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Keywords:

  • Fisheries management;
  • marine reserves;
  • data-limited fisheries;
  • spawning potential ratio

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

No-take marine reserves show great promise as conservation tools, yet the integration of reserves into assessment models for data-limited fisheries management is just emerging. We develop a framework for integrating marine reserves into two data-limited assessment models: spawning potential ratio (SPR) and yield per recruit (YPR). We use Monte Carlo simulation to test the applicability of the framework to a sedentary species with a dispersive larval stage under process and observation uncertainties. The reserve-based approach increased estimates of spawning potential while reducing YPR and had a consistent estimation bias of less than 15%. Using the framework, we assessed a commercial fishery targeting grass rockfish (Sebastes rastrelliger) in southern California, USA and found that inclusion of reserves reduced the probability of overfishing. The reserve-based assessment approach may create win–win policy solutions for conservation and fisheries objectives in many nearshore fisheries with well-enforced marine reserves that target sedentary species with a dispersive larval stage.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Sixty-four percent of global fisheries, comprising 80% of the global fish catch, lack the data and resources to perform formal stock assessments and are estimated to be overfished (Costello et al. 2012). Increased fishing pressure from a growing global human population poses serious threats to the continued decline of data-limited fisheries and the resilience of coastal ecosystems. Innovative approaches to assess data-limited fisheries are necessary to inform management decisions and restore stocks to biomass levels that achieve higher yields, increase economic opportunities, and promote ecosystem resiliency (Hilborn et al. 2005).

No-take marine reserves (hereafter reserves) are being established worldwide (Cressey 2011) to maintain spatial population structure of fish stocks (Berkeley et al. 2004), protect essential fish habitat, hedge against management uncertainty (Gell & Roberts 2003), and reduce mortality within reserve borders (Kay & Wilson 2012). Enhanced biological production inside reserves (Lester et al. 2009) can benefit adjacent fisheries through adult spillover (Roberts & Polunin 1991, Allison et al. 1998; McClanahan & Mangi 2000) and larval export (Cudney-Bueno et al. 2009; Pelc et al. 2010), especially in situations where the size of the reserve is larger than the adult home range size, and smaller than the scale of larval dispersal (Gerber 2003). The conservation benefits of reserves are many, yet without effective management controls outside reserve borders, benefits to fisheries may be minimal (Halpern et al. 2004). Novel management solutions that integrate reserves with fisheries assessments at local scales can simultaneously improve management decisions outside borders while accounting for benefits that accrue inside reserve borders (Wilson et al. 2010).

Assessment methods such as yield per recruit (YPR) and spawning potential ratio (SPR) are often used in data-limited situations (e.g., unknown stock-recruit relationship) to set reference points and guide management decisions (Mace & Sissenwine 1993). The YPR (Beverton & Holt 1956) is a relative measure of the yield of a single recruit over its lifetime under different fishing rates. The SPR (Mace & Sissenwine 1993) is the lifetime reproductive potential of a recruit in a fished population compared to its reproductive potential in an unfished population (Goodyear 1993). The relationship between fishing mortality (F) and target YPR and SPR values are used to design fisheries management harvest control rules that maximize yields and minimize the chance of stock collapse. For example, control rules can be set to harvest a stock at Fmax, the fishing mortality rate that maximizes YPR, and F30-50, the harvest rate that achieves a SPR target between 30 and 50%. YPR and SPR models can be parameterized to incorporate information from marine reserves to estimate the status of the local resource (Beverton and Holt 1957). However, the formalization of these approaches and the application to data-limited fisheries management is lacking.

Here we present a management strategy for data-limited fisheries that incorporates fishery independent data collected inside and outside of marine reserves into YPR and SPR models. We used simulation analysis to examine the accuracy of these models under several types of process and observation uncertainty. We then applied the reserve-based SPR and YPR framework to a case study in which we collected data in a collaborative fisheries research (CFR) program designed to evaluate the impacts of a network of marine reserves on the dynamics of grass rockfish (Sebastes rastrelliger) in the Santa Barbara Channel (SBC), CA, USA (SBC). We provide an example of how marine reserves can simultaneously contribute to improving assessments and enhancing conservation outcomes for data-limited fisheries.

Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

We developed an assessment framework that utilized fishery independent sampling data from inside and outside of marine reserves and empirical growth rate parameters to estimate total mortality (Z), natural mortality (M), and fishing mortality (F). Mortality estimates were used to parameterize SPR and YPR models that incorporated information from marine reserves. A simulation study was conducted to evaluate the biases associated with application of this model to sedentary nearshore species with highly dispersive larval stages under nine unique scenarios. We then applied the model to an exemplary data-limited fishery for S. rastrelliger in CA.

