On Measures of Gametic Disequilibrium

Various measures have been proposed for characterizing the statistical association that arises between alleles at different loci. Hedrick has compared these measures with the standardized measure D' proposed by Lewontin on the grounds that this latter measure is independent of allele frequency. Although D' has the same range for all allelic frequencies, in fact, D' is not "independent" of allele frequency, and no measure with that general property is possible for the multilocus association problem. The insolubility of this problem arises from the ill-defined nature of general "association."     

Likelihood Analysis of Recombinational Disequilibrium in Multiple-Locus Gametic Frequencies

Likelihood methods are developed for the estimation and testing of multiple-locus gametic disequilibria, using log-linear models of parametric effects. The estimates of disquilibrium are related to Kimura's Z-measure, and may be extended to multiple alleles and multiple loci. Likelihood ratio test criteria are constructed, which are asymptotically distributed as chi(2). The analysis is partitioned into various components corresponding to two-locus, residual three-locus, and higher order disequilibria. A four-locus example from Hordeum vulgare L. is utilized to illustrate the analysis. Most of the multiple-locus disequilibrium is accounted for by two-locus effects, and closely linked loci show considerably more disequilibrium than unlinked loci. It is shown that all possible pairwise comparisons are not statistically independent.     

Gametic Disequilibrium Measures: Proceed with Caution

Five different measures of gametic disequilibrium in current use and a new one based on R. C. Lewontin's D', are examined and compared. All of them, except the measure based on Lewontin's D', are highly dependent upon allelic frequencies, including four measures that are normalized in some manner. In addition, the measures suggested by A. H. D. Brown, M. F. Feldman and E. Nevo, and T. Ohta can have negative values when there is maximum disequilibrium and have rates of decay in infinite populations that are a function of the initial gametic array. The variances were large for all the measures in samples taken from populations at equilibrium under neutrality, with the measure based on D' having the lowest variance. In these samples, three of the measures were highly correlated, D2, D (equal to the correlation coefficient when there are two alleles at each locus) and the measure X(2) of Brown et al. Using frequency-dependent measures may result in mistaken conclusions, a fact illustrated by discussion of studies inferring recombinational hot spots and the effects of population bottlenecks from disequilibrium values.     

Genetic Coadaptation in the Chromosomal Polymorphism of DROSOPHILA SUBOBSCURA. I. Seasonal Changes of Gametic Disequilibrium in a Natural Population

Seasonal changes in gene arrangement and allozyme frequencies have been investigated in Drosophila subobscura for several years. Some arrangements (O_st and O₃₊₄₊₇) show seasonal variation, which suggests that chromosomal polymorphism is flexible in this species. Seasonal changes in allozyme frequencies for Lap and Pept-1 loci, both located within the same inversions of chromosome O, are significant only inside the O_st arrangement, but not inside O₃₊₄ arrangement. This arrangement-dependent response of allozyme generates variation in arrangement-allozyme disequilibrium. The historical hypothesis on the maintenance of disequilibria cannot explain these seasonal changes, and some kind of natural selection must be invoked. Association between Lap and Pept-1 is also seasonal inside O_st but not inside O₃₊₄. We propose that O_st probably consists of a finite array of supergenes that are differentially favored in each season by natural selection. The present evidence on this supergene selection and other genetic, biogeographic and phylogenetic data points to O₃₊₄ as the most primitive gene order among the present arrangements.     

Multivariate classification of human populations. I. Allocation of Yanomama indians to villages.

A set of 12 anthropometric measures and six genetic traits, available for 520 Yanomama Indians from 19 villages in nine clusters, were used to allocate individuals to villages. On the basis of anthropometrics alone, 36% of the individuals were allocated to the right village and 60% to the right cluster. On the basis of genetic traits alone, 16% were allocated to the right village and 26% to the right cluster. A combination of all 18 characters yielded 41% allocation to the right village and 63% to the right cluster. Of the 924 possible combinations of six anthropometric measures, only one provided poorer resolution than did the six genetic traits. We explain the better resolution of the anthropometric traits by noting that the anthropometric traits are not totally heritable and that genetic traits are not continuously distributed. Randomization studies indicated that all of the observed correct-allocation fractions are far in excess of random expectation. We infer that the village phenotype distributions overlap only partially, and that they represent real and substantial population differentiation.     

The Genetical Response to Natural Selection by Varied Environments. IV. Gametic Disequilibrium in Spatially Varied Environments

Gametic disequilibria between allozyme loci were related to spatial variation of the environment in caged populations of Drosophila melanogaster . Two experiments, one with flies collected at "Chateau Tahbilk," South Australia, and the other with flies from "Groningen," The Netherlands, were sampled at generations 16 and 32. Spatial variation of the environment was stimulated using three food media. Eight polymorphic allozyme loci were used to estimate gametic disequilibria from digenic combinations of allotypes. All populations were duplicated within an environment and maintained at about 2500 adults. Standardized gametic disequilibria were compared by a weighted least squares analysis of the z-transformed statistical correlation of allele frequencies. Gametic disequilibria were strongly dependent upon food niche and food-niche interactions. The effects also varied with sampling time and were similar in duplicate populations. Gametic disequilibria were most often detected in the "Groningen"-derived populations and their strength was not strongly associated with recombination fraction. Many of the disequilibria concerned unlinked loci. The strength of selection was probably considerable and populations were evolving genetic architectures which reflected niche selection by the different foods without marked genetic isolation between foods; gene frequencies did not vary between niches within a population cage.     

