Periodic oscillations in an ideal-free predator-prey distribution

Simulated the habitat selection behavior in a 3 population predator-prey system with a mid-level predator that is also prey. There were 2 habitats, one of which was a relative refuge from predation. Individuals moved to wherever they could improve their fitness, as if subject to the rules of the ideal-free distribution, but the 3 populations could generally not achieve 3 simultaneous ideal-free distributions. Instead, individuals shifted back and forth between the habitats. Such oscillations were stabilized in 3 ways: 1) increase in the protection provided by the refuge; 2) increase in intraspectific 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. -Authors