A generalization of Pontryagin's maximum principle for dynamic evolutionary games among relatives

We present two theorems that generalize Pontryagin's maximum principle to t he setting of dynamic evolutionary games between genetically related indivi duals. The two theorems correspond to two types of interactions among indiv iduals: patch-structured populations in which individuals locally "play the field" and pairwise interactions. These generalizations can be used in the same way that Pontryagin's maximum principle is used and they are valid fo r diploid organisms under a single locus, diallelic genetic model. These ge neralizations involve an interesting, dynamic version of Hamilton's Rule fr om inclusive fitness theory. We illustrate how these theoretical results ca n be applied by modeling the evolution of lifetime resource allocation to g rowth and reproduction in an annual plant when there is competition for res ources among related individuals, (C) 2000 Academic Press.