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 General Framework for the Analysis of Animal Resource Selection from Telemetry Data

We propose a general framework for the analysis of animal telemetry data through the use of weighted distributions. It is shown that several interpretations of resource selection functions arise when constructed from the ratio of a use and availability distribution. Through the proposed general framework, several popular resource selection models are shown to be special cases of the general model by making assumptions about animal movement and behavior. The weighted distribution framework is shown to be easily extended to readily account for telemetry data that are highly auto-correlated; as is typical with use of new technology such as global positioning systems animal relocations. An analysis of simulated data using several models constructed within the proposed framework is also presented to illustrate the possible gains from the flexible modeling framework. The proposed model is applied to a brown bear data set from southeast Alaska.

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.

Benefit Cost Scenarios of Potential Oral Rabies Vaccination for Skunks in California

Scenario-based analyses were computed for benefits and costs linked with hypothetical oral rabies vaccination (ORV) campaigns to contain or eliminate skunk-variant rabies in skunks (Mephitis mephitis) in California, USA. Scenario 1 assumed baiting eight zones (43,388 km2 total) that comprised 73% of known skunk rabies locations in the state. Scenario 2 also assumed baiting these eight zones, but further assumed that added benefits would result from preventing the spread of skunk-variant rabies into Los Angeles County, USA. Scenarios assumed a fixed bait cost ($1.24 each) but varied campaigns (one, two and three annual ORV applications), densities of baits (37.5/km2, 75/km2 and 150/km2), levels of prevention (50%, 75%, and 100%), and contingency expenditures if rabies recurred (20%, 40%, and 60% of campaign costs). Prorating potential annual benefits during a 12-yr time horizon yielded benefit-cost ratios (BCRs) between 0.16 and 2.91 and between 0.34 and 6.35 for Scenarios 1 and 2, respectively. Economic issues relevant to potentially managing skunk-variant rabies with ORV are discussed.

SCWDS BRIEFS: Volume 20, Number 2 (July 2004)

National Veterinary Services Laboratories in Ames, Iowa, confirmed vesicular stomatitis (VS) in horses at one premises in Texas. As of July 21, 2004, infected animals were identified on a total of 45 premises in Colorado (11), New Mexico (21), and Texas (13). These are the first reports of VS in livestock in the United States since the 1998 epizootic. SCWDS VS Studies Chronic Wasting Disease Developments: nearly 118,000 wild white-tailed deer, mule deer, and elk were tested in the United States from October 2002 to September 2003, with 592 animals testing positive for the CWD prion. More than $38,000,000 was spent by federal and state wildlife and animal health agencies on CWD-related activities during this same period. The Second International Chronic Wasting Disease Symposium, hosted by the Wisconsin Department of Natural Resources, will be held in Madison, Wisconsin, July 12-14, 2005. Crow Decoys Used in West Nile Virus Study Although Lyme disease caused by a spirochete bacterium, Borrelia burgdorferi, is relatively rare in the southeastern United States, a Lyme disease-like infection referred to as Southern Tick-Associated Rash Illness (STARI) and thought to be caused by Borrelia lonestari, has been recognized in people in this region. The Ohio Division of Wildlife joined SCWDS as an associate member beginning July 1, 2004. The Final Report of the 2003 Hemorrhagic Disease (HD) Surveillance project has been completed and distributed to all cooperators. New of Caroline Duffie, Robbie Edalgo and wife Jen, Clay George, Darrell Kavanaugh, Lynn Lewis-Weiss’s husband, Dr. Kevin Weiss, and Nate Mechlin. New SCWDS staff include Brian Chandler, Jay Cumbee, Ginger Goekjian, Bill Hamrick, Sabrina McGraw, Kerri Pedersen, and Ben Wilcox. Recent SCWDS Publications Available