Genealogical structure and correlations in gene extinction.
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Biomedical subjects
Publications and source records attributed to E A Thompson.
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Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.
A log-linear analysis has been applied to the survival probabilities of the genes of the founders of Tristan da Cunha. This analysis enables a large set of probabilities to be viewed as a single function, and the features of this function to be analysed. Features of the structure of the ancestral genealogy are thereby illuminated, and the dependence and interactions between founders with regard to the descent of their genes to the current population may be quantified.
The aromatization of androstenedione in human ovarian microsomes is inhibited by an antibody to porcine hepatic microsomal NADPH-cytochrome c reductase. Likewise, the antibody inhibits aromatization in mitochondria isolated from human ovaries and placentae. A given quantity of the antibody produces the same percent inhibition of aromatization in microsomes and mitochondria of both ovaries and placentae. These data, in addition to the low specific activity observed for the mitochondrial aromatase, indicate that aromatization in mitochondria probably results from microsomal contamination.
A pedigree and linkage analysis was performed on a corrected version of the Habbanite pedigree 2 of Slatis et al. [1]. The trait "arch on any digit" was examined for major gene inheritance and possible linkage to several blood and serum group markers. The results confirm the proposed dominant major gene inheritance of this trait with almost complete penetrance. In addition, the analysis suggests linkage with the haptoglobin locus with evidence against linkage with Pl and Rhesus. These results are of particular interest in view of recently reported dermatoglyphic associations with haptoglobin.
Previous approaches to the ascertainment problem have been in terms of a registry-type situation in which the sampled structure is a random variable. However, with the exception of Bailey (1951), previous authors have conditioned on this structure. In extending the theory to pedigrees, a registry situation may also be considered, providing neither the structure nor any part of it (e.g., ages of individuals) are conditioned upon, but it may often be neither practicable nor relevant to do so. In many studies the sampling scheme may fix the number of pedigrees, analyzed, and classical "ascertainment probabilities" are no longer applicable. In an infinite population, in which the ascertainment of and phenotypic observations on, affect neither the distribution of other ascertainments or phenotypic distributions on other pedigrees and chance multiple ascertainments cannot occur, ascertainment corrections are relatively straightforward. However, effective population sizes with regard to particular rare traits may often be small, and the problem of ascertainment corrections in this case has not been fully analyzed, although some preliminary results are presented.
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When an unusually high frequency of an allele is encountered in a population, "founder effect" is often invoked as an explanation. As usually used, the term implies the disproportionate increase through chance (rather than selection) of an allele contributed to the population by a particular ancestor. While genetic theory leaves no doubt this is a possible explanation, problems arise when we try to determine how likely this explanation is for any specific finding in any specific, finite population, i.e., just how rare is this rare event? In this communication we consider the question in the context of Amerindian tribal populations, deriving specific probabilities under defined conditions. Our interest in the question has been whetted by the finding to date of some eight possible examples of a founder effect in studies of twelve different tribes.
In studies extending over the past dozen years, we have observed eight examples of "private" genetic polymorphisms in 12 Amerindian tribes surveyed for electrophoretic variants of an average of 25 proteins. Each of these is presumed to trace to a single mutation. In a preceding communication [Thompson, E.A. & Neel, J.V. (1978) Proc. Natl. Acad. Sci. USA 75, 1442-1445] the statistical theory was developed for estimating the likelihood of such a founder effect in a tribal population of this type. In this paper that theory is applied to the distribution defined by these eight variants. It is demonstrated that on the assumption that the phenotypes in question are selectively neutral, such findings are most compatible with a mutation rate of 7 X 10(-6)/locus per generation. This figure applies only to variants that can be detected by the electrophoretic technique.
The Tristan da Cunha data for the MN-blood types and for retinitis pigmentosa are analysed according to the methods for ancestral inference developed in the preceding paper. Joint and marginal likelihoods for the MN data show that it is possible to make inferences about the types of original founder genes, although relative values are in some cases not large. Although relative likelihoods are robust against small changes in gene frequency, they can be distorted by assuming values that differ widely from the maximum likelihood estimate. In the case of retinitis pigmentosa, under an assumed allele frequency of 0.01, we conclude, contrary to expectations, that the couple (975, 798) are substantially the most likely founders to have been responsible for the introduction of the allele. The inferences for this trait are complicated by the fact that it is recessive, and genotypes are therefore not observable. Extinction probabilities for a variety of sets of original founder genes on the Tristan da Cunha ancestral pedigree are also computed and discussed.
A method for inferring the ancestral genotypes for the founders of a population is developed. This method uses the algorithms for the computation of probabilities on pedigrees of arbitrary complexity, developed by Cannings et al. (1978) and implemented by Thompson (1977b). When characteristics are simply determined by underlying genotypes the inference problem is simplified, and larger and more complex pedigrees may therefore be analysed. The problem of estimating the allele frequencies to be used in computing prior genotype probabilities for those founders on whom a likelihood function is not required is discussed. The same method allows us to compute extinction probabilities for any combination of original founder genes; these probabilities are interesting parameters of pedigree structure, which, since they relate to the actual genes present in a population, help to provide a clearer understanding of observed distributions of autosomal traits.
One aim in the analysis of pedigree data may be to infer the mode of inheritance of a characteristic. If only "interesting" pedigrees are analysed, the ascertainment bias may lead to some modes of inheritance being unintentionally preferred. Also, it is clearly most efficient in attempting to make such inferences, if a decision on whether to continue sampling a pedigree is made conditional on the types of individuals who have been observed; an a priori decision to examine 500 members of a pedigree may lead to much wasted effort, since the pedigree may prove to be largely uninformative. The present paper shows that provided all observed families are included in the analysis, even those which appeared "uninteresting" or "sporadic" and were not sampled further, and provided a decision to continue sampling is made conditional on types observed up to that point, the correct likelihood for the mode of inheritance may be easily computed. This opens the way for a more detailed study of the wider problem of optimal samplings rules on pedigrees.
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Nuclear material can produce inhibition or stimulation of healty leucocytes under different experimental conditions, Reactivity could not be produced in cultures using intact nuclei and allogeneic lymphocytes. The effect of nuclear and cytoplasm fractions was compared with that of whole cells on intact healthy lymphocytes. The HLA activity in the individual fractions was assessed. Stimulation was produced by certain nuclear and cytoplasmic fractions and these were closely related to the peaks of HLA activity. The response to these fractions showed less activity than that achieved in conventional one way MLC tests.
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