Bilirubin binding by variant albumins in Yanomama Indians

Sera of Yanomama Indians homozygous for the common albumin allele exhibited greater total effective-binding capacities for bilirubin than did sera of individuals homozygous for the Yan-2 albumin variant in the in vitro experiments described herein. Total effective binding capacities of heterozygous samples were close to those of homozygotes for AlA. Individuals homozygous for Yan-2 might experience a higher risk of bilirubin toxicity and related disorders during the neonatal period. Further studies of binding and displacement of bilirubin by competitors, such as dietary or medicinal coumarins, might help explain the existence of these polymorphisms and the significance of phenotypic differences in binding to bilirubin.     

The genetic structure of a tribal population, the Yanomama indians. VII. Anthropometric differences among Yanomama villages

Anthropometric data on 12 variables in 19 villages of the Yanomama Indians demonstrate significant heterogeneity in physique among villages of this tribe. Mahalanobis' distances (D²) calculated from the data lead to the tentative conclusion of a general correspondence between anthropometric and geographic distances separating villages. The mean stature of the Yanomama is smaller than that of most other South American tribes which have been measured, and the Yanomama are genetically distinct from the other small Indians as shown by genetic distances based on allele frequencies for a variety of genetic markers. Since some subjects were measured more than once by the same and by different observers, it was possible to calculate approximate estimates of variance within and between observers. Univariate analysis indicates that face height and nose height are especially susceptible to systematic differences in technique between observers. The variances obtained in this field study compare favorably with those of some classical laboratory studies described in the literature. It was found that measurement error nevertheless probably makes a substantial contribution to anthropometric distance between villages. The median error variance as a fraction of that of Herskovits ('30) is 0.62 for the seven measurements in common with this study. The median value of the error variance for the 12 variables in this study is between 16% and 17% of the total variance.     

Disequilibrium Pattern Analysis. I. Theory

We have developed a method, disequilibrium pattern analysis, for examining the disequilibrium distribution of the entire array of two locus multiallelic haplotypes in a population. It is shown that a selected haplotype will produce a distinct pattern of linkage disequilibrium values for all generations while the selection is acting. This pattern will also presumably be maintained for many generations after the selection event, until the disequilibrium pattern is eventually broken down by genetic drift and recombination. Related haplotypes, sharing an allele with a selected haplotype, assume a value of linkage disequilibrium proportional to the frequency of the unshared allele and have a single negative value of the normalized linkage disequilibrium. The analysis assumes zero linkage disequilibrium for all allelic combinations initially. The same basic results continue to apply if the selection involves a new mutant, the occurrence of which creates linkage disequilibrium for some haplotypes. The disequilibrium pattern predicted under selection is robust with respect to the influence of migration and random genetic drift. This method is applicable to population data having linked polymorphic loci including that determined from protein or DNA sequencing.     

Gametic conflict versus contact in the evolution of anisogamy

Anisogamy refers to gametes that differ in size, and characterizes the difference between males and females. The evolution of aniosgamy is widely interpreted as involving conflict between gamete producers with small sperm parasitizing on the investment made by the eggs. Using a population genetic model for evolution at a locus that codes jointly for sperm and egg sizes of a hermaphrodite, we show that the origin of anisogamy in an externally spawning population need not involve conflict between gamete producers. Gamete size dimorphism may be an adaptation that increases gamete encounter rates when large zygotes are selected, and we show this in a mechanistically general individual selection model. We use the Vance survival function without specific allometric assumptions to model the zygote fitness dependence on its size, and hence obtain ecological and life-history correlates of isogamy and anisogamy, which we successfully compare with data from Volvocales.     

Isolation and Genetic Analysis of Mutant Strains of CHLAMYDOMONAS REINHARDI Defective in Gametic Differentiation

Impotent mutant strains of Chlamydomonas reinhardi, mating-type (mt) plus, are described that have normal growth and motility but fail to differentiate into normal gametes. Procedures for their isolation and their genetic analysis are described. Five of the imp strains (imp-2, imp-5, imp-l, imp-7, and imp-8) exhibit no flagellar agglutination when mixed with mt- or mt+ gametes and the mutations are shown to be unlinked to the mt locus (with the possible exception of imp-7). Two of the strains (imp-3 and imp-4) carry leaky mutations that affect cell fusion; neither mutation is found by tetrad analysis to be linked to mt or to the other. Cells of the imp-1 strain agglutinate well with mt- gametes and active agglutination continues for up to 48 hours, but cell fusion occurs only very rarely. Analysis of these rare zygotes indicates that imp-1 is closely linked to the mt+ locus, and fine-structural studies reveal that imp-1 gametes produce a mutant mating structure involved in zygotic cell fusion. The development of sexuality in C. reinhardi therefore appears amenable to genetic dissection.     

