Size and scaling of predator-prey dynamics

We propose a scaled version of the Rosenzweig–MacArthur model using both Type I and Type II functional responses that incorporates the size dependence of interaction rates. Our aim is to link the energetic needs of organisms with the dynamics of interacting populations, for which survival is a result of a game-theoretic struggle for existence. We solve the scaled model of predator–prey dynamics and predict population level characteristics such as the scaling of coexistence size ranges and the optimal predator–prey size ratio. For a broad class of such models, the optimal predator–prey size ratio given available prey of a fixed size is constant. We also demonstrate how scaling predictions of prey density differ under resource limitation vs. predator drawdown. Finally, we show how evolution of predator size can destabilize population dynamics, compare scaling of predator–prey cycles to previous work, as well as discuss possible extensions of the model to multispecies communities.