AUTOLOGISTIC MODEL OF SPATIAL PATTERN OF PHYTOPHTHORA EPIDEMIC IN BELL PEPPER: EFFECTS OF SOIL VARIABLES ONDISEASE PRESENCE

The pathogen Phytophthora capsici causes lesions on the crown, stem, and leaves of bell pepper, and rapidly causes the plant to die. The spatial patterns of disease in an agricultural field contain information about pathogen dispersal mechanisms and can be useful for developing methods of control of disease. Soil water content, soil pathogen population density, and disease incidence data were collected on a 20 x 20 grid in two naturally infested commercial bell pepper fields. In one field the initial pattern of disease closely matched the soil water content pattern and disease developed in areas where the pathogen population levels were high. In the other field no such correspondence was obvious from maps of disease and soil water content. The auto logistic model is a flexible model for predicting presence or absence of disease based on soil water content and soil pathogen population, while taking spatial correlation into account. In the autologistic model the log odds of disease in a particular quadrat are modeled as a linear combination of disease in neighboring quadrats and the soil variables. Neighboring quadrats can be defined as adjacent quadrats within a row, quadrats in adjacent rows, quadrats two rows away, and so forth. The regression coefficients give estimates of the increase in odds of disease if neighbors within a row or in adjacent rows show disease symptoms; thus we obtain information about the degree of spread in different directions. The coefficients for the soil variables give estimates of the increase in odds of disease as soil water content or pathogen population density increase. In this problem, soil water content is also highly correlated over quadrats. This introduces a kind of collinearity between water content and the disease in neighboring quadrats, making estimation and interpretation of the parameters of the auto logistic model more difficult. We discuss fitting and evaluating the autologistic model when the covariates are themselves spatially correlated. Additional keywords: spatial correlation, disease incidence, Markov random field, multidimensional binary data, pseudolikelihood estimation.