Multilocus Structure of Natural Populations of HORDEUM SPONTANEUM

The association of alleles among different loci was studied in natural populations of Hordeum spontaneum, the evolutionary progenitor of cultivated barley. The variance of the number of heterozygous loci in two randomly chosen gametes affords a useful measure of such association. The behavior of this statistic in several particular models is described. Generally, linkage (gametic phase) disequilibrium tends to increase the variance above the value expected under complete independence. This increase is greatest when disequilibria are such as to maximize the sum of squares of the two-locus gametic frequencies.—When data on several loci per individual are available, the observed variance may be tested for its agreement with that expected under the hypothesis of complete interlocus independence, using the sampling theory of this model. When applied to allozyme data from 26 polymorphic populations of wild barley, this test demonstrated the presence of geographically widespread multilocus organization. On average, the variance was 80% higher than expected under random association. Gametic frequencies for four esterase loci in both of these populations of wild barley and two composite crosses of cultivated barley were analyzed. Most generations of the composites showed less multilocus structure, as measured by the indices of association, than the wild populations.     

Multilocus structure in Pinus contorta Dougl.

We studied isozyme variation at 21 loci in 66 populations from three subspecies of Pinus contorta Dougl.; 35 in spp. latifolia, 20 in spp contorta and 11 in spp. murrayana. The objectives were to assess gametic disequilibria and multilocus structure. There was considerable differentiation of allele frequencies at 19 polymorphic loci across the 66 populations and within the subspecies. Allele frequencies at many loci correlated with geographic variables. Genetic variability varied considerably among populations within subspecies but the subspecies means were similar. The mean number of polymorphic loci and the mean heterozygosity over 19 polymorphic loci were, respectively, 13 and 0.194 in latifolia, 12 and 0.196 in murrayana, and 12 and 0.180 in contorta. The mean heterozygosity correlated with longitude and altitude across the 66 populations and with latitude in latifolia. Gametic disequilibria were evident in 40 populations; 29 in latifolia, eight in murrayana and three in contorta. Gametic disequilibria correlated with latitude across the 66 populations and with longitude in latifolia. The single-locus F _ST averaged 0.0339 in latifolia, 0.0567 in murrayana, and 0.0764 in contorta. The multilocus F _STM was 0.1227 in latifolia, 0.2926 in murrayana, and 0.3328 in contorta. Multilocus Wahlund and founder effects, migration patterns, and natural selection, probably played significant roles in generating and maintaining the multilocus genetic structure in P. contorta in general and the subspecies latifolia in particular.     

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.     

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.     

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.     

Dynamics of correlated genetic systems. II. Simulation studies of chromosomal segments under selection

The dynamics of chromosomal segments under selection are investigated by comparing experimental data to simulations of simple models of selection. The simulations assume 93 loci distributed evenly along an entire chromosome. The two issues addressed in this paper concern rates of decay of linkage disequilibria for chromosomes under selection and rates of gene frequency change after perturbation of gametic frequencies to states near the edge of the gametic frequency simplex. The findings are: (1) If reasonable values of inbreeding depression are assumed, linkage disequilibria decays to zero but at a rate nearly twice that expected from neutral theory. Experimental results also show accelerated decay rates. The acceleration of decay seems to be a simple consequence of the increased heterozygosity produced by selection. It is, therefore, argued that massive linkage disequilibria, of the kind found by Franklin and Lewontin (1970) in their simulations, are unlikely to characterize the genetic structure of natural populations of random mating organisms. (2) It is possible to distinguish between two time-honored models of multilocus selection, known as the symmetric overdominant and classical models, on the basis of gene frequency change near the edge of the gametic frequency simplex assuming linkage disequilibria is intense. (3) Examination of experimental data from perturbation experiments shows that neither of these elementary models adequately account for observed rates of gene frequency change, although the symmetric overdominant model does provide the better fit. Instead the experimental data suggest a markedly nonuniform distribution of selective effects along the chromosome. The data also suggest that these selective effects combine in markedly nonadditive ways in determining joint fitness.     

