Effects of Spatial Heterogeneity on Jones's Model for Cyst-Nematode Population Dynamics and Crop Root Damage

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Abstract
Jone''s purely deterministic mathematical models of the population dynamics of cyst-nematodes and their damaging effects on the roots of host crops (Jones and Perry 1978; Perry and Jones 1981) may require stochastic modifications to account realistically for 4 sources of variation encountered within fields. Two of these sources are considered: spatial heterogeneity both of population densities and of parameter values. Stochastic analogs that include such variation were produced using simple simulation and results were compared with those from deterministic models. When a field is sampled from several positions before a host-crop is planted, and a range of initial nematode densities is obtained, then each of these sampled densities should be used as input to Jones''s model to determine local post-harvest populations or expected root damage. It can then be decided whether or not a single mean value for the whole field is representative. Using a single (mean) initial nematode density for the field may give serious discrepancies in predictions, and these would be most pronounced when populations are dense and highly aggregated.

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