Improving inference for aerial surveys of bears: The importance of assumptions and the cost of unnecessary complexity

Abstract

Obtaining useful estimates of wildlife abundance or density requires thoughtful attention to potential sources of bias and precision, and it is widely understood that addressing incomplete detection is critical to appropriate inference. When the underlying assumptions of sampling approaches are violated, both increased bias and reduced precision of the population estimator may result. Bear (Ursus spp.) populations can be difficult to sample and are often monitored using mark‐recapture distance sampling (MRDS) methods, although obtaining adequate sample sizes can be cost prohibitive. With the goal of improving inference, we examined the underlying methodological assumptions and estimator efficiency of three datasets collected under an MRDS protocol designed specifically for bears. We analyzed these data using MRDS, conventional distance sampling (CDS), and open‐distance sampling approaches to evaluate the apparent bias‐precision tradeoff relative to the assumptions inherent under each approach. We also evaluated the incorporation of informative priors on detection parameters within a Bayesian context. We found that the CDS estimator had low apparent bias and was more efficient than the more complex MRDS estimator. When combined with informative priors on the detection process, precision was increased by >50% compared to the MRDS approach with little apparent bias. In addition, open‐distance sampling models revealed a serious violation of the assumption that all bears were available to be sampled. Inference is directly related to the underlying assumptions of the survey design and the analytical tools employed. We show that for aerial surveys of bears, avoidance of unnecessary model complexity, use of prior information, and the application of open population models can be used to greatly improve estimator performance and simplify field protocols. Although we focused on distance sampling‐based aerial surveys for bears, the general concepts we addressed apply to a variety of wildlife survey contexts.

Rejection of Schmidt et al.'s estimators for bear population size

“…We note the Becker and Quang (2009) population estimate of 618.4 brown bears (26.3 brown bears/1,000 km 2 ) is much lower than the MRDS_2PN model estimate of 746.1 (Table 2) due mainly to un-modeled heterogeneity in the full independence model used by Becker and Quang (2009). Schmidt et al (2017) are not justified in dropping the MR data since 2 of their reported MR probabilities were calculated using a full independence MRDS model (Becker & Quang, 2009) and, as a result, are biased high due to un-modeled heterogeneity.…”

“…Laake and Borchers (2004) state that population estimates from MRDS models "obtained under the assumption of full independence will tend to be negatively biased compared to estimates obtained under the assumption of point independence." Schmidt et al (2017) justify dropping the MR model with the statement: "marginal detection probabilities at the apex of the detection function are quite high for both the pilot and observer (Becker & Christ, 2015;Becker & Quang, 2009;Walsh et al, 2010) suggesting that the joint p d may approach 1.0 in many cases." Schmidt et al (2017) justify dropping the MR model with the statement: "marginal detection probabilities at the apex of the detection function are quite high for both the pilot and observer (Becker & Christ, 2015;Becker & Quang, 2009;Walsh et al, 2010) suggesting that the joint p d may approach 1.0 in many cases."…”

“…Schmidt et al (2017) propose the CDS_OpenHnBayes model to estimate p a (the probability a bear is available to be detected given it is in the study area) and claim using this estimate on a CDS half-normal model will correct for missed bears. Based on our experience, including those detailed above, we feel the number of undetectable bears at apex distances is 0 or very close to 0.…”

“…Unlike the three approaches proposed by Schmidt et al (2017), the MRDS approach taken by Becker and Christ (2015) uses a twopiece normal detection function to take advantage of the whole dataset to model both sides of the detection apex. They do not assume perfect detection at some fixed distance but rather estimate this parameter with a mark-recapture model at the distance associated with the apex of bear detection.…”

“…One main premise of Schmidt et al (2017) is that the estimation bias from removing covariates and mark-recapture data is small and better inferences about changes in population size can then be made using their methods. For this reason, we disagree with the conclusions of Schmidt et al (2017) that their models are "better" than those of Becker and Christ (2015). Their "Becker-Christ approach" model contains no covariates in either the distance model (two-piece normal detection function) or the point independence MR model.…”