Estimation of mortality rates

Our approach required estimates of annualized total mortality (Z), natural mortality (M), and instantaneous rates of fishing mortality (F) made from length frequency distributions (LFD) collected from a scientific sampling program inside and outside of reserves, as well as von Bertalanffy growth estimates. In the first step, a calculation of Z was made on the outside reserve LFD data set using Ehrhardt and Ault's (1992) bounded mortality estimator:

  • display math(1)

where L is the mean asymptotic length (cm) of the von Bertalanffy growth equation, Lc is the size of fish at full recruitment, in this case the minimum size limit of 30.4 cm, Lλ is calculated by estimating the age at Lc (using the von Bertalanffy equation) and adding the number of years since a known harvest rate policy change (age at Lc + time since harvest rate policy change), and converting back to length, is the mean length of fish between Lc and Lλ.

Natural mortality (M) was estimated using an average of four commonly used life history invariant approaches including: (1) a rule of thumb approach (Quinn & Deriso 1999), (2) Jensen's method (Jensen 1996), (3) a technique developed by Hoenig (1983) for calculating Z that Punt et al. (2005) found to be reliable for estimating M for data-limited stocks; and (4) the bounded mortality estimator (Equation (1)), in which the harvest rate policy change is the establishment of reserves. In this case, Equation (1) is applied to the reserve LFD. Calculation of F was made by subtracting M from Z.

Reserve-based YPR and SPR models

Calculation of YPR and SPR requires inputs on growth rates, natural mortality, age at maturity, weight at age, and fecundity at age. Beverton & Holt (1957) showed that the establishment of reserves reduced estimates of YPR by reducing a proportion of available biomass to harvest, yet little work has been done to incorporate reserves into SPR models to demonstrate resulting conservation gains arising from protecting an equal proportion of biomass. Therefore, we focus on reserve-based SPR to describe the effect of marine reserves on the expected egg production of a single individual:

  • math image(2)

where a = age, fa is the mean fecundity at age, ma is the maturity at age, and K is the fraction of habitat set aside in a marine reserve. Numbers at age for the fished population Na,fished outside of reserves are calculated from an equilibrium age-structured population described in Wilson et al. (2012). Numbers at age for the unfished population Na,unfished inside reserves are calculated using the same model without fishing mortality.

Simulation analyses

To glean general insight on the influence of reserves in SPR and YPR models, we applied different fractions of reserve size (0–50%) in 10% intervals to Equation (2). The population dynamics are based on characteristics of S. rastrelliger, and we make the assumption that larvae disperse and recruit uniformly across the region with no adult movement (Wilson et al. 2012).

To test the data-limited assessment approach for accuracy and precision across various types of assumptions and uncertainty, we developed a simulation analysis that consisted of (1) an operating model that included the population and fleet dynamics for a fishery that resembled S. rastrelliger in the SBC, (2) a sampling model that represented a scientific sampling protocol inside and outside of a marine reserve, and (3) an estimation and assessment model described in the previous two sections. We tested the model accuracy and precision in nine separate scenarios that are known to disrupt equilibrium conditions (Gedamke and Hoenig 2006) and bias estimates. These scenarios included: (1) a deterministic baseline scenario, (2) random annual recruitment deviates, (3) temporal autocorrelation in recruitment and (4) harvest rates, (5) different forms of vulnerability to fishing and sampling gear, (6) variability in historical fishing pressure, (7) incorrect estimates of natural mortality, (8) deviations from assumptions regarding von Bertalanffy growth, and (9) a combination of all the uncertainties. Details of the simulation model, assumptions and outputs can be found in the online Appendix.

Application of model

We applied the assessment model to data collected in a CFR program for S. rastrelliger in the SBC, CA, USA. S. rastrelliger is a nearshore, sedentary species harvested in a live fish fishery (Love & Johnson 1999). The fishery is data-limited and is managed using precautionary catch levels (Restrepo et al. 1998) and a minimum size limit of 30.4 cm (12 in.). S. rastrelliger have limited adult annual movement of less than 1 km (Hanan 2012, J.R. Wilson, unpublished data), and larval dispersal distance averages 10 km generation−1 (Buonaccorsi et al. 2004).

