Fisheries Assessment and Management in Data-Limited Situations 487 Alaska Sea Grant College Program • AK-SG-05-02, 2005

Fisheries Assessment and Management in Data-Limited Situations 487 Alaska Sea Grant College Program • AK-SG-05-02, 2005 Minimum Stock Size Thresholds: How Well Can We Detect Whether Stocks Are below Them? Z. Teresa A’mar and André E. Punt University of Washington, School of Aquatic and Fishery Sciences, Seattle, Washington Abstract Management of marine fi sheries in U.S. waters is based on the Magnuson- Stevens Fishery Conservation and Management Act. Rebuilding plans need to be developed for fi sh stocks that have been depleted to below a minimum stock size threshold, MSST. Whether a stock is below MSST is based on the results from a stock assessment. Two types of error can arise when a stock is assessed relative to MSST: (a) it can be assessed to be above MSST when it is not, or (b) it can be assessed to be below MSST when it is not. Simulation is used to assess the likelihood of making these two types of errors as a function of the true status of the resource, the stock assessment method applied, and the quality and quantity of the data available for assessment purposes. All three of the methods of stock assessment considered in this study (two age-structured methods and a production model) make the two errors, especially when the true status of the resource is close to MSST. The major factor infl uencing the likelihood of under- and over-protection errors is the extent of variability in recruitment, the impact of which is larger than that of data quality and quantity, at least within the range for data quality and quantity considered in this paper. Introduction The objectives for the management of the world’s marine renewable resources generally include striking an appropriate balance between “optimum” utilization of the available resources for the benefi t of the na- tion involved and the long-term conservation of the resources and their associated ecosystem. In the United States, the need for this balance is 488 A’mar and Punt—Minimum Stock Size Thresholds refl ected in National Standard 1 of the Magnuson-Stevens Fishery Conser- vation and Management Act, viz. “Conservation and management mea- sures shall prevent overfi shing while achieving, on a continuing basis, the optimum yield from each fi shery for the United States industry.” National Standard 1 has been made operational through a system of guidelines (e.g., Restrepo et al. 1999, Restrepo and Powers 1999). These guidelines distinguish between overfi shing and being in an overfi shed state. “Overfi shing” means that the level of fi shing mortality exceeds a maximum fi shing mortality threshold (MFMT), which is currently set at the rate associated with maximum sustainable yield (MSY), and “being in an overfi shed state” means that the current spawning output is less than a minimum stock size threshold (MSST). For many stocks, MSST has been 1 defi ned to be half of SMSY (the spawning output corresponding to MSY). Stocks that are found to be below MSST are determined to be overfi shed (i.e., depleted) and there is a need for the National Marine Fisheries Ser- vice to develop a rebuilding plan to restore the stock to SMSY, which is then treated as the target level of spawning output. Assessing a stock relative to some management threshold level (be it SMSY, 0.5 SMSY, or some proxy level) will be referred to as a status determination in this paper. The use of SMSY as the target for fi sheries management can be criti- cized for a variety of reasons (e.g., Larkin 1997, Punt and Smith 2001). However, it remains the most common target reference point for fi sheries management. For example, legislation in New Zealand dictates that management arrangements must be selected to move the resource toward SMSY (Annala 1993). Although ideally MSST should be defi ned in terms of SMSY, the use of proxies for both the target spawning output and MSST are permitted because the data for particular species may be insuffi cient to estimate the shape of the relationship between spawning output and subsequent recruitment. For example, for groundfi sh species managed by the Pacifi c Fishery Management Council, the proxy for MSST has been set to 25% of the estimated unfi shed level of spawning output, S0, and the target level has been set to 40% of S0 (Pacifi c Fishery Management Council 2003). Figure 1 shows the control rule used by the Pacifi c Fishery Management Council to set optimum yields for groundfi sh species off the U.S. West Coast (Pacifi c Fishery Management Council 2003). The ability to apply control rules such as Fig. 1 requires that it is pos- sible to estimate a variety of quantities (current spawning output, MSY, and SMSY or their proxies). The estimates