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."     

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.     

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.     

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.     

Quantitative character dynamics: Gametic model

A gametic model of quantitative character dynamics is introduced that fills the gap between the two existing models: genic and zygotic/phenotypic. In this model, a gamete is treated as the elementary unit of evolution, all biological processes at the levels below gametic remain unspecified, and a gamete is characterized by its effect on the quantitative character rather than by the genotype. The hereditary and developmental processes are accounted for in a generalized form by gametogenetic and developmental functions defined for a pair of gametic effects representing an individual. A parameterization of these functions is suggested that imposes constraints on the heredity of quantitative characters similar to the constraints imposed by traditional genic models. It is shown that this parameterization can be derived for some polygenic additive models. General expressions for the dynamics of the mean and variance of additive quantitative characters are obtained, and the dynamics under random mating for sex-independent, sex-controlled, and sex-linked characters are considered. Comparisons with the dynamics predicted by genic models are made.     

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.     

Proceed with Care: Direct Predictive Testing for Huntington Disease

The cloning of the Huntington disease (HD) gene allows highly accurate predictive testing using direct analysis of the CAG repeat. This new test provides results with almost complete certainty but poses unique counseling issues related to direct testing for an adult-onset disease. These include testing individuals who are at 25% risk, without the need for blood from a 50% at risk relative; the assessment of symptomatic individuals; the need for ongoing counseling despite simplification of laboratory procedures; and counseling of persons from families who represent a new mutation for HD. This paper describes protocols for direct predictive testing for adult and prenatal assessment, on the basis of the experience of the Canadian Collaborative Study on Predictive Testing (CCSPT). Over the past 8 years, we have provided >400 results by using linked markers and, more recently, 416 results by using direct assessment of CAG expansion in the HD gene. The vast majority (86%) of requests for direct predictive testing have been from persons who have not previously received results by using linked markers. Despite the ability to now directly assess for the mutation associated with HD, we still recommend assessment of DNA from an affected relative, as this may significantly enhance the accuracy of information to be provided to the at-risk individual. Distance from a genetics center has previously limited the availability of testing, and therefore we have developed approaches to providing predictive testing in the patient's own community.     

Quantitative characters under assortative mating: Gametic model

The gametic model introduced by Gimelfarb (1982, Theor. Pop. Biol. 22, 324-366) is applied to investigating the dynamics, represented in the model by a second-order recurrence equation, the the variance of sex-independent and sex-controlled characters under assortative mating. It is shown that, for any additive character, there always exists a unique equilibrium for the variance, which is stable. Dynamical properties of the variance under positive and negative matings are considered, and numerical evaluations of the equilibrium values as well as of the dynamical changes of the variance are presented. Comparisons with results from a biological experiment are made.     

基因型错误对数量性状精细定位的哈迪-温伯格不平衡指数的效应

使用紧密相邻的标记位点且与标记基因频率无关的哈迪-温伯格不平衡(HWD)指数被用来对数量性状位点(QTL)进行精细定位.本文讨论了当存在基因型错误时HWD指数的性质.文章指出,当存在基因型错误时,对于在群体的标记基因频率已知的情形使用的两个HWD指数尽管受基因型错误的影响但仍然有效;而仅仅极端样本的标记基因频率已知的情形下使用的两个HWD指数同时与基因型错误和标记基因频率有关.计算机模拟表明,仅仅极端样本的标记基因频率已知的情形下使用的两个HWD指数在精细定位时会产生偏差,不适宜作精细定位.     

Gametic Differentiation of Chlamydomonas reinhardtii: Control by Nitrogen and Light

Gametic differentiation of the unicellular green alga Chlamydomonas reinhardtii proceeds in two steps controlled by the extrinsic signals nitrogen deficiency and light. Nitrogen deprivation induces the differentiation of vegetative cells to sexually immature pregametes. A light signal is required to convert the pregametes to gametes. Both signals are also required for the maintenance of mating competence. Two converging signal transduction chains are proposed to control gamete formation. For the differentiation of pregametes to gametes, a fluence rate-dependent reaction, requiring continuous irradiation, is suggested by photobiological experiments.     

Gametic and pleiotropic defects in mouse fetuses with Hertwig's macrocytic anemia

Pleiotropic effects on germ cell number, hematologic status, and body size are described in 12- to 15-day WBB6F1 normal (+/-) and defective (an/an) mouse fetuses, with special emphasis on gametogenesis. Differences between genotypes were apparent by Day 12. At 12 days, normal testes contained many germ cells and frequent normal mitoses, and the number of germ cells increased rapidly from Day 12 to Day 15. By contrast, 12-day an/an testes contained fewer germ cells, frequently degenerating, and many abnormal mitoses. Their number of germ cells decreased rapidly, so that almost none persisted to Day 15. Normal ovaries contained many germ cells, with much normal mitosis on Day 12 and 13, followed by meioses, but the smaller an/an ovaries contained few germ cells, with little mitosis, some meiosis, and very much degeneration. The erythrocyte counts of both normal and anemic fetuses increased approximately fourfold between 12 and 15 days, but at comparable ages, total counts were always lower in an/an fetuses than in normal littermates. At all ages, Hertwig's anemic (an/an) fetuses were somewhat smaller than their normal littermates. Although both W/Wv and Sl/Sld mice also show macrocytic anemia and germ cell failure, the great difference in etiology of their germ cell defects indicates that an/an gene action must be qualitatively different from that in either W/Wv or Sl/Sld mice.