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.

ECOLOGICAL CONTROL OF BIRD HAZARD TO AIRCRAFT

The Canadian Wildlife Service has had twenty-five years experience with the problem caused by bird contacts with aircraft. I experienced my first bird strike, while flying as an observer on a waterfowl survey in August, 1940. Officers of the Service investigated bird problems at airports at Yarmouth, Nova Scotia, and Cartierville, Quebec, in the late 1940's. Those incidents involving gulls and low speed piston-engined aircraft caused minor damage to the aircraft but considerable disturbance to the operators. As aircraft speeds increased and airports became more numerous and busier the problem increased in extent and complexity. By 1960 it was apparent that the problem would grow worse and that work should be directed toward reducing the number of incidents. In 1960 an electra aircraft crashed at Boston, Massachusetts, killing 61 passengers. Starlings were involved in the engine malfunction which preceded the crash. In November, 1962 a viscount aircraft was damaged by collision with two swans between Baltimore and Washington and crashed with a loss of 17 lives. Those incidents focused attention on the bird hazard problem in the United States.