Elsevier

Fisheries Research

Volume 238, June 2021, 105900
Fisheries Research

A rebuilding time model for Pacific salmon

https://doi.org/10.1016/j.fishres.2021.105900Get rights and content

Highlights

  • Overfished stocks require projections of rebuilding time.

  • The model projects future abundance based on past abundance and autocorrelation.

  • Projected rebuilding times were generally unbiased when compared to simulated data.

  • The model has minimal data requirements and can be implemented for many stocks.

Abstract

We describe a new model developed for the purpose of projecting rebuilding periods for overfished Pacific salmon stocks as defined by the Pacific Fishery Management Council. The model has relatively low data requirements as it relies on past estimates of abundance to project future abundance, accounting for positive lag-1 autocorrelation if there is evidence of its existence. Replicate applications of the model allow for computation of the probability of achieving rebuilt status in future years. Application to simulated abundance and escapement data suggested that model-projected rebuilding times generally corresponded to simulated rebuilding times as raw errors were median unbiased. Simulations also suggested that results were generally robust to parameter misspecification and that increased levels of lag-1 autocorrelation in abundance were associated with longer rebuilding periods. The application of the model to five overfished stocks in 2018–2019 illustrated the differences in projected rebuilding times under alternative rebuilding management strategies. The model filled a need for relatively rapid assessment of alternative rebuilding strategies for Pacific salmon stocks, a need that will likely remain given current biological reference points and fluctuations in salmon abundance.

Introduction

Ending overfishing and rebuilding overfished stocks is a priority for many countries, however reducing fishing mortality rates and rebuilding stock biomass has socioeconomic consequences (NRC, 2014). The choice of management strategies for rebuilding depleted stocks involves considering tradeoffs between the severity of fishery reductions (e.g., in terms of catch or effort) and the duration of such reductions (Hilborn et al., 2011; Wetzel and Punt, 2016). The United States Magnuson-Stevens Fishery Conservation and Management Act1 (hereafter MSA) requires that rebuilding plans for overfished stocks specify rebuilding periods. As of June 2020, there were 49 overfished stocks in the United States, all of which require the development of a rebuilding plan and an estimated rebuilding period.

Since 2012, the Pacific Coast Salmon Fishery Management Plan (FMP; PFMC (Pacific Fishery Management Council), 2016) has specified that a stock meets the criteria for overfished status if the geometric mean of the most recent three years of spawner escapement falls below the Minimum Stock Size Threshold (MSST). The MSST ranges by stock from 0.50 to 0.75 of the spawner escapement that is expected, on average, to produce maximum sustainable yield (SMSY). The default criterion for achieving rebuilt status is a geometric mean of the most recent three years of spawner escapement meeting or exceeding SMSY. The use of a multi-year criteria for determining overfished and rebuilt status recognizes the dynamics of short-lived and semelparous salmon populations that can exhibit large annual fluctuations.

In 2018, five Pacific salmon stocks, two Chinook and three coho, met the criteria for overfished status and rebuilding plans were required to be prepared for Pacific Fishery Management Council (PFMC) consideration within one year. In the salmon FMP, there are currently 25 stocks with specified MSST and SMSY values that are used to assess overfished and rebuilt status. There are a substantial number of other stocks in the FMP that do not have these associated reference points because they are either listed under the United States Endangered Species Act, are managed as part of a stock complex, or are a hatchery stock. While the number of overfished salmon stocks in 2018 was unprecedented for the PFMC, if the current stock reference points (e.g., MSST, SMSY) and overfished criterion were applied to past years, this number of overfished stocks would be somewhat unremarkable (Fig. 1). Hence, the ability to produce rebuilding plans with projections of rebuilding periods for multiple stocks within a short time frame will likely be necessary into the future. Prior to 2018 there were no accepted methods for projecting the rebuilding period for salmon stocks. This contrasts with some FMPs where very specific guidelines are in place for developing rebuilding analyses. For example, terms of reference have been developed for conducting rebuilding analyses for Pacific Coast groundfish, using standardized software (developed by A. Punt, University of Washington, USA, based on Punt and Ralston, 2007), which includes calculation of minimum and maximum times to recovery (PFMC (Pacific Fishery Management Council), 2018).

