Abstract
A mathematical model for the population dynamics of conjugationally transmitted plasmids in bacterial populations is presented and its properties analyzed. Consideration is given to nonbacteriocinogenic factors that are incapable of incorporation into the chromosome of their host cells, and to bacterial populations maintained in either continuous (chemostat) or discrete (serial transfer) culture. The conditions for the establishment and maintenance of these infectious extrachromosomal elements and equilibrium frequencies of cells carrying them are presented for different values of the biological parameters: population growth functions, conjugational transfer and segregation rate constants. With these parameters in a biologically realistic range, the theory predicts a broad set of physical conditions, resource concentrations and dilution rates, where conjugationally transmitted plasmids can become established and where cells carrying them will maintain high frequencies in bacterial populations. This can occur even when plasmid-bearing cells are much less fit (i.e., have substantially lower growth rates) than cells free of these factors. The implications of these results and the reality and limitations of the model are discussed and the values of its parameters in natural populations speculated upon.
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