Commentary: statistical analysis or biological analysis as tools for understanding biological causes.
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Biomedical subjects
Publications and source records attributed to R C Lewontin.
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In order to understand both the past and future directions of research in evolutionary biology we need to begin by understanding in what way these programs of research differ from the model of most scientific work. The study of evolutionary processes and, in particular, the genetics of the evolutionary process must confront special difficulties in both the conceptual and the methodological aspects of research. On the conceptual side, unlike for molecular, cellular, and developmental biology, there is no basic mechanism that evolutionists are attempting to elucidate. There is no single cause of the evolutionary change in the properties of members of a species. Natural selection may be involved but so are random events, patterns of migration and interbreeding, mutational events, and horizontal transfer of genes across species boundaries. The change in each character of each species is a consequence of a particular mixture of these causal pathways.
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In the comparison of DNA and protein sequences between species or between paralogues or among individuals within a species or population, there is often some indication that different regions of the sequence are divergent or polymorphic to different degrees, indicating differential constraint or diversifying selection operating in different regions of the sequence. The problem is to test statistically whether the observed regional differences in the density of variant sites represent real differences and then to estimate as accurately as possible the location of the differential regions. A method is given for testing and locating regions of differential variation. The method consists of calculating G(x(k)) = k/n - x(k)/N, where x(k) is the position of the kth variant site along the sequence, n is the total number of variant sites, and N is the total sequence length. The estimated region is the longest stretch of adjacent sequence for which G(x(k)) is monotonically increasing (a hot spot) or decreasing (a cold spot). Critical values of this length for tests of significance are given, a sequential method is developed for locating multiple differential regions, and the power of the method against various alternatives is explored. The method locates the endpoints of hot spots and cold spots of variation with high accuracy.
A study of polymorphism and species divergence of the dpp gene of Drosophila has been made. Eighteen lines from a population of D. melanogaster were sequenced for 5200 bp of the Hin region of the gene, coding for the dpp polypeptide. A comparison was made with sequence from D. simulans. Ninety-six silent polymorphisms and three amino acid replacement polymorphisms were found. The overall silent polymorphism (0.0247) is low, but haplotype diversity (0.0066 for effectively silent sites and 0.0054 for all sites) is in the range found for enzyme loci. Amino acid variation is absent in the N-terminal signal peptide, the C-terminal TGF-beta peptide and in the N-terminal half of the pro-protein region. At the nucleotide level there is strong conservation in the middle half of the large-intron and in the 3' untranslated sequence of the last exon. The 3' untranslated conservation, which is perfect for 110 bp among all the divergent species, is unexplained. There is strong positive linkage disequilibrium among polymorphic sites, with stretches of apparent gene conversion among originally divergent sequences. The population apparently is a migration mixture of divergent clades.
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Regions of differing constraint, mutation rate or combination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.
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Studies of genetic variation in natural populations at the sequence level usually show that most polymorphic sites are very asymmetrical in allele frequencies, with the rarer allele at a site near fixation. When the rarer allele at a site is present only a few times in the sample, say below five representatives, it becomes very difficult to detect linkage disequilibrium between sites from tests of association. This is a consequence of the numerical properties of even the most powerful test of association, Fisher's exact test. Sites with fewer than five representatives in the sample should be excluded from association tests, but this generally leaves few site pairs eligible for testing. A test for overall linkage disequilibrium, based on the sign of the observed linkage disequilibria, is derived which can use all the data. It is shown that more power can be achieved by increasing the length of sequence determined than by increasing the number of genomes sampled for the same total work.
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It has long been realized that age-specific cancer mortality in Familial Adenomatous Polyposis (FAP) was bimodal, and a theory was proposed in which the involved locus was polymorphic in the general population. After the molecular cloning of the region 5q21, it has been suggested that the phenotypic variability in FAP may be due to the interaction of two loci, one of which is polymorphic. We show that these two hypotheses lead to different predictions of the correlation between relatives for a phenotypic trait, and use colorectal cancer mortality data from the Italian Polyposes Registry to verify them. We conclude that the first of the two is more likely and suggest that the same variation that we observe among the affected subjects is present in the general population, thus causing a significant difference between individuals for colon cancer susceptibility.
Variable number of tandem repeat (VNTR) sequences are used to link defendants with crimes by matching DNA patterns. The probative value of a match is often calculated by multiplying together the estimated frequencies with which each particular VNTR pattern occurs in a reference database. However, this method is liable to potentially serious errors because ethnic subgroups within major racial categories exhibit genetic differences that are maintained by endogamy. The multiplication procedure currently in use can be made scientifically valid only by extensive sampling of VNTR frequency distributions in a variety of ethnic groups, similar to the ethnic studies of various blood groups done in the past. Alternative approaches for dealing with subpopulation heterogeneity are discussed.
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