Statistical arrival models to estimate missed passage counts at fish weirs

Abstract

Missed counts are commonplace when enumerating fish passing a weir. Typically “connect-the-dots” linear interpolation is used to impute missed passage; however, this method fails to characterize uncertainty about estimates and cannot be implemented when the tails of a run are missed. Here, we present a statistical approach to imputing missing passage at weirs that addresses these shortcomings, consisting of a parametric run curve model to describe the smoothed arrival dynamics of a fish population and a process variation model to describe the likelihood of observed data. Statistical arrival models are fit in a Bayesian framework and tested with a suite of missing data simulation trials and against a selection of Pacific salmon (Oncorhynchus spp.) case studies from the Yukon River drainage, Alaska, USA. When compared against linear interpolation, statistical arrival models produced equivalent or better expected accuracy and a narrower range of bias outcomes. Statistical arrival models also successfully imputed missing passage counts for scenarios where the tails of a run were missed.