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Quantifying Wheat Yield Across the Field as a Function of Wheat Streak Mosaic Intensity: A State Space Approach

Wheat streak mosaic virus (WSMV), vectored by the wheat curl mite Aceria tosichella, is one of the major limiting factors in wheat production in the Texas Panhandle. The mites are blown by wind into wheat fields from nearby volunteer wheat fields or fields supporting vegetation which harbor virulent mites. Consequently, gradients of wheat streak severity are often observed stretching from the edges of wheat fields into the center or beyond. To describe the magnitude of the spatial relationships between grain yield and wheat streak intensity across the field, studies were conducted in 2006 and 2007 in three infected fields. Wheat streak severity was quantified with reflectance measurements (remote sensing) at 555-nm wave length using a hand-held radiometer. Measurements were taken in several equally spaced 1 m² locations along a total of eight transects and grain yield was assessed from a 0.8 m² area of each location. State space analysis was used to describe the relationships in which yield data and reflectance values were used as dependent and explanatory variables, respectively. A structural time series model was formulated as a state space model where the unobserved components were modeled explicitly. In the analysis the state of yield at current location (d) was related to the state of wheat streak intensity either at current locations (d) or lagged locations with autoregressive values of the first order (d--1) or greater. There were significant cross-correlations between yield and wheat streak intensity up to distances of 150 m (P ≤ 0.05). Grain yield at the current position was significantly correlated with reflectance values at the same location and/or at lagged locations. The spatial aspects of the yield-reflectance relationships were best described by state space models with stochastic trends without slopes or deterministic trends with or without slopes. The models correctly predicted almost all of the observed yield values as a function of wheat streak intensity across the field within the 95% confidence interval. Results obtained in this study suggest that state space methodology can be a powerful tool in the study of plant disease spread as a function of other variables.