Spatio-Temporal Organization Mediated by a Hierarchy in Time Scales in Ensembles of Predator-Prey Pairs

Spatio-temporal organization refers to functional changes in a system’s interaction network mediated by system dynamics. Complex, even chaotic, dynamics are claimed to be characteristic for an ecological community as a whole. In systems of this type the emphasis should be shifted from predicting individual trajectories to investigating organizational properties at the level of the system as a whole such as the relationship between dynamic diversity, spatio-temporal organization and system function. Such effects are illustrated with a model where a hierarchy of different time scales is introduced into an ensemble of predator-prey pairs (PPP) by distributing the latter along the body weight axis. The PPPs share a common pool of a limiting resource. Model versions comprising a single PPP are characterized by a time-invariant steady state. As soon as further PPPs are added the system becomes unstable exhibiting first periodic and then chaotic oscillations. In spite of the chaotic and unpredictable dynamics of the single PPPs, a number of system properties were found to be independent of the initial conditions chosen. The efficiency of resource utlization increases with an increasing number of PPPs due to the associated increase of the temporal organization of the network as a whole. The effects of spatio-temporal organization on system function are further illustrated by results from model versions where a dimension of space was introduced by assuming that the species diffuse along one spatial dimension.