for these quantities are derived from stock assessments. Several analytical methods are used to conduct stock assessments in the United States (e.g., National Research Council 1998). However, the bulk of the assessments are conducted using two basic approaches: ADAPT (Gavaris 1988) and Integrated Analysis (Fournier 1 Spawning output is variously defi ned as egg production or the biomass of spawning fi sh. Fisheries Assessment and Management in Data-Limited Situations 489 Optimum Yield 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 200 400 600 800 1000 Spawning output Figure 1. An example of the 40-10 control rule applied to U.S. West Coast groundfi sh species. and Archibald 1982; Methot 1993, 2000). Integrated Analysis is currently the “method of choice” for assessments of the groundfi sh species managed by the Pacifi c Fishery Management Council (e.g., Jagielo et al. 2000, Williams et al. 2000, Hamel et al. 2003). Unfortunately, it is well known that stock assessments are subject to not inconsiderable uncertainty, especially in data-poor situations. In the context of conducting evaluations relative to the application of control rules (such as that in Fig. 1), the questions that arise include: what is the probability that a stock is assessed to be above MSST when it is not (under-protection error), and what is the probability that a stock is assessed to be below MSST when it is not (over-protection error). The probability of making these two errors depends on the quality of the data available for assessment purposes and the suitability of the population dynamics model underlying the stock assessment. Simulation is therefore used in this study to assess the likelihood of making these two types of errors as a function of the true status of the resource, the stock assessment method applied, and the quality and quantity of the data available for assessment purposes. 490 A’mar and Punt—Minimum Stock Size Thresholds Methods The most common method used to determine how well a stock assessment method is likely to perform is Monte Carlo simulation (e.g., de la Mare 1986, Patterson and Kirkwood 1995, Sampson and Yin 1998, Punt et al. 2002). Evaluation of the properties of a statistical estimation method (including its bias and precision) by simulation involves the following steps. 1. Defi nition of a mathematical model of the system to be assessed; this model (often referred to as the operating model) will represent the truth for the simulations. 2. Use of the operating model to generate the data sets that will be used by the assessment methods. 3. Application of a number of alternative stock assessment methods to the generated data sets. 4. Comparison of the estimates of stock status provided by the stock assessment methods with the true state of the stock as given by the operating model. Although some of the stock assessments for West Coast groundfi sh species have evaluated the status of stocks relative to the target level of spawning output and MSST in probabilistic terms (e.g., Ianelli et al. 2000, Hamel et al. 2003, Cope et al. 2004), the bulk of stock assessments for these species is based on the “best” estimates of quantities such as current spawning output, S0, etc. Although there is a need to evaluate probabilistic methods for assessing fi sh stocks, this study focuses on a more immediate need, namely to evaluate stock assessment methods that base their status determinations on the point estimates from a stock assessment. Each of the 250 replicates that constitute a simulation trial therefore involves generating an artifi cial data set for which the true status relative to SMSY and MSST are known exactly, applying each of the assessment methods under consideration to estimate the time-series of historical spawning outputs and SMSY, and comparing how often the stock assessment correctly determines the status of the resource relative to the SMSY and MSST. The performances of the various stock assessment methods are assessed relative to the following questions. a. Is the stock below SMSY at present? b. Is the stock below 0.4 S0 at present? c. Is the stock below 0.5 SMSY at present? d. Is the stock below 0.25 S0 at present? Fisheries Assessment and Management in Data-Limited Situations 491 The simulations therefore consider performance relative to both the target level of SMSY and MSST. Consideration was given to assessing performance relative to the proxies for SMSY and MSST as well as to SMSY and MSST themselves (0.4 S0 is the proxy for SMSY and 0.25 S0 is the proxy for 0.5 SMSY) because of initial concern that it may prove very diffi cult to estimate SMSY reliably (e.g., Maunder and Starr 1995) using the (noisy and sparse) data collected from the fi shery.

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