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.     

Genetic Diversity and Linkage Disequilibrium in Drosophila melanogaster with Different Rates of Development

We have examined eight enzyme polymorphisms in groups of Drosophila melanogaster flies with fast, intermediate and slow development. The allelic frequencies are similar in all three developmental classes, but the distribution of the genotypes among the classes is significantly heterogenous for the three loci on the second chromosome. When the total sample of 300 individuals is examined, significant gametic disequilibrium appears in 3 out of 13 pairs of genes located on the same chromosome and in 4 out of 15 pairs of genes located on different chromosomes. This 25% incidence of disequilibrium between pairs of genes is larger than previously observed in other natural populations (but similar to the incidence observed in laboratory populations). The greater frequency of significant gametic disequilibrium in our study is probably due to the larger number of genomes sampled.-Some models specifically predict that individuals with faster rates of development (i.e., greater fitness) should be more heterozygous (and exhibit more linkage disequilibrium) than individuals with slower development. This hypothesis is not supported by our results.     

Genetic microstructure in two Spanish cat populations. II: gametic disequilibrium and spatial autocorrelation

In a previous publication, we described some aspects of the microgenetic structure of two Spanish cat populations (in Barcelona and Alicante). In the present study, the possible existence ofgametic disequilibrium and spatial genetic structure for these populations, at the coat colour pattern and length genes O, A, T D, L, S and W, was analyzed. There was little gametic disequilibrium between pairs of these loci, despite certain pairs that showed significant systematic gametic disequilibrium (a-d and O-S), which appears to show the action of natural selection on domestic cat populations. Nevertheless, we believe that the major cause of the small amount of gametic disequilibrium found was probably a combination of gene drift and gene flow. The results obtained here were clearly in disagreement with those of Hedrick (1985), who concluded that epistatic selection was the cause of the gametic disequilibrium that he found in cat populations. We also found that although Hardy-Weinberg equilibrium could not be demonstrated, the gametic disequilibrium statistics were not affected by this fact, adding credence to the estimates obtained. We found no genetic spatial structure inside the city of Barcelona, as shown by analysis of the spatial autocorrelation of the individual loci, and analysis of the coordinates of the two first axes of a multidimensional scale. However, some gametic disequilibrium statistics showed certain spatial patterns, which leads us to consider the possibility of several evolutionary processes acting upon some of Barcelona's cat colonies.     

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

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

Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

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

Modeling extent and distribution of zygotic disequilibrium: implications for a multigenerational canine pedigree

Unlike gametic linkage disequilibrium defined for a random-mating population, zygotic disequilibrium describes the nonrandom association between different loci in a nonequilibrium population that deviates from Hardy-Weinberg equilibrium. Zygotic disequilibrium specifies five different types of disequilibria simultaneously that are (1) Hardy-Weinberg disequilibria at each locus, (2) gametic disequilibrium (including two alleles in the same gamete, each from a different locus), (3) nongametic disequilibrium (including two alleles in different gametes, each from a different locus), (4) trigenic disequilibrium (including a zygote at one locus and an allele at the other), and (5) quadrigenic disequilibrium (including two zygotes each from a different locus). However, because of the uncertainty on the phase of the double heterozygote, gametic and nongametic disequilibria need to be combined into a composite digenic disequilibrium and further define a composite quadrigenic disequilibrium together with the quadrigenic disequilibrium. To investigate the extent and distribution of zygotic disequilibrium across the canine genome, a total of 148 dogs were genotyped at 247 microsatellite markers located on 39 pairs of chromosomes for an outbred multigenerational pedigree, initiated with a limited number of unrelated founders. A major portion of zygotic disequilibrium was contributed by the composite digenic and quadrigenic disequilibrium whose values and numbers of significant marker pairs are both greater than those of trigenic disequilibrium. All types of disequilibrium are extensive in the canine genome, although their values tend to decrease with extended map distances, but with a greater slope for trigenic disequilibrium than for the other types of disequilibrium. Considerable variation in the pattern of disequilibrium reduction was observed among different chromosomes. The results from this study provide scientific guidance about the determination of the number of markers used for whole-genome association studies.     

Association between a genetic trait and a marker: Discrimination between epistasis and gametic disequilibrium

Summary We reconsider the method of Ott and Falk (1982) for the analysis of genetic linkage and of epistasis in the presence of phenotypic association. Their approach is extended to allow for gametic disequilibrium between marker and trait loci. We show that epistasis and tight linkage with gametic disequilibrium may be indistinguishable as explanations of association even in a very large pedigree.     

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.     

A long-term study on seasonal changes of gametic disequilibrium between allozymes and inversions in Drosophila subobscura

Seasonal variation (spring, early summer, late summer, and autumn) of gametic disequilibrium between gene arrangements (OST and O3+4) of the O chromosome and Lap, Pept-1, and Acph allozyme loci, located inside these inversions, has been recorded in a natural population of Drosophila subobscura during seven years over a 15-year period. The length of the study allowed us to investigate the temporal variation of the allozyme-inversion associations by statistical methods of time series analysis. Cyclic seasonal changes of allozyme-inversion associations for both Lap and Pept-1 are detected in the natural population. In both cases, the patterns of seasonal change are due to the seasonal change of frequency of Lap and Pept-1 allozymes occurring exclusively within the OST gene arrangement. In contrast, the allozyme frequencies at these loci within the O3+4 gene arrangement are stable along seasons. The patterns of temporal variation of allozyme-inversion associations for Lap and Pept-1 in the natural population are contrasted with those previously published that correspond to gene arrangements of the O chromosome and nucleotide polymorphism at the rp49 region located inside these inversions, suggesting that natural selection is operating on these allozyme-inversion associations.     