In this paper, we describe a Monte Carlo simulation approach developed to predict rebuilding periods for overfished salmon stocks. The approach has low data requirements and therefore can be applied to a wide variety of stocks with different levels of data richness. It relies upon past estimates of abundance to project future abundance, accounting for positive lag-1 autocorrelation if the time series of abundance suggests it exists. This autocorrelation may implicitly capture the effects of an autocorrelated environment or other biological processes operating on a short time scale, without explicitly modeling them. It does not require information on stock productivity or production capacity. The model structure is consistent with the annual salmon season planning process where stock-specific forecasts of abundance are applied to control rules that specify maximum allowable exploitation rates from all salmon-directed fisheries (e.g., commercial, recreational, and tribal). Harvest models are then used to project stock-specific exploitation rates and spawner escapements, given the planned salmon fisheries. The rebuilding time model explicitly accounts for abundance forecasting error, exploitation rate implementation error, and spawner escapement observation error. Implementation of this method in 2018–2019 established projected rebuilding times for alternative rebuilding strategies, as required by the MSA (PFMC (Pacific Fishery Management Council), 2019b; PFMC (Pacific Fishery Management Council), 2019c; PFMC (Pacific Fishery Management Council), 2019d, PFMC (Pacific Fishery Management Council), 2019e; PFMC (Pacific Fishery Management Council), 2019f). In addition, the projected rebuilding times were used by stakeholders and fishery managers to evaluate alternative rebuilding strategies by weighing potential reductions in the salmon fishery against the time it would take to rebuild the stocks.

After specifying the rebuilding time model, model performance is evaluated under alternative parameter assumptions, data ranges, and levels of autocorrelation in abundance through application to simulated data. The model implementation for the five overfished stocks in years 2018–2019 is then described. We end with a discussion of potential modifications to model structure that could be considered in future applications.

Section snippets

Model specification

Log-scale, pre-fishery ocean abundance in year t, logNt, is characterized by lag-1 autocorrelated draws from a Normal distribution with parameters estimated from past stock abundances. Abundance is specified in terms of adult (age ≥ 3) spawner equivalent units (PFMC (Pacific Fishery Management Council), 2016). Simulated log-scale abundance in year t is a function of log abundance in the previous year logNt-1, the lag-1 autocorrelation coefficient ρˆ, and a draw from the distribution

Application to simulated data

Estimated parameters for the rebuilding time model varied around the values used to simulate abundance data (Fig. 4). Estimated parameters varied more around assumed parameter values when the data series was shorter. Estimated ρˆ were generally lower than values assumed for data simulation under both data length scenarios, though the differences were more pronounced for the shorter, 15 year data series simulations. For cases where data were simulated with ρ=0, the median value of ρˆ was also

Discussion

Projected rebuilding periods are used to aid the rebuilding strategy decision making process for stakeholders and fishery managers. The rebuilding time model described here has modest data requirements, which is desirable because sufficient data do not readily exist for many salmon stocks to fit stock-recruitment relationships and develop more complex population dynamics models. While in some cases having a more explicit link between the spawning stock and recruits to the fishery would be

CRediT authorship contribution statement

Michael R. O’Farrell: Conceptualization, Methodology, Formal analysis, Writing - original draft, Visualization. William H. Satterthwaite: Methodology, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We would like to thank members of the PFMC’s Salmon Technical Team and Scientific and Statistical Committee for providing input and review of the rebuilding time model as it was being developed. E.J. Dick and John Field provided many helpful suggestions during manuscript development, and two anonymous reviewers made several helpful suggestions that improved the paper. Will Atlas, Cameron Freshwater, Carrie Holt, and Jordan Watson provided valuable insights into salmon management beyond the

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