Simultaneous modelling of movement, measurement error, and observer dependence in mark-recapture distance sampling: An application to Arctic bird surveys

Abstract

Mark-recapture distance sampling is a promising method for surveying bird populations from aircraft in open landscapes. However, commonly available distance sampling estimators require that distances to target animals are made without error and that animals are stationary while sampling is being conducted. Motivated by a recent bird survey where these requirements were routinely violated, we describe a marginal likelihood framework for estimating abundance from double-observer data that can accommodate movement and measurement error when observations are made consecutively (as with front and rear observers), when animals are uniformly distributed during detection by the first observer, and when detections consist of both moving and stationary animals. Assuming that all animals are subject to measurement error and that some animals can move between detections, we integrate over unknown animal locations to construct a marginal likelihood for detection, movement, and measurement error parameters. Estimates of animal abundance are then obtained using a modified Horvitz–Thompson-like estimator. In addition, unmodelled heterogeneity in detection probability can be accommodated through observer dependence parameters. Using simulation, we show that our approach yields low bias compared to approaches that ignore movement and/or measurement error, including in cases where there is considerable detection heterogeneity. Applying our approach to data from a double-observer waterfowl helicopter survey in northern Canada, we are able to estimate bird density accounting for movement and measurement error and corrected for observer heterogeneity. Our approach appears promising for generating unbiased estimates of bird abundance necessary for reliable conservation and management.