Population Dynamics of Gene Transfer

Horizontal transfer of nucleic acid sequences is a widespread process of genetic change in bacterial populations, one taking on a variety of specific forms. A model capturing some of the general features of this process is formulated. Two major subsidiary variants of this model are analyzed. The first lacks competition between cells. In this case, the transferred genetic element can approach fixation asymptotically if cells bearing it are viable, but not otherwise. The second variant of the proposed model has competition. This gives rise to complex dynamical possibilities, but never fixation of the transferred genetic element. It is argued that the evolutionary transition from gene transfer polymorphism to obligatory genetic exchange, and thus the origin of sex, requires either population dynamics which are not subject to growth rate density-dependence or cell-dependence on transferred genetic elements, although such dependence does not require that the element be beneficial.