The Influence of a Hierarchy in Time Scales on the Dynamics of, and the Coexistence within, Ensembles of Predator-Prey Pairs

One approach to developing general model concepts for ecological systems is to base them on the properties associated with the body weight of the component organisms. The dynamic characteristics of species may be described according to allometric relationships. In the model presented here an ensemble of predator-prey pairs, which share a common pool of an abiotic nutrient, are distributed along the body weight axis, introducing thus a hierarchy of different time scales. Model versions comprising a single predator-prey pair are chararacterized by a time-invariant steady state. As soon as further pairs are added the system becomes instable, exhibiting first periodic and then chaotic oscillations. In spite of the chaotic dynamics, certain statistical trends are independent of the initial conditions chosen. The variability in global system variables (nutrient concentration, metabolic activity) decreases with increasing number of pairs, revealing thus an increase in the efficiency of nutrient utilization. In the non-equilibrium situation an unlimited number of differently sized predator-prey pairs may coexist, the time-averaged biomass being evenly distributed among all pairs. Such observations contrast with expectations derived from the steady state.