A Unimodal Model for Double Observer Distance Sampling Surveys

Abstract

Distance sampling is a widely used method to estimate animal population size. Most distance sampling models utilize a monotonically decreasing detection function such as a half-normal. Recent advances in distance sampling modeling allow for the incorporation of covariates into the distance model, and the elimination of the assumption of perfect detection at some fixed distance (usually the transect line) with the use of double-observer models. The assumption of full observer independence in the double-observer model is problematic, but can be addressed by using the point independence assumption which assumes there is one distance, the apex of the detection function, where the 2 observers are assumed independent. Aerially collected distance sampling data can have a unimodal shape and have been successfully modeled with a gamma detection function. Covariates in gamma detection models cause the apex of detection to shift depending upon covariate levels, making this model incompatible with the point independence assumption when using double-observer data. This paper reports a unimodal detection model based on a two-piece normal distribution that allows covariates, has only one apex, and is consistent with the point independence assumption when double-observer data are utilized. An aerial line-transect survey of black bears in Alaska illustrate how this method can be applied.

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

“…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.…”

“…Certainty about perfect detection at the detection apex is extremely difficult to obtain when aircraft is used. For aerially collected data, different MRDS models were developed by Manley, McDonald, and Garner (1996) for polar bears (Ursus maritimus), Quang and Becker (1996) for Pacific and common loons (Gavua pacifica and G. immer), Quang and Becker (1999) for brown bears (Ursus arctos), Becker and Quang (2009) for brown bears, and Becker and Christ (2015) for brown and black bears (Ursus americanus). Early development of MRDS models was driven in part by developing models for aerially collected data.…”

“…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."…”

“…population size in Alaska (Becker & Christ, 2015). population size in Alaska (Becker & Christ, 2015).…”

“…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.…”