In 2003, CA, USA implemented the Northern Channel Islands State Marine Protected Areas, which formed a network of ten reserves in the SBC ecosystem (Figure 1). The Channel Islands reserves protect approximately 20% of the nearshore habitat at the Channel Islands (CDFG 2008). The average size of reserves in this region is 3.1 km alongshore distance while the spacing between reserves ranges from 20 to 40 km.

image

Figure 1. Map of the SBC, including the mainland coast and four northern Channel Islands (left to right: San Miguel, Santa Rosa, Santa Cruz, and Anacapa). Open circles represent our sampling locations inside and outside of marine reserves.

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The S. rastrelliger fishery in the SBC is an ideal study system to explore the integration of marine reserves in cohort-based assessment models due to the sedentary nature of adult fish, the moderately dispersive larval stage, and protection by a network of marine reserves. We sampled S. rastrelliger populations collaboratively with fishers inside and outside of five marine reserves using standardized, commercial set long lines in 2007–2009. Total lengths of fish (cm) were recorded for 1,316 individual fishes from inside the five reserves, and 809 S. rastrelliger from outside of reserves spread equally across the study area (Figure 1). All fishing was conducted onboard fishing vessels of our collaborative research partners in a stratified design (online Appendix).

In addition to the onboard scientific sampling, we collected a port sampling data set with 2,174 measurements of S. rastrelliger landed by fishers and returned to port for sale. All port-sampled fish were caught using similar gear and hook sizes at the same water depths and general locations as our outside-of-reserve samples. Length data greater than the minimum size limit of 30.4 cm collected during collaborative research outside of reserves were combined with the port sampling data (also outside of reserves) to standardize between fishery independent and dependent sampling, yielding an outside-reserve length distribution data set of 3,490 fish (Table 1). LFD inside and outside of reserves were statistically evaluated for differences using a KS test and a t-test.

Table 1. Sample sizes of S. rastrelliger from collaborative fisheries research monitoring inside and outside of five marine reserves at the Channel Islands, CA
LocationSample size
Harris Point, San Miguel Island 
Inside reserve85
Outside reserve368
Carrington Point, Santa Rosa Island 
Inside reserve162
Outside reserve260
South Point, Santa Rosa Island 
Inside reserve218
Outside reserve924
Gull Island, Santa Cruz Island 
Inside reserve332
Outside reserve1,309
Anacapa Island 
Inside reserve14
Outside reserve19
Naples Reef, Mainland 
Outside reserve609

We used length data from the 4,299 S. rastrelliger sampled from inside and outside reserves to estimate mortality rates and reserve-based YPR and SPR. Growth rates were calculated by fitting the von Bertalanffy growth function to ages of fish estimated from 176 S. rastrelliger sampled during a simultaneous study within the study region (Wilson et al. 2012). To explore uncertainty around our model results we executed 5,000 nonparametric bootstrap samples with replacement of the LFD and the age at length data. For each sample data set we estimated Z, M, F, SPR, and YPR. We also evaluated a counterfactual scenario in which the fraction of reserves (K; Equation (2)) was set to 0, implying that the entire population was subject to fishing pressure. We refer to the actual reserve scenario as “with reserve,” which reflects the actual status of the fishery in the SBC, and the counterfactual scenario as “no reserve.”

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Simulation analyses

The integration of reserves in YPR and SPR models indicated that SPR increased relative to the proportion of habitat in reserves, while YPR decreased with reserve size (Figure 2) supporting results of Beverton & Holt (1956). Under the life history parameters and demographic rates used in the initial simulation, a harvest rate between 0.05 and 0.2 maximized YPR. Reserve fractions above 40% maintained SPR levels above the target reference point of 50% across harvest rates, suggesting that with 40% protection in reserves, managers should seek to maximize YPR by adjusting F to desired levels. Such tradeoffs in YPR and SPR can be used to evaluate management actions that achieve desired target levels of each metric.

image

Figure 2. (A) SPR and (B) YPR outputs for a model fish with similar life history traits as S. rastrelliger (Wilson et al. 2012). Lines corresponding to percentages indicate the fraction of the cohort set aside inside no-take marine reserves.

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Simulation results estimating M, Z, F, and SPR indicated that under deterministic conditions the assessment model can accurately estimate these values with high precision (online Appendix). The model was robust to uncertainty in random annual recruitment deviation, misspecification of the selectivity function, high historical fishing mortality, and a misspecification of the correct growth function. However, the model had increased difficulty estimating mortality with autocorrelation in recruitment and fishing mortality (online Appendix). Across all scenarios for all time periods, the estimates of current SPR ranged within 15% of the true SPR, indicating the model may help guide management decisions under violations of several equilibrium assumptions.

