was constructed with the help of visible markers and inversions. Both Hk and Est-9 are included in or are very near to inversions of the E chromosome. While Hk does not show linkage disequilibrium either with Est-9 or inversions, Est-9 does show disequilibrium in two ways: both with inversions and between different Est-9 genes. All natural populations studied show the same kind of association between Est-9 gene combinations and inversions. It is argued that these results are better explained by selection than by neutrality.     

Genes Affecting Productivity in Natural Populations of DROSOPHILA MELANOGASTER

Two hundred second chromosomes were extracted from a Japanese population in October of 1972, and the viabilities and productivities of homozygotes and heterozygotes from them were examined. Viability was measured by the Cy method and productivity by the number of progeny produced per female. The frequency of lethal-carrying chromosomes was 0.315. When the average heterozygote viability was standardized as 1.000, the average homozygote viability was 0.595 including the lethal lines, and 0.866 excluding them. The frequency of recessive sterile chromosomes among 131 non-lethal lines was 0.092 in females and 0.183 in males. There were two instances in which homozygosis for the second chromosome caused sterility in both sexes, which was close to the number expected (2.2) on a random basis of 0.092 x 0.183 x 131. When the average heterozygote productivity of 200 lines was standardized as 1.000, the average homozygote productivity was 0.532 including female steriles, and 0.584 excluding them. The ratio of detrimental load to lethal load was 0.383, while the ratio of partial sterility load to complete sterility load was 5.767. The average viability of lethal heterozygotes was slightly, but not significantly, lower than that of lethal-free heterozygotes, while the average productivity of lethal heterozygotes was significantly lower than that of lethal-free heterozygotes. There was a significant association of sterility in either sex with low viability of homozygotes. However, no statistically significant differences in viability and productivity were detected between sterile heterozygotes and non-sterile heterozygotes. The heterozygous effects of viability and productivity polygenes were examined by regressions of the heterozygotes on the sum of corresponding homozygotes. The regression coefficients were slightly positive for both viability and productivity if lethal and sterile chromosomes were excluded. The correlation between viability and productivity in homozygotes was significantly positive when sterile chromosomes were included, but the significance disappeared when the sterile chromosomes were excluded. In the heterozygotes there were no detectable correlations between them.