Population dynamics of transposable elements: Copy number regulation and species invasion requirements

A deterministic population dynamics model of the spread of transposable elements (TE) in sexually reproducing populations is presented. The population is modeled by a three-parameter equation describing host reproductive capacity, population size and the strength of the density dependence, while TE dynamics were modeled based also on three parameters, the maximum ability of the element to copy itself in the absence of regulation (T(0)), the regulatory effect of copy number decreasing transposition (C(0.5)), and the deleterious effect of each new transposition on host fitness (d). The mechanism of transposition control is therefore a function of the number of new TE copies. Our results indicate that non-regulated elements cannot fix in host populations, and that prediction of stable copy number following successful invasion is mainly a function of the combination of T(0) and C(0.5) values. Fitness reduction does not affect the final copy number after successful invasion of the element. Fitness reduction, however, will affect the surface of the {T(0) x C(0.5)} parameter space leading to successful invasion of the TE. Invasion of host populations by eight or more individuals containing elements with appropriate parameters will lead to successful element fixation at any size of the host population. Host population extinction due to the invasion of TE’s is observed in a small area of the {T(0) x C(0.5)} parameter space. These results are qualitatively preserved under alternative choices for the shape of the functions defining regulation of transposition and distinct sets of parameters determining host population dynamics.