A Mathematical Analysis of the Genetic Feedback Mechanism

When genetic change is taken into account, ecological principles must be reexamined. For example, even if total numbers of a prey population are essentially resource-limited, the prey may, through its genotypic composition, regulate a predator at relatively low levels, below those for which self-damping terms or effects of the predators on overall prey numbers need be taken into account. The system considered would not persist without genetic feedback. It is further shown that a situation described by a "series" model, rather than a "parallel" one, is one in which a genetic feedback mechanism for predator population regulation is more likely to be successful. Exact conditions on the selection coefficients are given for the existence of a stable equilibrium. Theorem 2 also provides a natural procedure for the choice of acceptable parameters for simulations. The model has been developed in accordance with a model suggested by Pimentel (1961), and thus certain of its quantitative predictions are subject to change when Pimentel's assumptions are replaced by others. I hope, however, that some of the insights into the nature of an evolutionary system gained through this model are robust. As Mailer (1970) says, "If the universe was a lock, its key was metaphor rather than measure."