Period Dependent Selection in Continuous Culture of Viruses in a Periodic Environment

Selection in a cellstat culture of two mutant strains of a bacteriophage under periodically fluctuating temperature was analyzed mathematically and numerically. Each of the two viral strains (P1 and P2) was assumed to have a different Arrhenius activation energy for its reproduction reaction. A phase diagram of the final state in the continuous culture was drawn. The most noticeable was that there were both P1-only and P2-only phases of competitive exclusion depending on the period of oscillation and the dilution rate. The period-dependent selection was proved that it was based on the feedback effect via the host-population change. At a short period of oscillation, the strain with larger arithmetic average fitness ultimately dominated in the population; on the other hand, at a long period of oscillation, the strain with larger geometric average fitness ultimately dominated. There was a co-existence phase between the two exclusion phases. The results suggest the feasibility of a method to escape from trapping at local optima on a fitness landscape in evolutionary molecular engineering.