Stability with Inheritance in the Conditional Strategy

The conditional strategy is a theoretical framework that explains the existence within populations of individuals that express alternative behavioral, physical or life history tactics (phenotypes). An example is fighters and sneakers in many animal mating systems. In the conditional strategy the alternative tactics are chosen by individuals based on their state, for example large or small bodied. Since state is often heritable, due for example to additive genetic variance, the alternative tactics may also have inheritance. As the tactics do not have equal fitnesses, it is generally believed that any such inheritance would prevent the evolutionary stability of the conditional strategy. However, in previous work we introduced an Inheritance Theorem and were able to prove that a conditional strategy with tactic inheritances can have a unique equilibrium proportion of the tactics. We now prove a second property of our Inheritance Theorem, namely the stability of the equilibrium. This means that if the tactics are perturbed from their equilibrium proportions, they will return across generations to their equilibrium proportions. An example is provided in mites. We have therefore established an Inheritance Theorem which includes both the existence of an equilibrium and its stability for alternative tactics in a conditional strategy.