Spatiotemporal model for studying insect dynamics in large-scale cropping systems

Insect ecologists have turned to models to aid them in understanding species dynamics in cropping systems. These models are used mainly to study insect-habitat relationships and to investigate factors affecting population stability in homogeneous cropping systems. The paucity of models for insect species interactions in large heterogeneous systems is very apparent. We develop and describe the framework for a spatiotemporal model that can be used to study insect dynamics in regional (heterogeneous) systems. This model is quite robust and integrates ideas from spatially explicit population models, coupled map lattices, and integrodifference equations. In spatially explicit population models, information on the environment of the organism is incorporated explicitly into the model. Our model combines an insect population simulation model with a resource (habitat) map. The population model is an age-structured Nicholson-Bailey model, whereas the resource map describes a 2-dimensional spatially heterogeneous habitat. Subpopulations in the spatial system are linked through dispersal and the pattern of dispersal is determined by the redistribution kernel used. Using a 2-dimensional discrete space counterpart of an integrodifference equation model we can couple prey reproduction with their dispersal, and we can redistribute adult natural enemies over the spatial region. The integrodifference equation format implies a mathematical convolution over space in each time step that can be solved, efficiently with Fourier transforms. At each time step, spatial movement for the insects can be solved with a simple rapid calculation. The assumptions, merits, and limitations of the model also are discussed.