Distribution of transposable elements in prokaryotes

We consider models for the distribution of the number of elements per host genome for families of transposable elements (TEs). The hosts are assumed to be prokaryotes. These models assume a constant rate of infection of uninfected hosts by TEs, replicative transposition within each host, and a reduction of the fitness of a host dependent on the number of TEs it contains. No provision was made for the deletion of individual TEs within a host or for recombination, since both are relatively rare events in prokaryotes. These models mostly assume that the TE performs no function for the host, and that the reduction in fitness with increased copy number is due to effects such as the impairment of beneficial genes by transposition or homologous recombination. We also consider a model in which the TEs can convey a selective advantage to the host. The equilibrium distributions of copy number are determined for these models, and are of a variety of classical types. Relevant parameters of the models are estimated using data on the distribution of insertion sequences in natural isolates of Escherichia coli.