Genetic diversity and multilocus associations in Cunninghamia lanceolata (Lamb.) Hook from The People's Republic of China

Open-pollinated seeds were assayed for allozyme polymorphisms at 24 loci to assess genetic diversity and multilocous associations in 16 populations of Cunninghamia lanceolata (Lamb.) Hook in the People's Republic of China. On average, the percentage of polymorphic loci was 88.0, the number of alleles per locus was 3.0, and the expected heterozygosity was 0.394. The distribution of genetic diversity was not correlated with the geographic and climatic variables of the populations. However, allele frequencies correlated linearly with the mean annual temperature of the populations at Mdh-1, Mdh-2, Mnr-2, Pgi-1, and Skdh-1 and with the altitude of the populations at Aph-4 and 6Pg-2. Of the total gene diversity 6% was attributed to among-population differentiation; 94% resided within populations. Two-locus gametic disequilibria were found in 15 of the 16 populations, and higher-order gametic disquilibria were significant in most populations. The gametic disequilibria did not correlate with geographic and climatic variables. The results suggest that population subdivision, founder effect, occurrence across diverse environments, a mating system dominated by inbreeding, and historical events from 2000 years of cultivation are contributing factors in the generation and maintenance of the multilocus genetic structure in this conifer.     

Enzyme Variability in Natural Populations of DAPHNIA MAGNA III. Genotypic Frequencies in Intermittent Populations

In temporary habitats populations of the cyclical parthenogen, Daphnia magna, are re-established each year from sexual eggs and reproduce parthenogenetically for two or at most three generations. The genetic effects of this breeding system have been investigated by analyzing allozyme frequencies in nineteen intermittent populations.—Genotypic frequencies at polymorphic loci were ordinarily found to be in good agreement with Hardy-Weinberg proportions and disequilibria between loci were not observed. Although significant changes in gene frequencies were observed both during and between successive cycles, there was no evidence of the marked instability of genotype frequencies characteristic of permanent populations. The recombinational degradation of genotypes at the end of each annual cycle in temporary habitats effectively prevents the genotypic structuring which develops when continued parthenogenesis is possible.     

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.     

Multilocus and Multitrait Measures of Differentiation for Gene Markers and Phenotypic Traits

Multilocus measures of differentiation taking into account gametic disequilibrium are developed. Even if coupling and repulsion heterozygotes cannot be separated at the multilocus level, a method is given to calculate a composite measure of differentiation (CF(st)) at the zygotic level, which accounts for allelic associations combining both gametic and nongametic effects. Mean and maximum differentiations may be relevant when multilocus measures are computed. Maximum differentiation is the highest eigenvalue of the F(st) matrix, whereas mean differentiation corresponds to the mean value of all eigenvalues of the F(st) matrix. Gametic disequilibrium has a stronger effect on maximum differentiation than on mean differentiation and takes into account the anisotropy that may exist between within- and between-population components of disequilibria. Multilocus mean and maximum differentiation are calculated for a set of 81 Quercus petraea (sessile oak) populations assessed with eight allozyme loci and two phenotypic traits (bud burst and height growth). The results indicate that maximum differentiation increases as more loci (traits) are considered whereas mean differentiation remains constant or decreases. Phenotypic traits exhibit higher population differentiation than allozymes. The applications and uses of mean and maximum differentiations are further discussed.     

Allozyme Frequency Changes Associated with Selection for Increased Grain Yield in Maize (ZEA MAYS L.)

Frequency changes of alleles at eight enzyme loci were monitored in four long-term maize selection experiments. The results indicate that changes in frequencies of the alleles at these loci are associated with changes due to selection for improved grain yield. The frequencies changed more than is consistent with the hypothesis of selective neutrality. In addition, significant deviations from a random-drift model were nearly always accompanied by significant linear trends as would result if allozyme frequencies respond to directional selection. Evaluations of linkages and linkage disequilibria in the selected populations indicate that the eight enzyme loci responded independently as selection progressed.     

The strength of the selection barrier between populations

Genetic differences among populations exposed to selection form barriers against genetic exchange by mortality among hybrids. The strength of such a selection barrier, with which one (recipient) population reacts against immigration from another (donor) population, may be measured as the cumulative mean fitness of hybrids and their descendants relative to the fitness of the recipient population. Previous work analysed a case of weak selection with pairwise epistatic interactions by assuming small genetic distance between two populations in contact. The present study allows large genetic difference between the donor and recipient populations and considers weak multilocus selection with arbitrary epistatic interactions between two or more linked loci. An approximate analytical expression for the barrier strength is obtained as an expansion in which the strength of selection plays the role of a small parameter. It is shown that allele frequencies and gametic linkage disequilibria contribute in different ways to the strength of the selection barrier.     

