Periodic Oscillations in an Ideal-Free Predator-Prey Distribution

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Abstract
We simulated the habitat selection behavior in a three population predator-prey system with a mid-level predator that is also prey. There were two habitats, one of which was a relative refuge from predation. Individuals in the model moved to wherever they could improve their fitness, as if subject to the rules of the ideal-free distribution. However, the three populations could generally not achieve three simultaneous ideal-free distributions. Instead, individuals shifted back and forth between the habitats. Such oscillations were stabilized in three ways: 1) increase in the protection provided by the refuge; 2) increase in intraspecific competition among the prey; 3) the presence of a threshold in fitness difference, below which individuals would not change habitats. In the presence of a threshold, population distributions became stable without having achieved a simultaneous ideal-free distribution.