Reinforcement of Gametic Isolation in Drosophila

Reinforcement, a process by which natural selection increases reproductive isolation between populations, has been suggested to be an important force in the formation of new species. However, all existing cases of reinforcement involve an increase in mate discrimination between species. Here, I report the first case of reinforcement of postmating prezygotic isolation (i.e., barriers that act after mating but before fertilization) in animals. On the slopes of the African island of São Tomé, Drosophila yakuba and its endemic sister species D. santomea hybridize within a well-demarcated hybrid zone. I find that D. yakuba females from within this zone, but not from outside it, show an increase in gametic isolation from males of D. santomea, an apparent result of natural selection acting to reduce maladaptive hybridization between species. To determine whether such a barrier could evolve under laboratory conditions, I exposed D. yakuba lines derived from allopatric populations to experimental sympatry with D. santomea, and found that both behavioral and gametic isolation become stronger after only four generations. Reinforcement thus appears to be the best explanation for the heightened gametic isolation seen in sympatry. This appears to be the first example in animals in which natural selection has promoted the evolution of stronger interspecific genetic barriers that act after mating but before fertilization. This suggests that many other genetic barriers between species have been increased by natural selection but have been overlooked because they are difficult to study.     

Gametic imprinting and expression of the gene Fused in the house mice

The discovery of the gametic imprinting phenomena in mammals makes it possible to have a new look at some facts concerning the expression and inheritance of genes with variable penetrance. Fused (Fu) is a dominant mutation located on chromosome 17, one of the few examples uses to demonstrate gametic imprinting in mice. This mutation has maternal effect connected with decrease in its penetrance. It was shown that t12 haplotype significantly reduces penetrance of the Fu in the progeny of Fu/t12 females. The results of reciprocal crosses of heterozygotes for t12 haplotypes indicate that penetrance of maternal Fu gene is reduced. Far more strong influence on the fused penetrance have the dominant suppressors, located beyond the chromosome 17. The penetrance of the fused gene decreases in that case up to 8-17%. Results of the experiments show strong influence of gametic pathway on penetrance of the gene by which the gene is transmitted to the next generation. The results also made it possible to describe the regularities of gametic imprinting. This phenomenon clearly indicates the existence of gametic and zygotic ontogenetic phases. According to the hypothesis proposed gametic phase of ontogenesis in mammals starts after initialization, i. e. after a process of chromosome erasing from epigenetic information and preparing to enter the next ontogenetic cycle.     

Linkage Disequilibrium Analysis of Chromosomal Inversion Polymorphisms of Drosophila

The linkage disequilibrium pattern analysis is a method that allows one to detect present and past events of selection. We applied it to our data on the inversions of Drosophila mediopunctata and to published data of Drosophila subobscura, which are systems probably under complex modes of selection. The method gave meaningful results showing that it might be an excellent exploratory tool to identify problems worthy of further study. It is also suggested that it can be used as a criterion to determine the roots of inversion phylogenies.     

Gametic isolation in guppies (Poecilia reticulata)

Post-mating reproductive isolating mechanisms may be among the earliest reproductive barriers to emerge among incipient species. Trinidadian guppy, Poecilia reticulata, populations in the Caroni and Oropouche drainages in Northern Trinidad exhibit marked genetic divergence and provide an ideal system in which to search for these barriers. We inseminated virgin females with equal amounts of sperm from two males, a 'native' male from the female's own population and a 'foreign' male from the other drainage. Artificial insemination ensured that mating order and mate choice did not affect the outcome. Paternities were assigned to the resulting broods using microsatellite markers. As predicted, sperm from native males had precedence over foreign sperm. Moreover, this effect was symmetrical for both drainages. In contrast, we detected no native sperm precedence in controls, in which females received sperm from the same and another population within the same drainage. Our results show that gametic isolation can arise between geographically proximate, though genetically divergent, populations of a single species and highlight the potential role of this process in speciation.     

Gametic coupling as a cause of correlations

Ohne Zusammenfassung

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Gametic coupling as a cause of correlations

     

Action Spectrum for the Light-Dependent Step in Gametic Differentiation of Chlamydomonas reinhardtii

Differentiation of Chlamydomonas reinhardtii vegetative cells to gametes requires two environmental signals: nitrogen starvation and light. Vegetative cells incubated without nitrogen differentiate into pregametes. Pregametes can be converted into sexually mature gametes by irradiation with light. The action spectrum for the light-dependent step in gamete formation showed two maxima at 370 and 450 nanometers. This is similar to the spectrum of other blue light/ultraviolet light-A-absorbing photoreceptors.     

The Polynomial Model in the Multivariate Analysis of Variance

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy-coded or effect-coded design matrices) the so-called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.