On Genome Evolution with Accumulated Change and Innovation

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We introduce and analyse a simple discrete probabilistic model of genome evolution. It is based on four fundamental evolutionary events: gene duplication, loss, change and innovation, and it is called DLCI model. This is the first such model rigorously analysed. The focus of the paper is around the size distribution of gene families. The formulas for equilibrium gene family sizes are derived showing that they follow a logarithmic distribution. We consider also a disjoint union of DLCI models and we present the result of this study. Some empirical results for microbial genomes are presented.