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Linkage Disequilibrium And Homozygosity Of Chromosome Segments In Finite Populations.
Published 1971 · Biology, Medicine
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In considering populations of finite size, there are two approaches to studying the correlation of genotype frequencies at two linked loci. The first is based on disequilibrium parameters, and the second on identity-by-descent methods. The basic connection between the two approaches may be stated in the following way. The expected square of the correlation of gene frequencies at two loci r2 = D2pApapBpb, is approximately equal to Q, the probability that, given two genes at one locus which are identical by descent, then the two genes at the second locus will be identical by descent through the same pathways. Using this relationship it is shown that for a monoecious population of effective size Ne with no selection, the expected value of r2 will tend to approximately 1(1 + 4Nec), where c is the recombination frequency, the rate of approach being given by (1 − 12Ne)(1 − c)2. Computer simulation has shown that this formula holds with reasonable accuracy, and that it is also quite accurate in populations with heterozygote advantage stabilizing gene frequencies. It is suggested that the measurement of linkage disequilibrium in natural populations might thus be used to give information about the effective population size. The identity-by-descent approach is extended to derive the distribution of the length of homozygous chromosome segment surrounding a locus which is identical by descent. The mean such length is approximately 12Ne(log Ne − 1). It is suggested that a general theory of stability of the genotype in small populations might be based on parameters such as this.