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The distribution of the fraction of the genome identical by descent in finite random mating populations

  • P. Stam (a1)

The probability distribution of the heterogenic (non-identical by descent) fraction of the genome in a finite monoecious random mating population has been derived. It was assumed that in any generation the length of both heterogenic and homogenic segments are exponentially distributed. An explicit expression is given for the expected number of ‘external junctions’ (sites that mark the end of a heterogenic segment) per unit map length in any generation. The latter necessitates the introduction of two higher-order identity relations between three genes, and their recurrence relations. Theoretical results were compared with the outcome of a series of simulation runs (showing a very good fit), as well as with the results predicted by Fisher's ‘theory of junctions’. In contrast to Fisher's approach, which only applies when the average heterogeneity is relatively small, the present model applies to any generation.

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J. H. Bennet (1953). Junctions in inbreeding. Genetica 26, 392406.

R. A. Fisher (1954). A fuller theory of ‘junctions’ in inbreeding. Heredity 8, 187197.

R. A. Fisher (1959). An algebraically exact examination of junction formation and transmission in parent–offspring inbreeding. Heredity 13, 179186.

I. R. Franklin (1977). The distribution of the proportion of the genome which is homozygous by descent in inbred individuals. Theoretical Population Biology 11, 6080.

J. A. Sved (1977). Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theoretical Population Biology 2, 125141.

J. A. Sved & M. W. Feldmann (1973). Correlation and probability methods for one and two loci. Theoretical Population Biology 4, 129132.

B. Weir & C. C. Cockerham (1974). Behaviour of pairs of loci in finite monoecious populations. Theoretical Population Biology 6, 323354.

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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
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