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.

Capture versus tagging impacts on chum salmon freshwater spawning migration travel times

“…Model fits used three parallel chains each with a 4,000 iteration burn-in period, a 10-iteration thinning rate and a total of 1,000 posterior parameter draws stored per chain. Arrival curve priors for Pacific salmon runs were specified following Sethi and Bradley (2016); Supporting Information Text S1).…”

“…Arrival models were fit in a Bayesian framework using WinBUGS (Lunn, Thomas, Best, & Spiegelhalter, ) and package R2WinBUGS (Sturtz, Ligges, & Gelman, ) in the R statistical programming environment (R Core Team, ) following computer code provided in Sethi and Bradley (). Model fits used three parallel chains each with a 4,000 iteration burn‐in period, a 10‐iteration thinning rate and a total of 1,000 posterior parameter draws stored per chain.…”

“…An assumption of the arrival curve fitting methodology outlined here is that fish runs follow an underlying unimodal run curve (Sethi & Bradley, ). Chum salmon data from 2015 indicated a classic unimodal run curve, providing opportunity to fit unimodal arrival curves to tagging site data and both Henshaw and Gisasa weir data (Supporting Information Figure S1).…”

“…Here, potential impacts from radio tagging on spawning migration behaviour of chum salmon are evaluated by assessing travel times of wild chum salmon for two study years along both short [~60 river km (rkm)] and long (~730 rkm) migration routes to spawning grounds in the free‐flowing Koyukuk River in western Alaska, USA. Using a novel combination of direct observations on tagged fish and run curve modelling, separate radio tagging vs capture impacts on chum salmon migration behaviour were assessed by comparing the travel times of three groups of fish: (a) chum salmon fitted only with spaghetti tags, representing subjects captured for tagging but with minimal tag deployment impacts (e.g., Davidson, Sheehan, & Davie, ; Eames & Hino, ; Smith, McCall, & Sutton, ); (b) fish additionally fitted with oesophageally implanted gastric radio tags, providing information on migration behaviour impacts associated with receiving and carrying a radio tag; and finally (c) fish never captured and handled for which travel times were inferred by fitting statistical arrival curve models to tagging catch‐per‐unit‐effort data and weir counts (Sethi & Bradley, ). Together, information on travel times from these three groups of fish allows for the separation of potential impacts associated with gastric tagging among capture or tag deployment processes, providing insight to inform chum salmon movement ecology study design.…”

Bayesian arrival model for Atlantic salmon smolt counts powered by environmental covariates and expert knowledge

“…Su et al (2001) continued their work with hierarchical Bayesian approach enabling learning from years with more data to those with missing data. Furthermore, Sethi and Bradley (2016) introduced a Bayesian approach to estimate missing passage at weirs with run curve model to account for arrival dynamics and process variation model to describe the observed data. While these studies attempt to account for uncertainty, they do not discuss their model assumptions against biological knowledge.…”