A stochastic approach to stock reduction analysis

2006 ◽  
Vol 63 (1) ◽  
pp. 212-223 ◽  
Author(s):  
Carl J Walters ◽  
Steven J.D. Martell ◽  
Josh Korman
Keyword(s):  
Probability Distributions ◽  
Stochastic Approach ◽  
Reference Points ◽  
Stock Size ◽  
Structured Population Models ◽  
Alternative Hypotheses ◽  
Detailed Assessment ◽  
Importance Resampling ◽  
Age Structured ◽  
Fully Bayesian

Stock reduction analysis (SRA) can complement more detailed assessment methods by using long-term historical catches to estimate recruitment rates needed to have produced those catches, yet still end up with stock sizes near those estimated by the detailed methods. A longer historical perspective can also add information to the estimation of reference points such as unfished biomass (B0) or target biomass (BMSY). Deterministic SRA models provide a single stock size trajectory that is vanishingly unlikely to have actually occurred, while stochastic SRA attempts to provide probability distributions for stock size over time under alternative hypotheses about unfished recruitment rates and about variability around assumed stock–recruitment relationships. These distributions can be generated with age-structured population models by doing large numbers of Monte Carlo simulation trials and retaining those sample trials for which the stock would not have been driven to extinction by historical catches. By resampling from these trials using likelihood weights (sampling – importance resampling method), it is possible to move into fully Bayesian, state–space assessment modeling through a series of straightforward steps and to provide understandable visualization of how much the data help to reduce uncertainty about historical fishing impacts and stock status.

Analytical models for fishery reference points

1998 ◽  
Vol 55 (2) ◽  
pp. 515-528 ◽  
Author(s):  
Jon T Schnute ◽  
Laura J Richards
Keyword(s):  
Fishery Management ◽  
Reference Points ◽  
Analytical Models ◽  
Model Parameters ◽  
Harvest Management ◽  
Structured Population Models ◽  
General Utility ◽  
Special Cases ◽  
Age Structured ◽  
Mathematical Definitions

Fishery reference points are widely applied in formulating harvest management policies. We supply precise mathematical definitions for several reference points in common use. We then derive analytical expressions for these quantities from age-structured population models. In particular, we explain how the maximum sustainable harvest rate and catch (h*, C*), two quantities of management importance, can replace the classical recruitment parameters ( alpha , beta ) in the Beverton-Holt and Ricker recruitment curves. We also demonstrate dependencies of various reference points on subsets of model parameters. Although our analysis is restricted to special cases, our models still have general utility. For example, simple calculations from analytical formulas enable checks on the output from more complex models and guide the choice of reference points for fishery management.

scholarly journals Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa

2010 ◽  
Vol 67 (6) ◽  
pp. 1185-1197 ◽  
Author(s):  
C. Fernández ◽  
S. Cerviño ◽  
N. Pérez ◽  
E. Jardim
Keyword(s):  
Time Series ◽  
Stock Assessment ◽  
Reference Points ◽  
Assessment Model ◽  
Marine Science ◽  
Fishing Mortality ◽  
Change Over Time ◽  
Age Structured ◽  
Available Information ◽  
Over Time

Abstract Fernández, C., Cerviño, S., Pérez, N., and Jardim, E. 2010. Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa. – ICES Journal of Marine Science, 67: 1185–1197. A Bayesian age-structured stock assessment model is developed to take into account available information on discards and to handle gaps in the time-series of discard estimates. The model incorporates mortality attributable to discarding, and appropriate assumptions about how this mortality may change over time are made. The result is a stock assessment that accounts for information on discards while, at the same time, producing a complete time-series of discard estimates. The method is applied to the hake stock in ICES Divisions VIIIc and IXa, for which the available data indicate that some 60% of the individuals caught are discarded. The stock is fished by Spain and Portugal, and for each country, there are discard estimates for recent years only. Moreover, the years for which Portuguese estimates are available are only a subset of those with Spanish estimates. Two runs of the model are performed; one assuming zero discards and another incorporating discards. When discards are incorporated, estimated recruitment and fishing mortality for young (discarded) ages increase, resulting in lower values of the biological reference points Fmax and F0.1 and, generally, more optimistic future stock trajectories under F-reduction scenarios.

scholarly journals A two-stage biomass model to assess the English Channel cuttlefish (Sepia officinalis L.) stock