On supergenes. II. The estimation of gametic excess in natural populations

The behaviour of supergenes (closely linked blocks of co-adapted loci) can be studied by using various parameters of gametic excess (= linkage disequilibrium). Three useful parameters are the gametic determinant (D), the relative determinant (D'), and the log of the eross product ratio. The behaviour of the gametic determinant under mating and recombination is described. Formulae are given for estimating gametic excess in natural populations, Recombination, and the fitness of double heterozygotes, may be estimated from the determinants at different stages of the life cycle; this would be useful in human population genetics.     

Polymorphism in a Cyclic Parthenogenetic Species: SIMOCEPHALUS SERRULATUS

A survey of sixteen isozyme loci using electrophoretic techniques was conducted for three isolated natural populations and one laboratory population of the cyclic parthenogenetic species, Simocephalus serrulatus. The proportion of polymorphic loci (33%-60%) and the average number of heterozygous loci per individual (6%-23%) in the three natural populations were found to be comparable to those found in most sexually reproducing organisms. Detailed analyses were made for one of these populations using five polymorphic loci. The results indicated that (1) seasonal changes in genotypic frequencies took place, (2) apomicitic parthenogenesis does not lead to genetic homogeneity, and (3) marked gametic disequilibrium at these five loci was present in the population, indicating that selection acted on coadapted groups of genes.     

Paternity exclusion and the paternity index for two linked loci

Algebraic expressions for the average exclusion frequency and the paternity index are derived for two linked loci, each with two alleles segregating in a population. The effects of recombination and gametic disequilibrium on these two statistics are discussed. As long as recombination is known to exist, the average exclusion frequency is similar for different recombination fractions. The paternity index, on the other hand, depends very much on both the recombination fraction and gametic disequilibrium. The effects of multiple alleles and dominance on these statistics are also briefly discussed.     

Analysis of complex allozyme polymorphisms in a barley population

Genotypes of 68,230 individuals taken from 10 generations (F₄–F₆, F₁₄–F₁₇, F₂₄–F₂₆) of an experimental population of barley were determined for four esterase loci. The results show that frequencies of gametic ditypes changed significantly over generations and that striking gametic phase disequilibrium developed within a few generations for each of the six pairwise combinations of loci which were monitored. The complex behavior of these four enzyme loci in the population is attributed to interactions between selection and restriction of recombination resulting from the effects of linkage and/or inbreeding.     

Isolation of 21 polymorphic microsatellite markers for the Virginia opossum (Didelphis virginiana)

Twenty-one polymorphic microsatellite markers were developed for the Virginia opossum (Didelphis virginiana). The number of alleles ranged from two to 13 and observed heterozygosities ranged from 0.464 to 0.964. Significant heterozygote deficiencies were observed at three loci and null alleles were detected at five loci. Evidence for gametic disequilibrium was observed between three sets of paired loci after a sequential Bonferroni correction was applied. These markers will enable us to investigate the mating tactics, movement behaviour and social structure of Virginia opossum populations inhabiting fragmented agricultural landscapes.     

Definition and Properties of Disequilibrium Statistics for Associations between Nuclear and Cytoplasmic Genotypes

We define and establish the interrelationships of four components of statistical association between a diploid nuclear gene and a uniparentally transmitted, haploid cytoplasmic gene: an allelic (gametic) disequilibrium (D), which measures associations between alleles at the two loci; and three genotypic disequilibria (D1, D2, D3), which measure associations between two cytotypes and the three respective nuclear backgrounds. We also consider an alternative set of measures, including D and the residual disequilibrium (d). The dynamics of these disequilibria are then examined under three conventional models of the mating system: (1) random mating; (2a) assortative mating without dominance (the "mixed-mating model"); and (2b) assortative mating with dominance ("O'Donald's model"). The trajectories of gametic disequilibria are similar to those for pairs of unlinked nuclear loci. The dynamics of genotypic disequilibria exhibit a variety of behaviors depending on the model and the initial conditions. Procedures for statistical estimation of cytonuclear disequilibria are developed and applied to several real and hypothetical data sets. Special attention is paid to the biological interpretations of various categories of allelic and genotypic disequilibria in hybrid zones. Genetic systems for which these statistics might be appropriate include nuclear genotype frequencies in conjunction with those for mitochondrial DNA, chloroplast DNA, or cytoplasmically inherited microorganisms.     

POPULATION GENETICS OF INTRAGAMETOPHYTIC SELFING

Intragametophytic selfing is a mode of reproduction occurring in homosporous ferns where two gametes from the same haploid gametophyte form a completely homozygous sporophyte. The inbreeding equilibrium is derived for a population with partial intragametophytic selfing, selfing, and outcrossing. Procedures for directly estimating the extent of intragametophytic selfing and selfing using parent-offspring data are given. The conditions for a stable polymorphism from a heterozygous-advantage fitness model are more restrictive for partial intragametophytic selfing than for selfing. The rate of decay of gametic disequilibrium is slower for partial intragametophytic selfing than for selfing. Based on these findings, one would predict that plants with intragametophytic selfing would have less polymorphism for loci with a heterozygous advantage and more gametic disequilibrium between neutral loci than is expected for populations with an equivalent amount of selfing. Data from several studies are consistent with these predictions.