Further study on the genetic correlation between members of a multigene family.

The extent of genetic similarity (in terms of identity coefficients) was investigated among members of a multigene family that is evolving under mutation, unequal crossing over and random genetic drift. The method of KIMURA and Ohta (1979) was used, but the possibility was incorporated that the length of the shift (in terms of the number of genes) involved in unequal crossing over can be more than one gene unit. Extensive numerical analyses show that, at equilibrium, the identity coefficients between two gene members are practically independent of their distance apart on the chromosome when the mean length of the shift at unequal crossing over is more than 10% of the total size of the family. In that case, the approximate treatment by OHTA (1980) is shown to be valid, but when the mean length of the shift is less than 10%, the average identity coefficient at equilibrium is underestimated. In order to clarify the effect of natural selection responsible for keeping the family size stable, Monte Carlo simulation studies were performed. The results indicate that the identity coefficients are not greatly influenced by natural selection on gene family size, particularly when the number of genes shifted is small compared to the family size. In addition, with sufficiently strong selection on family size, unequal crossovers with a large shift (such as with maximum shift of 90% of the family size) become ineffective and almost indistinguishable from those with a small shift.