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

Abstract

Aerial distance sampling of bears to estimate population size has been used throughout many parts of Alaska. The distance sampling models are complex since they need to account for undetected bears and differences in detection probabilities. This will require covariates and mark‐recapture data. The models proposed by Schmidt et al. do not use covariates or mark‐recapture data and are inappropriate for these surveys.

Estimating brown bear abundance and harvest rate on the southern Alaska Peninsula

“…Our MR model estimated apex detection at 0.920 (0.019, Table 3 ) indicating the need to estimate this parameter and how erroneous an assumption of perfect detection would be. The need to estimate apex detection has been documented in other distance sampling surveys of bears [ 22 ]. The MR model also indicated bedded bears were harder to detect than more upright bears (bed = -1.1194, Table 3 ), as distance increased more bears were missed (distance = -0.0013, Table 3 ), and bears were harder to detect as percent cover increased (Pcvr5 = -0.2971, Table 3 ).…”

“…Initially, progress was made, but ultimately the logistic function was not flexible enough to model the shape of the bear detection data. In desperation, the senior author used a half normal detection function to fit the data, the cost was an additional left truncation of 11.6% to 27.2% of the data which was deemed very inefficient [ 22 ]. The left truncated data was also a half normal distribution with a different scale parameter.…”

Comments on Integrating Distance Sampling and Minimum Count Data (Schmidt et al. 2019)

“…All these studies concurrently collected mark-resight and distance data, which were analyzed using mark-resight distance sampling (MRDS; Borchers et al 2006) models to estimate the maximum detection on the transect and population abundance. Failing to meet the perfect detection assumption when using a simple distance sampling model negates their pooling robustness (Buckland et al 2015), can have severe negative bias effects (−17.4% to −21.4%), and can underestimate the variance (Becker and Christ 2019). The bias will be larger than the difference between perfect detection (1.0) and the estimate of detection on the transect (Becker and Christ 2019) because of additional bias due to unmodeled heterogeneity in the detection probability estimation that results when a model is no longer robust to pooling data (Buckland et al 2015).…”

“…The bias will be larger than the difference between perfect detection (1.0) and the estimate of detection on the transect (Becker and Christ 2019) because of additional bias due to unmodeled heterogeneity in the detection probability estimation that results when a model is no longer robust to pooling data (Buckland et al 2015). An aerial distance survey for black bears estimated maximum transect detection at 0.926 (0.038 [SE]), but the relative bias between the MRDS model and a simple distance model with perfect detection was −20.0% not 7.4% (1.0-0.926 ;Becker and Christ 2019).…”

Integrating Distance Sampling and Minimum Count Data: A Reply to Becker and Herreman

“…The role of heterogeneity and the breakdown of pooling robustness are important concepts, but they do not modify the direct relationship between bias and the degree to which g(0) < 1. We address the proper interpretation of the referenced empirical counter example (Becker and Christ 2019) in detail below.…”