SIZE DISTRIBUTION OF GENE FAMILIES IN A GENOME

We consider a probabilistic model of genome evolution. We are interested in size distribution of gene families. The model is based on three fundamental evolutionary events: gene loss, duplication and accumulated change. We assume that the probability of gene loss and duplication is constant and the probability of gene mutation m(i) depends on the size i of a family. We prove that size distribution of paralogous gene families in a genome converges to the equilibrium as time goes to infinity. Moreover, we show how this equilibrium depends on the sequence (m(i)). Theoretical results are compared with the available genomic data.