Deterministic property changes in population models under random error perturbations

It was found that essential properties (periodic and chaotic dynamics) of s ome simple ecological models need not be changed or destroyed by small rand om error perturbations although the perturbations can obscure orbits of per iodic cycles of simple population models. It may not be generally realized that very small random error perturbations can significantly change the det erministic properties of some population models. We simulated 12 well-known population models. Among six of the 12 models, the deterministic propertie s are changed under random error perturbations. A host-parasitoid model was used as an example to illustrate our methodology. The observed property ch anges in that model included the following four aspects: (1) the periodic c ycles changed to chaos; (2) chaos changed to periodic; (3) oscillation magn itude changed; and (4) complex dynamics became two blurred periodic orbits. Of the five other models in which deterministic property changes were obse rved, two of them were one-dimensional models and three were multi-dimensio nal models. The changes in properties are more striking in multi-dimensiona l models than that in one-dimensional models. All simulation results show t hat under random error perturbations, the equilibrium points and the two pe riodic cycles of some population models are stable. However, some complex d ynamic behaviors of population models, such as n-periodic cycles (n greater than or equal to 4), the regime of period-doubling, and the periodic windo ws, would be changed or blurred by random error perturbations. Thus these p roperties are very difficult to observe in the field or to verify in biolog ical or ecological experiments. (C) 1999 Elsevier Science B.V. All rights r eserved.