Ontogenetic Scaling of Foraging Rates and the Dynamics of a Size-Structured Consumer-Resource Model

Abstract

The ontogenetic scaling of foraging capacity strongly influences the competitive ability of differently sized individuals within a species. We develop a physiologically structured model to investigate the effect of different ontogenetic size scalings of the attack rate on the population dynamics of a consumer-resource system. The resource is assumed to reproduce continuously whereas the consumer only reproduces at discrete time instants. Depending on the ontogenetic size scaling, the model exhibited recruit-driven cycles, stable fixed point dynamics, non-recruit juvenile-driven cycles, quasiperiodic orbits, or chaotic dynamics. The kind of dynamics observed was related to the maintenance resource levels required of differently sized individuals. Stable fixed point dynamics was, besides at the persistence boundary, only observed when the minimum resource levels were similar for newborns and mature individuals. The tendency for large population fluctuations over a wide range of the parameter space was due to the consumer's pulsed reproduction. Background mortality and length of season were major determinants of cycle length. Model dynamics strongly resembled empirically observed dynamics from fish and Daphnia populations with respect to both patterns and mechanisms. The non-recruit juvenile-driven dynamics is suggested to occur in populations with size-dependent interference or preemptive competition like cicada populations.