Evolutionary distributions in adaptive space

[摘要] An evolutionary distribution (ED), denoted byz(x,t), is a distribution of density of phenotypes over a set of adaptivetraitsx. Herexis ann-dimensionalvector that represents the adaptive space. Evolutionaryinteractions among phenotypes occur within an ED and between EDs.A generic approach to modeling systems of ED is developed. Withit, two cases are analyzed. (1) A predator prey inter-EDinteractions either with no intra-ED interactionsor withcannibalism and competition (both intra-ED interactions). Apredator prey system with no intra-ED interactions is stable.Cannibalism destabilizes it and competition strengthens itsstability. (2) Mixed interactions (where phenotypes of one ED bothbenefit and are harmed by phenotypes of another ED) producecomplete separation of phenotypes on one ED from the other alongthe adaptive trait. Foundational definitions of ED, adaptivespace, and so on are also given. We argue that in evolutionarycontext, predator prey models with predator saturation make lesssense than in ecological models. Also, with ED, the dynamics ofpopulation genetics may be reduced to an algebraic problem.Finally, extensions to the theory are proposed.

[学科分类] 应用数学