title: When mechanism matters: Bayesian forecasting using models of ecological diffusion.
abstract: Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.
authors.affiliation: Department of Statistics, Kansas State University, 205 Dickens Hall, 1116 Mid-Campus Drive North, Manhattan, KS, 66506, USA.
authors.forename: Trevor J
authors.initials: TJ
authors.lastname: Hefley
authors.affiliation: U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Department of Fish, Wildlife, and Conservation Biology, Department of Statistics, Colorado State University, 1484 Campus Delivery, Fort Collins, CO, 80523.
authors.forename: Mevin B
authors.initials: MB
authors.lastname: Hooten
authors.affiliation: U.S. Geological Survey, National Wildlife Health Center, 6006 Schroeder Road, Madison, WI, 53711, USA.
authors.forename: Robin E
authors.initials: RE
authors.lastname: Russell
authors.affiliation: U.S. Geological Survey, National Wildlife Health Center, 6006 Schroeder Road, Madison, WI, 53711, USA.
authors.forename: Daniel P
authors.initials: DP
authors.lastname: Walsh
authors.affiliation: Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, Utah, 84322.
authors.forename: James A
authors.initials: JA
authors.lastname: Powell
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D003670:Deer; D005260:Female; D005544:Forecasting; D008297:Male; D008962:Models, Theoretical; D015995:Prevalence; D034081:Wasting Disease, Chronic / Q000453:epidemiology* / Q000209:etiology; D014922:Wisconsin / Q000453:epidemiology
keywords: Agent-based model; Bayesian analysis; boosted regression trees; dispersal; generalised additive model; invasion; partial differential equation; prediction; spatial confounding