Application of model

LFD of S. rastrelliger were significantly different inside and outside of reserves (Figure 3), as revealed in the KS test (D = 0.3602, P < 0.001). The mean length of S. rastrelliger inside reserves (37.65 cm) was also significantly larger than the mean length outside of marine reserves (35.1 cm), as revealed in the t-test (t = 17.4634, df = 1185.932, P < 0.001).

image

Figure 3. LFD for S. rastrelliger sampled inside and outside of a network of five marine reserves at the northern Channel Islands, USA, in collaboration with commercial fishermen using set hook and line gear.

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Bootstrapped estimates of growth parameters resulted in the following values: L = 45.13 cm (±2.3 s.d.), K = 0.13 (±0.02), to = −1.32 cm (±0.6). The estimate of natural mortality (M) for S. rastrelliger was 0.15 (±0.02). The estimate of Z was 0.31 (±0.03) and the estimate of F was 0.16 (±0.03). Inclusion of reserves in the assessment process increased the estimates of SPR while decreasing the estimate of YPR. Such tradeoffs should be considered when implementing reserves and setting target fishing mortality rates. In the counterfactual “no reserve” scenario, the target of F50 was not met, indicative of overfishing. Accounting for reserves in the SPR model increased the estimate of SPR from 0.38 without reserves to 0.51 with reserves; a level that meets the target threshold of F50 that determines overfishing (Figure 4). YPR estimates decreased by 24% from 0.128 to 0.103 as reserves were factored into the assessments suggesting that lost yields may arise under the assumptions of our model.

image

Figure 4. Outputs from the assessment model for S. rastrelliger in the SBC. (A) Spawning potential ratio (SPR), (B). YPR. Dashed line depicts target reference point of F50. Solid grey lines depict median values of bootstrapped estimates for the “with reserve scenario.” Hashed black lines depict median values for the “without reserves” scenario. Grey and black vertical and horizontal hashed lines correspond with the estimated harvest rate and associated SPR values for “with reserve” and “without reserve” scenario, respectively.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Incorporation of marine reserves into SPR assessment models accounts for conservation gains that would otherwise not be credited in decision making. Crediting of reserves prevents a premature assessment of overfishing and can potentially improve stakeholder support for marine reserves and future management changes. The model framework we developed was robust to several forms of uncertainty and may be a viable method for informing management decisions in data limited fisheries for species with a sedentary adult stage and a dispersive larval stage and well-enforced reserves. The value of the SPR assessment method will increase with the establishment of marine reserves and their effective enforcement, thus advancing fisheries management concurrently with conservation. The policy advantages of a win–win scenario for fisheries management and conservation are probably manifold and synergistic.

Protection of 20% of the S. rastrelliger habitat inside the SBC reserves increased the estimated SPR above the minimum threshold reference point of F50 to a level consistent with target mortality rates. Without the incorporation of reserves into the model, the perceived overfishing of the resource would provide management an incentive to reduce fishing mortality thus leading to potential negative impacts on the fishery.

Our reserve-based assessment is not intended to replace conventional stock assessment approaches when data and resources are available, in part because data-limited fishery management requires making a set of well-recognized assumptions. Our assessment framework considers the fish populations to be demographically closed, to have age and time independent mortality, constant vulnerability to fishing gear, growth rings that are easily interpreted with little observer error, and the ability to collect an unbiased size sample representing the true population (Gedamke & Hoenig 2006). Per-recruit models also fail to account for compensatory effects in stock size on incoming recruits (Goodyear 1993), make assumptions that larval mortality is density independent, and that all larvae are released into a common larval pool and settle equally to all fished and not fished areas. Our incorporation of reserves into these models also assumes that adult biomass is evenly distributed throughout the respective areas so that the amount of adult biomass initially protected by a reserve is proportional to the reserve size (Halpern et al. 2004). Data limited fisheries inevitably suffer from violating one or more of these assumptions, and it is recommended that significant effort be allocated to understand the dynamics of the species and the fishery before assessing stock status.

Estimates of SPR were accurate under a suite of scenarios intended to disrupt equilibrium assumptions for the life history and demographic characteristics of our chosen model species. Alternative assumptions regarding dispersal, recruitment, adult movement, and enforcement of marine reserves may limit the utility of this approach and should be considered in future scenario testing. In situations where life history information is lacking, adoption of parameters from similar species or systems is a viable alternative and should also be examined (Punt et al. 2011). In the case of S. rastrelliger and other reef associated species, settlement, recruitment and survivorship are heterogeneous in space and time (Caselle et al. 2010) and recruitment overfishing is likely to occur at high rates of F. Such considerations should be carefully examined prior to management action.

