Developing an empirical yield-prediction model based on wheat and wild oat (Avena fatua) density, nitrogen and herbicide rate, and growing-season precipitation

To develop a more complete understanding of the ecological factors that regulate crop productivity, we tested the relative predictive power of yield models driven by five predictor variables: wheat and wild oat density, nitrogen and herbicide rate, and growing-season precipitation. Existing data sets were collected and used in a meta-analysis of the ability of at least two predictor variables to explain variations in wheat yield. Yield responses were asymptotic with increasing crop and weed density; however, asymptotic trends were lacking as herbicide and fertilizer levels were increased. Based on the independent field data, the three best-fitting models (in order) from the candidate set of models were a multiple regression equation that included all five predictor variables (R-2 = 0.71), a double-hyperbolic equation including three input predictor variables (R-2 = 0.63), and a nonlinear model including all five predictor variables (R-2 = 0.56). The double-hyperbolic, three-predictor model, which did not include herbicide and fertilizer influence on yield, performed slightly better than the five-variable nonlinear model including these predictors, illustrating the large amount of variation in wheat yield and the lack of concrete knowledge upon which farmers base their fertilizer and herbicide management decisions, especially when weed infestation causes competition for limited nitrogen and water. It was difficult to elucidate the ecological first principles in the noisy field data and to build effective models based on disjointed data sets, where none of the studies measured all five variables. To address this disparity, we conducted a five-variable full-factorial greenhouse experiment. Based on our five-variable greenhouse experiment, the best-fitting model was a new nonlinear equation including all five predictor variables and was shown to fit the greenhouse data better than four previously developed agronomic models with an R-2 of 0.66. Development of this mathematical model, through model selection and parameterization with field and greenhouse data, represents the initial step in building a decision support system for site-specific and variable-rate management of herbicide, fertilizer, and crop seeding rate that considers varying levels of available water and weed infestation.