Estimating the risk of a crop epidemic from coincident spatio-temporal processes

Fusarium Head Blight (FHB), or "scab," is a very destructive disease that affects wheat crops. Recent research has resulted in accurate weather-driven models that estimate the probability of an FHB epidemic based on experiments. However, these predictions ignore two crucial aspects of FHB epidemics: (1) An epidemic is very unlikely to occur unless the plants are flowering, and (2) FHB spreads by its spores, resulting in spatial and temporal dependence in risk. We develop a new approach that combines existing weather-based probabilities with information on flowering dates from survey data, while simultaneously accounting for spatial and temporal dependence. Our model combines two space-time processes, one associated with pure weather-based FHB risks and the other associated with flowering date probabilities. To allow for scalability, we model spatiotemporal dependence via a process convolutions approach. Our sample-based approach produces a realistic assessment of areas that are persistently at high risk (where the probability of an epidemic is elevated for extended time periods), along with associated estimates of uncertainty. We conclude with the application of our approach to a case study from North Dakota.