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.

Effectiveness of a White-Tailed Deer Exclusion Fence Based on Traction Limitations of the Hoof: The Slippery Fence

We hypothesized that an exclusion fence could be devised to capitalize on traction limitations of the hooves of white-tailed deer (Odocoileus virginianus). Hexagonal plots (9.8 m wide) enclosed by a 2.4 m field fence with two openings (4.9 m) were established. Data were collected daily on consumption of corn provided (2.27 kg) and events recorded by infrared monitors (IR) for treatment and control sites. Five-day treatment periods consisted of test panels (4.9 m x 2.4 m) placed in plot openings at 0°, 5° and 10° slopes, and lubricant applied at the 10° slope. Deer consumed all corn provided at control sites. At the 10° slope, daily corn consumption decreased (1.50 kg ± 0.26, p < .01), and IR events were lower (p < .01) at treatment sites (23.6 ± 3.2) compared to controls (50.3 ± 9.6). With the addition of a lubricant, corn consumption decreased further (p < .001) to 0.17 kg ± 0.03, and IR recorded events were lower (p < .001) at treatment sites (6.58 ± 0.89) compared to controls (44.8 ± 3.1). Results of this study indicate that traction limitation of the hoof can be exploited.