Evaluating Alternative Hierarchical Modeling Approaches for the Estimation of Salmonid Smolt Abundance

Abstract

Calibrated estimates of fisheries population abundance are vital in the development and appraisal of management actions. Capture–recapture (CR) experiments are invaluable monitoring tools for estimating abundance of biological populations in general. Many researchers, including those studying out‐migrating juvenile Chinook Salmon Oncorhynchus tshawytscha in the Klamath Basin of Oregon and California, have attempted to employ Bayesian B‐splines to smooth temporal variation in abundance estimates. However, concerns about overfitting and reduced precision are common with this approach. We conducted a simulation study assessing the relative fit of the standard Bayesian B‐spline implementation—a B‐spline model of abundance with a random effects (RE) binomial model of recapture probabilities—in comparison with that of three alternative model options: a B‐spline model of abundance with an autoregressive (AR) model of recapture; an AR model of abundance with an RE model of recapture, and an AR model of abundance with an AR model of recapture. We analyzed 1–3 years of CR data from three rotary screw trap sites and simulated data sets of variable completeness to assess each model’s strengths and weaknesses in estimating the underlying data. Results demonstrated that in general, an AR model of abundance coupled with an RE binomial model of recapture was the least biased model, consistently exhibiting no greater than 5% bias in abundance estimates across data sets. The B‐spline abundance models were able to produce narrower 95% credible intervals (CRIs), ranging from 15% to 30% of the parameterized annual abundance value, compared to CRI widths between 23% and 54% from the AR models. However, these narrower CRI widths were commonly errant, with coverage probability rates as low as 50–70% in half of the simulated data set collections compared to over 90% coverage for the AR models. These analyses provide valuable insight and caution for researchers employing modern methods of modeling abundance in natural populations.

Estimating multiple years, tributary‐specific, and overall Atlantic salmon smolt abundance in a large Canadian catchment using capture–mark–recapture experiments

“…There is no doubt that the probabilities of capture vary within the season at the RSTs in the Restigouche River associated with decreases in water levels and corresponding narrowing of the river width at the RST locations during the sampling period (Chaput et al, 2004). But with generally fewer than 50 recaptures at any sampling location in any year, in‐season temporally stratified CMR models such as described by Mäntyniemi and Romakkaniemi (2002), Bonner and Schwarz (2011), and Payton and Som (2021) are not feasible. A Bayesian hierarchical Lincoln–Petersen CMR model as described in Rivot and Prévost (2002) that takes advantage of the similarities in sampling gears, locations, operating dates, and sampling protocols among years was used in the case of the Restigouche River to provide more reliable estimates of the annual salmon smolt abundances.…”

“…To account for the temporally stratified migration process and sampling of animals such as smolts, Darroch (1961) introduced a time‐stratified version of the CMR model that considered capture probabilities within weekly periods. Modeling the in‐season movements of salmon and incorporating that process within CMR models were further explored in several studies (Bonner & Schwarz, 2011; Dempson & Stansbury, 1991; MacDonald & Smith, 1980; Mäntyniemi & Romakkaniemi, 2002; Payton & Som, 2021; Plante et al, 1998; Schwarz & Dempson, 1994). Such time‐stratified models are data intense, requiring a large number of recaptures corresponding to the number of time strata being modeled.…”