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.

Contributions of demography and dispersal parameters to the spatial spread of a stage-structured insect invasion

Stage-structured models that integrate demography and dispersal can be used to identify points in the life cycle with large effects on rates of population spatial spread, information that is vital in the development of containment strategies for invasive species. Current challenges in the application of these tools include: (1) accounting for large uncertainty in model parameters, which may violate assumptions of ‘‘local’’ perturbation metrics such as sensitivities and elasticities, and (2) forecasting not only asymptotic rates of spatial spread, as is usually done, but also transient spatial dynamics in the early stages of invasion. We developed an invasion model for the Diaprepes root weevil (DRW; Diaprepes abbreviatus [Coleoptera: Curculionidae]), a generalist herbivore that has invaded citrus-growing regions of the United States. We synthesized data on DRW demography and dispersal and generated predictions for asymptotic and transient peak invasion speeds, accounting for parameter uncertainty. We quantified the contributions of each parameter toward invasion speed using a ‘‘global’’ perturbation analysis, and we contrasted parameter contributions during the transient and asymptotic phases. We found that the asymptotic invasion speed was 0.02–0.028 km/week, although the transient peak invasion speed (0.03– 0.045 km/week) was significantly greater. Both asymptotic and transient invasions speeds were most responsive to weevil dispersal distances. However, demographic parameters that had large effects on asymptotic speed (e.g., survival of early-instar larvae) had little effect on transient speed. Comparison of the global analysis with lower-level elasticities indicated that local perturbation analysis would have generated unreliable predictions for the responsiveness of invasion speed to underlying parameters. Observed range expansion in southern Florida (1992–2006) was significantly lower than the invasion speed predicted by the model. Possible causes of this mismatch include overestimation of dispersal distances, demographic rates, and spatiotemporal variation in parameter values. This study demonstrates that, when parameter uncertainty is large, as is often the case, global perturbation analyses are needed to identify which points in the life cycle should be targets of management. Our results also suggest that effective strategies for reducing spread during the asymptotic phase may have little effect during the transient phase. Includes Appendix.