Genetic variation in small multigene families

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Abstract
SUMMARY: In order to understand the evolution of genetic systems in which two genes are tandemly repeated (small multigene family) such as has been recently found in the haemoglobin α loci of primates, haemoglobin β loci of mouse and rarbit and other proteins, a population genetics approach was used. Special reference was made to the probarility of gene identity (identity coefficient), when unequal crossing-over is continuously occurring as well as random genetic drift, inter-chromosomal recombination and mutation. Two models were studied, cycle and selection models. The former assumes that unequal crossing-over occurs in cycles of duplication and deletion, and that the equilibrium identity coefficients were obtained. The latter is based on more realistic biological phenomena, and in this model it is assumed that natural selection is responsible for eliminating chromosomes with extra or deficient gene dose. Unequal crossing-over, inter-chromosomal recombination and natural selection lead to a duplication-deletion balance, which can then be treated as though it were a cycle model. The basic parameter is the rate of duplication-deletion which is shown to be approximately equal to 2(u+ 2β)X, whereuis the unequal crossing-over rate, 2β is the inter-chromosomal recombination rate andXis the frequency of chromosomes with three genes or of that with one gene. Genetic variation of the globin gene family, of which gene organization is known in most detail, is discussed in the light of the present analyses.