2014 ◽  
Vol 71 (9) ◽  
pp. 2457-2468 ◽  
Author(s):  
Michaël Gras ◽  
Beatriz A. Roel ◽  
Franck Coppin ◽  
Eric Foucher ◽  
Jean-Paul Robin
Keyword(s):  
Reference Points ◽  
Sea Surface ◽  
Sepia Officinalis ◽  
Sustainable Utilization ◽  
English Channel ◽  
Two Stage ◽  
Stock Biomass ◽  
Exploitation Rate ◽  
Spawning Stock ◽  
Age Structured

Abstract The English Channel cuttlefish (Sepia officinalis) is the most abundant cephalopod resource in the Northeast Atlantic and one of the three most valuable resources for English Channel fishers. Depletion methods and age-structured models have been used to assess the stock, though they have shown limitations related to the model assumptions and data demand. A two-stage biomass model is, therefore, proposed here using, as input data, four abundance indices derived from survey and commercial trawl data collected by Ifremer and Cefas. The model suggests great interannual variability in abundance during the 17 years of the period considered and a decreasing trend in recent years. Model results suggest that recruitment strength is independent of spawning–stock biomass, but appears to be influenced by environmental conditions such as sea surface temperature at the start of the life cycle. Trends in exploitation rate do not reveal evidence of overexploitation. Reference points are proposed and suggestions for management of the sustainable utilization of cuttlefish in the English Channel are advanced.

scholarly journals Time-varying natural mortality in fisheries stock assessment models: identifying a default approach

2014 ◽  
Vol 72 (1) ◽  
pp. 137-150 ◽  
Author(s):  
Kelli F. Johnson ◽  
Cole C. Monnahan ◽  
Carey R. McGilliard ◽  
Katyana A. Vert-pre ◽  
Sean C. Anderson ◽  
...  
Keyword(s):  
Stock Assessment ◽  
Assessment Method ◽  
Reference Points ◽  
Natural Mortality ◽  
Time Varying ◽  
Fishing Mortality ◽  
Total Allowable Catch ◽  
Robust Approach ◽  
Structured Population Models ◽  
Trade Offs

Abstract A typical assumption used in most fishery stock assessments is that natural mortality (M) is constant across time and age. However, M is rarely constant in reality as a result of the combined impacts of exploitation history, predation, environmental factors, and physiological trade-offs. Misspecification or poor estimation of M can lead to bias in quantities estimated using stock assessment methods, potentially resulting in biased estimates of fishery reference points and catch limits, with the magnitude of bias being influenced by life history and trends in fishing mortality. Monte Carlo simulations were used to evaluate the ability of statistical age-structured population models to estimate spawning-stock biomass, fishing mortality, and total allowable catch when the true M was age-invariant, but time-varying. Configurations of the stock assessment method, implemented in Stock Synthesis, included a single age- and time-invariant M parameter, specified at one of the three levels (high, medium, and low) or an estimated M. The min–max (i.e. most robust) approach to specifying M when it is thought to vary across time was to estimate M. The least robust approach for most scenarios examined was to fix M at a high value, suggesting that the consequences of misspecifying M are asymmetric.

scholarly journals An explicit solution for calculating optimum spawning stock size from Ricker’s stock recruitment model

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e1623 ◽  
Author(s):  
Mark D. Scheuerell
Keyword(s):  
Explicit Solution ◽  
Model Fitting ◽  
Maximum Sustainable Yield ◽  
Reference Points ◽  
Stock Size ◽  
Points Of Interest ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Explicit Formulae ◽  
Recruitment Model

Stock-recruitment models have been used for decades in fisheries management as a means of formalizing the expected number of offspring that recruit to a fishery based on the number of parents. In particular, Ricker’s stock recruitment model is widely used due to its flexibility and ease with which the parameters can be estimated. After model fitting, the spawning stock size that produces the maximum sustainable yield (SMSY) to a fishery, and the harvest corresponding to it (UMSY), are two of the most common biological reference points of interest to fisheries managers. However, to date there has been no explicit solution for either reference point because of the transcendental nature of the equation needed to solve for them. Therefore, numerical or statistical approximations have been used for more than 30 years. Here I provide explicit formulae for calculating bothSMSYandUMSYin terms of the productivity and density-dependent parameters of Ricker’s model.

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