Accounting for behavioural response to capture when estimating population size from hair snare studies with missing data

1 Hair snares have become an established method for obtaining mark-recapture data for population size estimation of Ursids and have recently been used to study other species including other carnivores, small mammals and ungulates. However, bias due to a behavioural response to capture in the presence of missing data has only recently been recognized and no statistical methodology exists to accommodate it. In a hair snare mark-recapture experiment, data can be missing if animals encounter a hair snare without leaving a hair sample, poor-quality samples are not genotyped, a fraction of all samples collected are genotyped due to cost considerations (subsampling) and/or not all genotyped hair samples provide an individual identification. These are all common features of hair snare mark-recapture experiments. Here, we present methodology that accounts for a behavioural response to capture in the presence of missing data from (i) subsampling and (ii) failure of hair samples to produce an individual identification. Four subprocesses are modelled-animal capture, hair deposition, researcher subsampling and DNA amplification with key parameters estimated from functions of the number of hair samples left by individuals at traps. We assess the properties of this methodology (bias and interval coverage) via simulation and then apply this methodology to a previously published data set. Our methodology removes bias and provides nominal interval coverage of population size for the simulation scenarios considered. In the example data set, we find that removing 75% of the hair samples leads to a 40% lower estimate of population size. Our methodology corrects about half of this bias and we identify a second source of bias that has not previously been reported associated with differential trap visitation rates among individuals within trapping occasions. Our methodology will allow researchers to reliably estimate the size of a closed population in the presence of a behavioural response to capture and missing data for a subset of missing data scenarios. It also provides a framework for understanding this generally unrecognized problem and for further extension to handle other missing data scenarios.