A reassessment of Chao2 estimates for population monitoring of grizzly bears in the Greater Yellowstone Ecosystem

Abstract

The Yellowstone Ecosystem Subcommittee (YES) asked the Interagency Grizzly Bear Study Team (IGBST) to re-assess a technique used in annual population estimation and trend monitoring of grizzly bears in the Greater Yellowstone Ecosystem (GYE). This technique is referred to as the Chao2 approach and estimates the number of females with cubs-of-the-year (hereafter, females with cubs) and, in association with other demographic data, is used by the IGBST to produce annual population estimates. Females with cubs are an easily recognizable population segment, and trends for this reproductive segment of the population are assumed to be representative of trend for the entire population. The overarching objective of the analyses presented in this report was to provide a more accurate representation of the GYE grizzly bear population using the current methodologies in place. Specifically, we addressed two limitations of the current Chao2 approach: 1) underestimation bias associated with a distance criterion used to differentiate annual sightings of females with cubs into unique individuals and 2) limitations of the model-averaging approach to effectively distinguish among potential future population trajectories (decline, stability, and growth). The first issue addressed in this report is the underestimation bias associated with the rule set that Knight et al. (1995) developed to differentiate sightings of females with cubs into unique individuals (i.e., unique family groups). The rule set was originally designed to be conservative by reducing the risk of identifying more females with cubs than actually existed, primarily through use of a distance criterion of 30 km to separate sightings of unique females. This approach resulted in an underestimation bias, and previous research demonstrated that this bias increases with increasing number of females with cubs. Using location data from radio-marked females with cubs, we evaluated alternative distance criteria by simulating scenarios with varying numbers of true females with cubs and sightings. Findings from these analyses demonstrate that bias in estimates of females with cubs can be substantially reduced by changing the 30-km distance criterion in the rule set to 16 km, which produced relatively unbiased estimates. Findings also indicate, however, the importance of adaptability with regard to the distance criteria because of the complex relationships and biases among the various parameters involved in estimation of unique females with cubs. The total number of annual sightings and the true number of females with cubs play particularly important roles. Whereas these analyses remind us that there is no perfect approach to estimating the number of females with cubs from sightings under various scenarios, they provide us with new tools to determine when and how to adapt the monitoring program. The second issue we were tasked to investigate was the potential for improvement of the technique referred to as model-averaging, which serves to smooth relatively high variation in annual estimates. This technique was chosen by YES as the basis for monitoring the Yellowstone grizzly bear population, as described in the 2016 Conservation Strategy. This choice was made in part because the technique has been well documented and population estimates derived from counts of females with cubs are conservative. Using simulations of population trends, we demonstrate why the model-averaging technique currently used cannot distinguish between plausible future trend scenarios. As a suitable alternative to model averaging, we propose the use of generalized additive models (GAMs). Using a suite of simulated trend dynamics relevant to management, we demonstrate GAM performance for tracking trends in females with cubs within the context of the annual monitoring program. We demonstrate the ability to not only document directional changes in population trend but also patterns of stabilization or resiliency after such changes. Furthermore, the proposed monitoring framework provides objective measures useful for early detection of directional changes in trend. The new framework is flexible, allowing retrospective analysis of Chao2-based estimates and future applications to time series of other population metrics, such as vital rates. The aforementioned updates provide us with new tools to determine when and how to adapt the monitoring program. Within the context of current monitoring protocols and effort, and considering the full suite of simulations presented in this report and previous studies, the IGBST plans to incorporate the following changes to the population monitoring protocol: 1) modify the distance criterion, starting with 16 km under current sampling conditions and 2) revise the population monitoring framework using GAMs as the basis for smoothing of annual estimates and detecting trends and changes in trend. Implementation of the 16-km distance criterion combined with use of GAM techniques would affect some of the population metrics (e.g., annual population size and uncertainty, population trend, mortality rates) used to inform management responses. A primary consideration is that the 16-km distance criterion results in total population estimates derived from the Chao2 estimates that are greater than those we have reported in the past. This increase is due to a change in the implementation of the technique and more accurately represents the number of females with cubs in the GYE grizzly bear population. Additionally, interpretation of retrospective trend patterns may change due to the combination of a different distance criterion and enhanced trend monitoring based on the GAM approach we present here. Implementation will require relatively minor changes in the monitoring protocols described in Appendices B and C of the 2016 Conservation Strategy. Finally, we note that the IGBST has ongoing investigations into the merits of an Integrated Population Model (IPM), for which annual Chao2-based estimates are important input data. The IGBST plans to continue those investigations using the 16-km distance criterion to derive Chao2 estimates.