We introduce and analyse a simple probabilistic model of genome evolution. It is based on three fundamental evolutionary events: gene
nnovation, and it is called
. 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 DLI models and we present the result of this study. Some empirical results for microbial genomes are presented.