Traditional and geostatistical modeling of pink bollworm spatial dynamics in Arizona cotton with application to sampling and computer mapping.

The within-field spatial distribution of F₁, F₂, and F₃ pink bollworm (PBW) (Pectinophora gossypiella Saunders) generations were modeled with Taylor's power law (TPL), Iwao's patchiness regression (IPR), and the geostatistical semivariogram. Kriging interpolation was used to grid data for the generation of isarithmic maps. Distributional patterns and movements within a field are displayed in a time series of three maps depicting density across the field. The sampling protocol was replicated in eight commercial cotton fields in south-central Arizona during 1985 and 1986. Permanent sample stations were situated throughout the fields on a regular grid pattern. Samples were collected during the peak larval population and handled so as to maintain the integrity of site-specific samples (spatially identified by X,Y coordinates). TPL and IPR could not be used satisfactorily to model the F₁ generation. TPL fit the observed F₂ and F₃ data better than IPR. Both methods predicted the F₂ to be more highly aggregated than the F₃. For a given precision, optimum sample size increased when TPL and IPR model parameters were incorporated into sample size formulae relative to a formula which assumed random distribution. Ninety-five percent of the modeled PBW distributions were autocorrelated in 2-dimensional space and shown to conform to regionalized variable theory by the successful application of geostatistics. The semivariogram models are in conceptual agreement with traditional models and represent a worthy alternative to traditional modeling methodology. The semivariogram models have a large nugget effect proportion (average = 67%) which, in combination with low PBW density in commercial fields, limits the applicability of geostatistics in this system. Isarithmic maps showed that F₁ larvae are either localized near a field edge or generally scattered throughout the field. No consistent inter-generational dispersal pattern was identified. The use of systematic grid sampling is most advantageous (relative to random sampling) when density and the spatial dependence of samples is high, or many samples can be taken. Systematic sampling and kriging estimation yielded more precise estimates than random sampling and classical statistics, but the advantage was buffered by low PBW densities and large nugget effect