Distributed evolutionary games

Standard population models in ecology and evolutionary ecology assume that all individuals are identical and reproduce by cloning. Often, the connection between evolutionary ecology, genetics and mating systems is not explicit. Functionally similar species are modelled with separate equations (e.g. 'competing' species). Here, a theory is developed that: (i) views a population as a distribution of individuals over adaptive character values; (ii) identifies various evolutionary types (e.g. species) with special points along this distribution; (iii) treats individuals as different with respect to the adaptive character value; (iv) incorporates ecological interactions among individuals along distributions; and (v) incorporates assortative mating and mutations. A stable equilibrium distribution of individuals over the adaptive character (the strategy) is a distributed evolutionarily stable strategy (ESS). At the distributed ESS, individuals may be equally distributed over all values of the adaptive character. Conditions that give rise to a non-uniform distributed ESS are analysed. Organisms are classified into types - an abstract classification for which species, phenotypes, and so on are special cases. With distributions, when the stable distribution is not homogeneous with respect to the adaptive character, it makes no sense to talk about the fitness of an individual in isolation from that of others. We talk about a fitness distribution. At a distributed ESS, the distribution of fitness is stable and different individuals have different values of the adaptive character. The theory is extended to multiple characters and functionally different organisms (predators, prey, etc.). It remains intact with evolution of multiple characters with multiple ecological interactions in space and with mutations and assortative mating. A way to link distributed evolutionarily stable strategies to genetic mechanisms is outlined.