TY - JOUR

T1 - Evolutionary distributions in adaptive space

AU - Cohen, Yosef

PY - 2005

Y1 - 2005

N2 - An evolutionary distribution (ED), denoted by z(x, t), is a distribution of density of phenotypes over a set of adaptive traits x. Here x is an n-dimensional vector that represents the adaptive space. Evolutionary interactions 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-ED interactions either with no intra-ED interactions or with cannibalism and competition (both intra-ED interactions). A predator prey system with no intra-ED interactions is stable. Cannibalism destabilizes it and competition strengthens its stability. (2) Mixed interactions (where phenotypes of one ED both benefit and are harmed by phenotypes of another ED) produce complete separation of phenotypes on one ED from the other along the adaptive trait. Foundational definitions of ED, adaptive space, and so on are also given. We argue that in evolutionary context, predator prey models with predator saturation make less sense than in ecological models. Also, with ED, the dynamics of population genetics may be reduced to an algebraic problem. Finally, extensions to the theory are proposed.

AB - An evolutionary distribution (ED), denoted by z(x, t), is a distribution of density of phenotypes over a set of adaptive traits x. Here x is an n-dimensional vector that represents the adaptive space. Evolutionary interactions 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-ED interactions either with no intra-ED interactions or with cannibalism and competition (both intra-ED interactions). A predator prey system with no intra-ED interactions is stable. Cannibalism destabilizes it and competition strengthens its stability. (2) Mixed interactions (where phenotypes of one ED both benefit and are harmed by phenotypes of another ED) produce complete separation of phenotypes on one ED from the other along the adaptive trait. Foundational definitions of ED, adaptive space, and so on are also given. We argue that in evolutionary context, predator prey models with predator saturation make less sense than in ecological models. Also, with ED, the dynamics of population genetics may be reduced to an algebraic problem. Finally, extensions to the theory are proposed.

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U2 - 10.1155/JAM.2005.403

DO - 10.1155/JAM.2005.403

M3 - Article

AN - SCOPUS:33750108363

VL - 2005

SP - 403

EP - 424

JO - Journal of Applied Mathematics

JF - Journal of Applied Mathematics

SN - 1110-757X

IS - 4

ER -