Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Seeking a Second Opinion: Uncertainty in Disease Ecology

Analytical methods accounting for imperfect detection are often used to facilitate reliable inference in population and community ecology. We contend that similar approaches are needed in disease ecology because these complicated systems are inherently difficult to observe without error. For example, wildlife disease studies often designate individuals, populations, or spatial units to states (e.g., susceptible, infected, post-infected), but the uncertainty associated with these state assignments remains largely ignored or unaccounted for. We demonstrate how recent developments incorporating observation error through repeated sampling extend quite naturally to hierarchical spatial models of disease effects, prevalence, and dynamics in natural systems. A highly pathogenic strain of avian influenza virus in migratory waterfowl and a pathogenic fungus recently implicated in the global loss of amphibian biodiversity are used as motivating examples. Both show that relatively simple modifications to study designs can greatly improve our understanding of complex spatio-temporal disease dynamics by rigorously accounting for uncertainty at each level of the hierarchy.

The Eradication of Bovine Tuberculosis From Infected Wildlife Populations: A New Zealand Scenario

The Animal Health Board (AHB) is the agency responsible for controlling bovine tuberculosis (Tb) in New Zealand. In 2000, the AHB embarked on a strategy designed to reduce the annual period prevalence of Tb infected cattle and farmed deer herds from 1.67% to 0.2% by 2012/13. Under current rules of the Office International des Epizooties (OIE) this would allow New Zealand to claim freedom from Tb. The epidemiology of Tb in New Zealand is largely influenced by wildlife reservoirs of infection and control of Tb vector populations is central to the elimination of Tb from New Zealand’s cattle and deer herds. The AHB has classified New Zealand’s land area into Vector Risk Areas (VRAs) where Tb is established in wildlife (currently 39%) and Vector Free Areas (VFAs) where the disease is not established (61%). Within the VRAs the introduced Australian brushtail possum (Trichosurus vulpecula) is the primary wildlife maintenance host and the main source of infection for domestic cattle and deer herds. Southland is a region of New Zealand with a long history of wildlife associated Tb. Progress in reducing infected herd numbers has been impressive in recent years, primarily due to an intensive possum control program. As a result of this reduction, the focus is now shifting to that of providing increasing levels of confidence that Tb is absent from the remaining susceptible wildlife. High levels of confidence of Tb freedom in wildlife will allow the AHB to reduce the wildlife control programs and ultimately cease control altogether, with minimal risk of Tb reemerging. This paper examines the strategies being utilized to provide that confidence. The types of data, the format in which it is collected and the methods of analysis and review are outlined.