Coexistence of incompatible plasmids in a bacterial population living under a feast and famine regime
As a generalization of a model by \textit{F. M. Stewart} and \textit{B. R. Levin} [The population biology of bacterial plasmids: a priori conditions for the existence of conjugationally transmitted factors. Genetics 87, 209-228 (1977)] the following model is formulated for plasmid growth in a bacterial population: \[ \dot s=-f\circ s(eb+\sum^{P}_{i=1}w_ ie_ ip_ i),\quad \dot b=f\circ s(b+\sum^{P}_{i=1}(-\gamma_ ib+\tau_ i)p_ i, \] \[ \dot p_ i=f\circ s(w_ ip_ i+\gamma_ ibp_ i- \tau_ ip_ i),\quad i=1,2,...,P, \] where s is the food supply concentration, b is the concentration of plasmid free bacteria, and \(p_ i\) is the concentration of bacteria carrying the i th type of plasmids. Finally, P is the number of types of plasmids. The above system of equations is investigated under a series of initial conditions thus modelling the sequential transfer of the bacterial population. If \(P=1\) then the frequency of plasmid bearers \((p_ 1/(p_ 1+b))\) will tend to a stable equilibrium under appropriate conditions. If these conditions are not met this frequency might oscillate. If \(P=2\) then the two plasmids will sometimes be able to coexist, but only if they follow different survival strategies. If \(P=3\) then coexistence is impossible. The paper continues previous investigations of the same author [J. theor. Biol. 110, 411-423 (1984) and ibid. 117, 431-452 (1985)].
generalization of a model by \textit{F. M. Stewart} and \textit{B. R. Levin}
scientific article; zbMATH DE number 3963626