Predator-prey dynamics and movement in fractal environments

Previous research suggests that local interactions and limited animal mobility can affect population dynamics. However, the spatial structure of the environment can further limit the mobility of animals. For example, an animal confined to a river valley or to a particular plant cannot move with equal ease in all directions. We show that spatial architecture could influence the population dynamics of predator-prey systems using individual-based computer simulations parameterized with allometric relationships from the literature. Spatial forms (representing geographical features or plant architecture) of differing fractal dimension were generated, and simulated predators and prey were introduced into these computer environments. We claim that the alteration in interaction rates and population dynamics found in these simulations can be explained as a consequence of the anomalously slow rates of movement associated with fractal spaces and the diffusion-limited nature of predator-prey interactions. As a result, functional responses and numerical responses are substantially reduced in fractal environments, and the overall stability of the system is determined by the interaction between individual mobility and spatial architecture.