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.

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike’s information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

An Ecological Study of Helminths of Some Wyoming Voles (Microtus spp.) with a Description of a New Species of Nematospiroides (Heligmosomidae: Nematoda)

An ecological and taxonomic study of the helminth parasites of voles (Microtus spp.) in the Jackson Hole region of Wyoming is reported. Nematospiroides microti n. sp. from Microtus montanus nanus and M. richardsoni macropus is described and figured. A cestode, Paranoplocephala infrequens, and a nematode, Syphacia obvelata, were generally distributed throughout the region in all habitats except the sage flats. A trematode, Quinqueserialis hassalli, was recovered only from voles collected near streams at low altitudes. This was presumably due to the localized distribution of the molluscan intermediate host. Four helminths, viz., Hymenolepis horrida, Heligmosomum costellatum, Nematospiroides microti and Trichuris opaca, were restricted in their distribution to the alpine and sub-alpine meadows. Of these parasites, H. horrida and H. costellatum are reported for the first time from North America. Most of the other host and locality records are new. Available data indicate that host specificity was not a factor in restricting the distribution of parasites. Although the greatest numbers of parasites, both qualitative and quantitative, occurred in habitats where host density was greatest, it seems unlikely that host density is the only factor involved.

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.