Systems Analysis of Acarine Predator-Prey Interactions. II. The Role of Spatial Processes in System Stability

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Abstract
(1) A stochastic simulation model was used to analyse the effect of spatial features, such as (a) system size, (b) short and long-distance dispersal of individuals between plants, and (c) spatial coincidence between prey and predators within plants, on the population dynamics, peristence and stability of a system composed of a phytoseiid mite predator, a tetranychid mite prey and a host-plant. (2) The analyses showed that persistence increases with the number of plants in the system. A system consisting of few host-plants is very unstable, whereas larger systems can achieve overall stability for a wide range of parameter values. (3) The system exhibits cyclic stability. The amplitude of the oscillations increases with an increase in (a) the rates of dispersal of mites among plants, (b) the ratio between long- and short-distance emigrations, and (c) the efficiency of the predators in finding and killing prey at low prey densities. The above factors tend to bring unstable local predator-prey oscillations into phase. Once this occurs, the system becomes regionally unstable. (4) Low mobility of the mites increases spatial asynchrony but may result in serious damage to the host-plants inflicted by the phytophagous prey. (5) Demographic stochasticity causes endogenous perturbations. Since small perturbations may lead to a completely different behaviour of the system, predictability of population dynamics in a patchy environment will be low, even if physical factors were perfectly controlled.