Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models?

et al. (2012) Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models? PLoS ONE 7(12): e49410. doi:10.1371/journal.pone.0049410 Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models? Tabitha A. Graves 0 J. Andrew Royle 0 Katherine C. Kendall 0 Paul Beier 0 Jeffrey B. Stetz 0 Amy C. Macleod 0 Giuseppe Biondi-Zoccai, Sapienza University of Rome, Italy 0 1 School of Forestry, Northern Arizona University , Flagstaff , Arizona, United States of America, 2 United States Geological Survey, Patuxent Wildlife Research Center, Laurel, Maryland, United States of America, 3 United States Geological Survey, Northern Rocky Mountain Science Center, Glacier Field Station , Glacier National Park , Montana, United States of America, 4 Montana Cooperative Wildlife Research Unit, University of Montana, Missoula, Montana, United States of America, 5 University of Montana Cooperative Ecosystem Studies Unit, Glacier Field Station , Glacier National Park, Montana , United States of America Using multiple detection methods can increase the number, kind, and distribution of individuals sampled, which may increase accuracy and precision and reduce cost of population abundance estimates. However, when variables influencing abundance are of interest, if individuals detected via different methods are influenced by the landscape differently, separate analysis of multiple detection methods may be more appropriate. We evaluated the effects of combining two detection methods on the identification of variables important to local abundance using detections of grizzly bears with hair traps (systematic) and bear rubs (opportunistic). We used hierarchical abundance models (N-mixture models) with separate model components for each detection method. If both methods sample the same population, the use of either data set alone should (1) lead to the selection of the same variables as important and (2) provide similar estimates of relative local abundance. We hypothesized that the inclusion of 2 detection methods versus either method alone should (3) yield more support for variables identified in single method analyses (i.e. fewer variables and models with greater weight), and (4) improve precision of covariate estimates for variables selected in both separate and combined analyses because sample size is larger. As expected, joint analysis of both methods increased precision as well as certainty in variable and model selection. However, the single-method analyses identified different variables and the resulting predicted abundances had different spatial distributions. We recommend comparing single-method and jointly modeled results to identify the presence of individual heterogeneity between detection methods in N-mixture models, along with consideration of detection probabilities, correlations among variables, and tolerance to risk of failing to identify variables important to a subset of the population. The benefits of increased precision should be weighed against those risks. The analysis framework presented here will be useful for other species exhibiting heterogeneity by detection method. - Funding: Tabitha was supported by NSF-IGERT, NAU School of Forestry, the Hafen, Prather, and David-German Scholarships, the P.E.O. Scholar Award, the AAUW American Fellowship, and the David H. Smith Conservation Research Fellowship. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Many species exhibit individual heterogeneity in their susceptibility to different detection methods. When estimating population size is the goal, using multiple detection methods can reduce heterogeneity, increase accuracy and precision, and reduce cost through increasing the number, kind, and distribution of individuals sampled [13], e.g., [46]. However, we know of no research evaluating the benefits and risks of combining multiple detection methods when the goal is identification of environmental variables influencing local abundance, as in N-mixture models [7]. N-mixture models link a Poisson or negative binomial distribution that represents the local abundance of individuals with a binomial detection process that yields observed counts of individuals. Covariates for the two levels of the hierarchical process permit identification of variables explaining either abundance or detection [8,9]. Analyzing detection methods jointly may be appropriate and improve precision of estimates when both methods sample the entire population, when biases in sampling different components of the population can be accounted for with detection covariates, or when methods sample different subsets of the population, but both subsets are influenced similarly by environmental covariates. In contrast, analyzing datasets separately may be more appropriate when individuals more susceptible to capture via one method are influenced by the landscape differently than individuals not susceptible to that method. For instance if a bear that has been harassed with rubber bullets avoids hair snags (one detection method that uses a scent lure) and avoids high human use areas (habitat displacement influencing local abundance), combining detections of hair snags with a second detection method may mask the influence of high human use areas. We test a set of hypotheses and conduct a thought experiment to evaluate whether joint or separate analysis of multiple detection methods is most appropriate in a dataset from a natural population, when truth is unknown. If both methods sample the same population, the use of either data set alone should (1) lead to the selection of the same variables as important and (2) provide similar estimates of relative local abundance. In contrast, if different subsets of the population are sampled with each method and these groups respond differently to the landscape, separate analyses would identify different variables as important. If the variables identified as important differ greatly, the distribution of local abundance should also vary greatly. On the other hand, we hypothesized that the inclusion of 2 detection methods versus either method alone should (3) yield more support for variables identified in both of the single method analyses (i.e. fewer variables and models with greater weight), and (4) improve precision of covariate estimates for variables selected in both separate and combined analyses because sample size is larger. To evaluate these hypotheses we used a model that includes multiple detection methods in N-mixture models that we developed for the northern quarter of a population of grizzly bears (Ursus arctos) sampled in the year 2000 [10]. Previous work [6,11] found that inclusion of both detection methods increased the number of bears detected, particularly mal (...truncated)