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.

The Economics of Threatened Species Conservation: A Review and Analysis

Stabilizing human population size and reducing human-caused impacts on the environment are keys to conserving threatened species (TS). Earth's human population is ~ 7 billion and increasing by ~ 76 million per year. This equates to a human birth-death ratio of 2.35 annually. The 2007 Red List prepared by the International Union for Conservation of Nature and Natural Resources (IUCN) categorized 16,306 species of vertebrates, invertebrates, plants, and other organisms (e.g., lichens, algae) as TS. This is ~ 1 percent of the 1,589,161 species described by IUCN or ~ 0.0033 percent of the believed 5,000,000 total species. Of the IUCN’s described species, vertebrates comprised relatively the most TS listings within respective taxonomic categories (5,742 of 59,811), while invertebrates (2,108 of 1,203,175), plants (8,447 of 297,326), and other species (9 of 28,849) accounted for minor class percentages. Conservation economics comprises microeconomic and macroeconomic principles involving interactions among ecological, environmental, and natural resource economics. A sustainable-growth (steady-state) economy has been posited as instrumental to preserving biological diversity and slowing extinctions in the wild, but few nations endorse this approach. Expanding growth principles characterize most nations' economic policies. To date, statutory fine, captive breeding cost, contingent valuation analysis, hedonic pricing, and travel cost methods are used to value TS in economic research and models. Improved valuation methods of TS are needed for benefit-cost analysis (BCA) of conservation plans. This Chapter provides a review and analysis of: (1) the IUCN status of species, (2) economic principles inherent to sustainable versus growth economies, and (3) methodological issues which hinder effective BCAs of TS conservation.