Replicator dynamics for the game theoretic selection models based on state

The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and state-based approach of Houston McNamara. In new approach, individuals have different heritable strategies; however, carrying same strategy can differ in terms state, role or situation which they act. Thus, is completed by additional subsystem differential equations describing transitions between states. effect, interactions described structure, addition demographic payoffs (constituted births deaths), lead change state competing individuals. Special cases reversible irreversible incremental stage-structured models, where changes describe energy accumulation, developmental steps aging, are derived for discrete continuous versions. illustrated using example Owner-Intruder with explicit changes. model a generalization version Hawk-Dove game, difference being that opponents drawn from two separate subpopulations consisting Owners Intruders. Here, Intruders check random nest sites play Owner if occupied. Meanwhile, produce newborns become Intruders, since must find free site reproduce. An interesting feedback mechanism produced via fluxes subpopulations. addition, population growth suppression resulting fixation Bourgeois analyzed.