Groupe d’études et de recherche en analyse des décisions

On Lotka-Volterra Population Games

Vlastimil Krivan

Lotka-Volterra predator-prey and competition models played an instrumental role in developing fundamental principles of today population ecology. These dynamics assume that the interaction strength between different species is fixed (e.g., predator's food preferences are fixed and independent of prey densities). In other words, they do not consider animal behavior (e.g., food preferences, habitat preferences, predator avoidance etc.) that can change as a response to changing environment. Such adaptive animal behaviors have been documented empirically, and are often postulated in game theoretical evolutionary models. To integrate population dynamics with evolutionary models requires to specify time-scales on which these processes do operate. In my talk I will adopt the classical dogma of ecology where behavior is much fast when compared to population dynamics which are still much faster than evolutionary changes in traits. With this perspective I will discuss effect of adaptive animal behaviors on classical Lotka-Volterra predator-prey and competition models. I will show that adaptive animal behaviors when applied to the Lotka-Volterra models can strongly change their predictions and provide new hypothesis for species coexistence.