SYSTEMS ANALYSIS OF ACARINE PREDATOR-PREY INTERACTIONS. II. THE ROLE OF SPATIAL PROCESSES IN SYSTEM STABILITY

(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, persistence 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 longand 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 predatorprey 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.

[1]  C. Huffaker.  Experimental studies on predation : dispersion factors and predator-prey oscillations , 1958 .

[2]  C. S. Holling.  Some Characteristics of Simple Types of Predation and Parasitism , 1959, The Canadian Entomologist.

[3]  L. R. Taylor,et al.  Aggregation, Variance and the Mean , 1961, Nature.

[4]  C. Huffaker,et al.  Experimental studies on predation: Complex dispersion and levels of food in an acarine predator-prey interaction , 1963 .

[5]  D. Force.  Effect of Temperature on Biological Control of Two-Spotted Spider Mites by Phytoseiulus persimilis , 1967 .

[6]  P. J. Boer,et al.  Spreading of risk and stabilization of animal numbers , 1968 .

[7]  John H. Lawton,et al.  Concepts of Stability and Resilience in Predator-Prey Models , 1976 .

[8]  W. Gurney,et al.  Single-Species Population Fluctuations in Patchy Environments , 1978, The American Naturalist.

[9]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Peter Chesson,et al.  Predator-Prey Theory and Variability , 1978 .

[11]  G. Nachman,et al.  Temporal and Spatial Dynamics of an Acarine Predator-Prey System , 1981 .

[12]  G. Nachman,et al.  A MATHEMATICAL MODEL OF THE FUNCTIONAL RELATIONSHIP BETWEEN DENSITY AND SPATIAL DISTRIBUTION OF A POPULATION , 1981 .

[13]  P. Crowley.  Dispersal and the Stability of Predator-Prey Interactions , 1981, The American Naturalist.

[14]  Experimental validation of a simulation model of the interaction between Phytoseiulus persimilis and Tetranychus urticae on cucumber , 1983 .

[15]  G. Nachman.  ESTIMATES OF MEAN POPULATION DENSITY AND SPATIAL DISTRIBUTION OF TETRANYCHUS URTICAE (ACARINA: TETRANYCHIDAE) AND PHYTOSEIULUS PERSIMILIS (ACARINA: PHYTOSEIIDAE) BASED UPON THE PROPORTION OF EMPTY SAMPLING UNITS , 1984 .

[16]  C. Bernstein,et al.  A simulation model for an acarine predator-prey system (Phytoseiulus persimilis-Tetranychus urticae) , 1985 .

[17]  G. Nachman,et al.  Systems Analysis of Acarine Predator-Prey Interactions. I. A Stochastic Simulation Model of Spatial Processes , 1987 .