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.

Demography and population viability of polar bears in the Gulf of Boothia, Nunavut

We estimated demographic parameters and harvest risks for polar bears (Ursus maritimus) inhabiting the Gulf of Boothia, Nunavut, from 1976 to 2000. We computed survival and abundance from capture–recapture and recovery data (630 marks) using a Burnham joint live–dead model implemented in program MARK. Annual mean total survival (including harvest) was 0.889 ± 0.179 ( x ± 1 SE) for cubs, 0.883 ± 0.087 for subadults (ages 1–4), 0.919 ± 0.044 for adult females, and 0.917 ± 0.041 for adult males. Abundance in the last 3 yr of study was 1,592 ± 361 bears. Mean size of newborn litters was 1.648 ± 0.098 cubs. By age 7, 0.97 ± 0.30 of available females were producing litters. Harvest averaged 38.4 ± 4.2 bears/year in the last 5 yr of study; however, the 2002–2007 kill averaged 56.4 bears/yr. We used a harvested Population Viability Analysis (PVA) to examine impacts of increasing rates of harvest. We estimated the current population growth rate, λH, to be 1.025 ± 0.032. Although this suggests the population is growing, progressive environmental changes may require more frequent population inventory studies to maintain the same levels of harvest risk.

Psychological and Support Characteristics of Parents of Child Sexual Abuse Victims: Relationship with Child Functioning and Treatment

Child sexual abuse continues to be a prevalent and complex problem in today’s society as it poses serious and pervasive mental health risks to child victims and their non-offending parents. The main objectives of this study were (a) to elucidate the psychological symptoms and support needs of parents of child sexual abuse victims as they present to group treatment, (b) to examine changes in psychological symptoms and support needs and their relationship with child functioning over the course of a parallel group treatment, and (c) to examine the impact of these factors on completion of group treatment. Participants included 104 sexually abused youth and their non-offending parent presenting to Project SAFE Group Intervention, a 12-session cognitive-behavioral group treatment for sexually abused children and their non-offending parents. This project had a unique advantage of utilizing a variety of demographic, parent-, and child-report measures, allowing for a more comprehensive examination of change in symptomatology and needs over the course of treatment. Several significant findings were noted, including the identification of four clusters of youth at pre-treatment, which were maintained at post-treatment; elevations on the CTQ Sexual Abuse scale; parents of youth sexually abused by a non-family member had significantly higher PSI-Restriction of Role subscale scores; parental expectations of a negative impact on their child were worse for older children; several parent characteristics predicted client treatment retention (e.g., older parents, lower SCL-90-R GSI scores); and an early age of onset of abuse also increased treatment retention. Future directions, recommendations, and limitations were discussed.

Development and Characterization of 15 Polymorphic Microsatellite Loci Isolated From Rafinesque’s Big-Eared Bat, Corynorhinus rafinesquii

We developed and characterized 15 microsatellite markers for Rafinesque’s big-eared bat, Corynorhinus rafinesquii. In a population from Tennessee, the number of alleles per locus ranged from three to 13 and observed heterozygosities were 0.35 to 0.97 per locus. These loci will provide appropriate variability for estimation of population connectivity, demographic parameters, and genetic diversity for this species of concern.

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.