A mathematical study on the distribution of the number of repeated genes per chromosome

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Abstract
SUMMARY: I develop a mathematical model which can account for a distribution of the number of repeated genes per chromosome under the joint effects of sister chromatid exchange (SCE), inter-chromosomal crossing-over (ICC), and selection. The model can be applied not only to the cases of small gene clusters but also to multigene families. Based on this model, an appropriate mathematical formula is derived and used to obtain the equilibrium distribution. Assuming stabilizing selection and two simple schemes concerning SCE and ICC, I numerically calculate the equilibrium distribution and compare the result with observations on frequencies of single and triple α-haemoglobin genes in primates. It is also shown that if SCE and ICC occur according to the same probabilistic law, the distinction between them does not make much sense in the equilibrium distribution.