  A variety of genome transformations can occur as a microbial population
adapts to a large environmental change. In particular, genomic surveys indicate
that, following the transition to an obligate, host-dependent symbiont, the
density of transposons first rises, then subsequently declines over
evolutionary time. Here, we show that these observations can be accounted for
by a class of generic stochastic models for the evolution of genomes in the
presence of continuous selection and gene duplication. The models use a fitness
function that allows for partial contributions from multiple gene copies, is an
increasing but bounded function of copy number, and is optimal for one fully
adapted gene copy. We use Monte Carlo simulation to show that the dynamics
result in an initial rise in gene copy number followed by a subsequent fall due
to adaptation to the new environmental parameters. These results are robust for
reasonable gene duplication and mutation parameters when adapting to a novel
target sequence. Our model provides a generic explanation for the dynamics of
microbial transposon density following a large environmental changes such as
host restriction.
