1998

Dynamic Evolutionary Games Between Relatives

Game theory has provided an extremely important set of tools for constructing models in evolutionary biology. An interaction between individuals is considered a game if the fitness of each individual depends on the other's phenotype. An additional complication arises when the individuals are genetically related. This will be true whenever the population is geographically structured, or when individuals preferentially associate with kin. Under these conditions it becomes necessary to include elements of inclusive fitness theory into game-theoretic models.

I present a general method for constructing genetically valid game-theoretic models of kin selection for both haploid and diploid organisms. Using this method, I then develop some general results for the construction of dynamic games between relatives. By dynamic I mean that the characters of interest are sequences of decisions (see below for examples). Evolutionary models of such characters are usually constructed using either dynamic programming or Pontryagin's Maximum Principle (PMP). These cannot be used for games between relatives however, because they are simply maximization routines. I derive a suitable generalization of PMP for games between relatives that is genetically valid for both haploid and diploid organisms.

I then use these developments to model three phenomena: (i) What is the evolutionarily stable schedule of resource allocation to growth versus reproduction when individuals are competing with related neighbors? This appears to be the case for the plant Impatiens capensis, for example. (ii) When individuals interact over a period of time, how does the ESS level of altruism change. Also, can such repeated interactions favour the evolution of cooperation through mechanisms other than reciprocity? (iii) Can the evolution of the maternal age dependence in the frequency of trisomic conceptions be explained by meiotic drive? These three biological questions are of considerable interest in and of themselves, and they also provide nice illustrative examples of how the mathematical results that I obtain can be applied.