Theoretical population genetics of repeated genes forming a multigene family

The evolution of repeated genes forming a multigene family in a finite population is studied with special reference to the probability of gene identity, i.e., the identity probability of two gene units chosen from the gene family. This quantity is called clonality and is defined as the sum of squares of the frequencies of gene lineages in the family. The multigene family is undergoing continuous unequal somatic crossing over, ordinary interchromosomal crossing over, mutation and random frequency drift. Two measures of clonality are used: clonality within one chromosome and that between two different chromosomes. The equilibrium properties of the means, the variances and the covariance of the two measures of clonality are investigated by using the diffusion equation method under the assumption of constant number of gene units in the multigene family. Some models of natural selection based on clonality are considered. The possible significance of the variance and covariance of clonality among the chromosomes on the adaptive differentiation of gene families such as those producing antibodies is discussed.