Pooling robustness in distance sampling: Avoiding bias when there is unmodelled heterogeneity

Abstract

The pooling robustness property of distance sampling results in unbiased abundance estimation even when sources of variation in detection probability are not modeled. However, this property cannot be relied upon to produce unbiased subpopulation abundance estimates when using a single pooled detection function that ignores subpopulations. We investigate by simulation the effect of differences in subpopulation detectability upon bias in subpopulation abundance estimates. We contrast subpopulation abundance estimates using a pooled detection function with estimates derived using a detection function model employing a subpopulation covariate. Using point transect survey data from a multispecies songbird study, species‐specific abundance estimates are compared using pooled detection functions with and without a small number of adjustment terms, and a detection function with species as a covariate. With simulation, we demonstrate the bias of subpopulation abundance estimates when a pooled detection function is employed. The magnitude of the bias is positively related to the magnitude of disparity between the subpopulation detection functions. However, the abundance estimate for the entire population remains unbiased except when there is extreme heterogeneity in detection functions. Inclusion of a detection function model with a subpopulation covariate essentially removes the bias of the subpopulation abundance estimates. The analysis of the songbird point count surveys shows some bias in species‐specific abundance estimates when a pooled detection function is used. Pooling robustness is a unique property of distance sampling, producing unbiased abundance estimates at the level of the study area even in the presence of large differences in detectability between subpopulations. In situations where subpopulation abundance estimates are required for data‐poor subpopulations and where the subpopulations can be identified, we recommend the use of subpopulation as a covariate to reduce bias induced in subpopulation abundance estimates.

Understanding implications of detection heterogeneity in wildlife abundance estimation

“…Heterogeneity in detection probability is far less problematic for distance sampling based on the general property of pooling robustness (Buckland et al 2001), which means estimators of overall abundance are robust to pooling over various conditions that affect detection probability. If heterogeneity exists in detection probability and it is associated with some subset of interest for abundance estimation (e.g., variation in detection due to habitat characteristics), then incorporation of covariates should be considered or bias in subpopulation abundance will be introduced (Rexstad et al 2023).…”

Using fusion effects to decrease uncertainty in distance sampling models when collating data from different surveys

“…However, there is a bias‐variance trade‐off: a decrease in uncertainty may come at the price of an increase in bias. Bias (here, a working definition of bias is used as the resulting difference between the true value and the mean estimated value) in estimates of parameters can increase if detection functions are heterogeneous among species and/or surveys (see pooling robustness in Buckland et al, 2015 and Rexstad et al, 2023). When heterogeneity cannot be accounted for by explicit covariates, pooling observations with expected similar detection functions is a statistical technique to increase precision (Marques et al, 2007), and one of the modeler's tasks can be to identify, for a given data set, the pooling that best trades low values of uncertainty and bias.…”