Predicting the weed-free proportion of the field area with Taylor's power law

Crop weeds are patchily distributed. In weed management it is important to be able to estimate the weed-free fraction of the total field area, because this fraction determines the potential saving on herbicides that may be achieved by site-specific application (and not spraying those patches with no weeds). In this chapter, we model the weed-free fraction by combining Taylor¿s power law (TPL) for the variance-mean relationship with a prediction of the zero class frequency according to the negative binomial distribution. The resulting predictions of occupancy were compared to observations on weed density and occupancy in 32 data sets on occurrence of agricultural weeds in The Netherlands. The results using weed species specific parameters for TPL provided strong validation for the approach, with R2 prediction varying between 0.735 and 0.998 for 13 of the 14 species groups. Estimates of the slope parameter b of TPL varied substantially between weeds (from 0.78 for volunteer potatoes to 1.95 for Echinochloa crus-galli), but only slightly between data sets. Predictions based on a common slope parameter still had high coefficients of prediction for most weed species. Based upon a spatially explicit data set collected using counts in contiguous quadrats, the effect of scale of the sample unit was analysed. At levels of scale relevant to decision making in weed management, the effect of scale on occupancy was minor. We conclude that the relationship between density and occupancy for arable weeds is strong, and that there is scope for prediction of the weed-free area and prediction-based weed management