ASSOCIATIONS BETWEEN MITOCHONDRIAL AND NUCLEAR GENOTYPES IN CUTTHROAT TROUT HYBRID SWARMS

We examined mtDNA and nuclear allozyme genotypes in hybrid populations formed from interbreeding of westslope cutthroat trout (Oncorhynchus clarki lewisi) and Yellowstone cutthroat trout (O. c. bouvieri). These subspecies show substantial genetic divergence (Nei's D = 0.30; mtDNA P = 0.02). Diagnostic alleles at multiple nuclear loci and two distinct mtDNA haplotypes segregate in the hybrids. Nuclear and mtDNA genotypes are largely randomly associated, although there is slight disequilibrium in both nuclear and cytonuclear measures in some samples. Consistent positive gametic disequilibria for three pairs of nuclear loci confirm one previously reported linkage, and indicate two more. Allele frequencies provide no evidence for selection on individual chromosome segments. However, westslope mtDNA haplotype frequencies exceed westslope nuclear allele frequencies in all samples. This may be explained by differences in the frequency of occurrence of reciprocal F₁ matings, by viability, fertility, or sex ratio differences in the progeny of reciprocal matings, or by weak selection on mtDNA haplotypes.     

Evolution du polymorphisme enzymatique dans des populations expérimentales de Drosophila melanogaster III. Déséquilibre de linkage entre les locus Adh et α-Gpdh

Evolution of enzyme polymorphism in experimental populations of Drosophila melanogaster III. Linkage disequilibrium between alleles of the Adh and -Gpdh loci — The evolution of gametic frequencies and linkage disequilibria between alleles of the Adh and -Gpdh-loci was followed in two experimental populations of Drosophila melanogaster maintained at different temperatures. The results observed were compared with those expected on the basis of theoretical models of gametic selection. Gametic fitness values were estimated from the analysis of the productivity of the different homozygous genotypes.Our experimental results indicate that the selection favours an association between the alleles Adh-F and -Gpdh-S, but it is impossible to generate and/or maintain a stable linkage disequilibrium between the two alleles.     

Analysis of multilocus zygotic associations

While nonrandom associations between zygotes at different loci (zygotic associations) frequently occur in Hardy-Weinberg disequilibrium populations, statistical analysis of such associations has received little attention. In this article, we describe the joint distributions of zygotes at multiple loci, which are completely characterized by heterozygosities at individual loci and various multilocus zygotic associations. These zygotic associations are defined in the same fashion as the usual multilocus linkage (gametic) disequilibria on the basis of gametic and allelic frequencies. The estimation and test procedures are described with details being given for three loci. The sampling properties of the estimates are examined through Monte Carlo simulation. The estimates of three-locus associations are not free of bias due to the presence of two-locus associations and vice versa. The power of detecting the zygotic associations is small unless different loci are strongly associated and/or sample sizes are large (>100). The analysis of zygotic associations not only offers an effective means of packaging numerous genic disequilibria required for a complete characterization of multilocus structure, but also provides opportunities for making inference about evolutionary and demographic processes through a comparative assessment of zygotic association vs. gametic disequilibrium for the same set of loci in nonequilibrium populations.     

Multivariate Analysis of Gametic Disequilibrium in the Yanomama

The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.     

THE DETECTION OF GAMETIC DISEQUILIBRIUM BETWEEN ALLOZYME LOCI IN NATURAL POPULATIONS OF DROSOPHILA

The capacity of the usual tests (chi-square and related tests) to detect gametic disequilibrium between allozyme loci in natural populations of Drosophila has been investigated. We analyzed a large collection of previously reported gametic samples from natural populations involving a variety of loosely linked allozyme loci located along the O chromosome of Drosophila subobscura and the second chromosome of D. melanogaster. It is found that the statistical power of the individual tests to detect the sample disequilibria between allozyme loci is remarkably low, being the average (over pairs of loci) of power estimates close to 0.20 in both species. Moreover, the average minimum disequilibrium (D‘_min) that would be required to reject (90% probability) the hypothesis of gametic equilibrium is higher than 0.50 given the observed degree of polymorphism and sample sizes used. This means that statistically significant associations between allozyme loci would rarely be detected by single-sample tests even when much disequilibrium is present in natural populations of Drosophila. However, an alternative approach based on the analysis of disquilibrium for large sets of gametic samples, combining probabilities from single independent tests and assessing significance by a bootstrap procedure, reveals that most of the locus pairs within segment I and II of the O chromosome of D. subobscura and left arm of the second chromosome of D. melanogaster present significant nonrandom associations. Within these chromosomal sections, the observed average absolute value of disquilibrium (D‘) between loci is around 0.25 (under the more conservative estimation). Also, a positive relationship between the magnitude of disequilibrium and linkage was detected. These findings suggest that weak or moderate values of disequilibrium between loosely linked allozyme loci are more frequent in natural populations of Drosophila than is currently believed.