Incorporating marine reserves into fisheries assessment and management models recognizes the conservation value of increased reproductive potential resulting from protection. Integration of stakeholder involvement and the use of reserve-based approaches can be carried out in many fisheries for sedentary nearshore species with a dispersive larval stage and well-enforced marine reserves. Such an approach provides a simple and cost effective strategy for community-based co-management institutions to adaptively manage local resources.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

We thank J. Cope, J. Prince, C. Costello, J. Caselle, D. Reed, M. Love, and S. Gaines for helpful comments on the modeling and manuscript. I. Pearlman created Figure 1. Funding was provided by The California Ocean Protection Council (07-021), California Sea Grant (#NA10OAR4170060), the Bren School of Environmental Science and Management, and the Sustainable Fisheries Group (grants awarded by the Waitt Foundation and The Nature Conservancy). Support was also provided by the Santa Barbara Coastal LTER (SBC-LTER). This project was made possible by commercial fishermen J. Colgate, C. Hoeflinger, M. Brubaker, and many others.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information
  • Allison, G.W., Lubchenco, J. & Carr M.H. (1998). Marine reserves are necessary but not sufficient for marine conservation. Ecol. Appl. 8, S79-S92.
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  • Beverton, R.J.H. & Holt, S.J. (1956). A review of the lifespans and mortality rates of fish in nature, and their relation to growth and other physiological characteristics. Pages 142-177 in G.E.W. Westenholme & M. O'Connor, editors. The lifespan of animals, CIBA Foundation colloquia on ageing (Vol. 5), Little, Brown and Company, Boston, MA.
  • Beverton, R.J.H. & Holt, S.J. (1957). On the dynamics of exploited fish populations. Fish. Invest. UK Minist. Agric. Fish. Food., 19, 533.
  • Buonaccorsi, V.P., Westerman, M., Stannard, J. et al. (2004). Molecular genetic structure suggests limited larval dispersal in grass rockfish, Sebastes rastrelliger. Mar. Biol., 145, 779-788.
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  • Cressey, D. (2011). Plans for marine protection highlight science gap. Nature, 469, 146.
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  • McClanahan, T.R. & Mangi, S. (2000). Spillover of exploitable fishes from a marine park and its effect on the adjacent fishery. Ecol. Appl., 10, 1792-1805.
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Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information
FilenameFormatSizeDescription
conl12073-sup-0001-SuppMat.pdf1513K

Table A1. Parameter values and functional relationships for the nine simulated scenarios used to test the accuracy of the model under process and observation uncertainty. R = recruitment, F = fishing mortality, M = natural mortality. Functional forms of each equation can be found in the operating model text.

Table A2. Parameter values and definitions used in the operating and sampling models.

Figure A1. Scenario 1. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A2. Scenario 2. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A3. Scenario 3. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range and 95% confidence intervals.

Figure A4. Scenario 4. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range and 95% confidence intervals.

Figure A5. Scenario 5. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A6. Scenario 6. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A7. Scenario 7. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A8. Scenario 8. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A9. Scenario 9. Time series of estimates for Z, M, and F representing the error of 100 trials and 50 bootstrap estimates in the simulation analysis. Box plots represent the median, interquartile range, and 95% confidence intervals.

Figure A10. Spawning potential ratio and F plots for nine separate simulated scenarios, five years after reserve implementation. The numbers in the top right corner of each panel correspond to the scenario (Table S1). Dotted lines represent a target reference point at SPR50. The black solid lines depict the SPR outcomes, and the true F used in the simulation. The solid grey lines represent the estimated SPR and estimated F from the assessment model. Dotted grey lines represent 10th and 90th percentiles around the estimated SPR.

Figure A11. Spawning potential ratio and F plots for nine separate simulated scenarios, 10 years after reserve implementation. The numbers in the top right corner of each panel correspond to the scenario (Table S1). Dotted lines represent a target reference point at SPR50. The black solid lines depict the SPR outcomes, and the true F used in the simulation. The solid grey lines represent the estimated SPR and estimated F from the assessment model. Dotted grey lines represent 10th and 90th percentiles around the estimated SPR.

Figure A12. Spawning potential ratio and F plots for nine separate simulated scenarios, 25 years after reserve implementation. The numbers in the top right corner of each panel correspond to the scenario (Table S1). Dotted lines represent a target reference point at SPR50. The black solid lines depict the SPR outcomes, and the true F used in the simulation. The solid grey lines represent the estimated SPR and estimated F from the assessment model. Dotted grey lines represent 10th and 90th percentiles around the estimated SPR.

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