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.

scholarly journals An explicit solution for calculating optimum spawning stock size from Ricker's stock recruitment curve

2015 ◽  
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

Ricker’s stock recruitment model is widely used to describe the spawner-offspring relationship for fishes. After model fitting, the spawning stock size that produces the maximum sustainable yield (SMSY), 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 both SMSY and UMSY in terms of the productivity and density-dependent parameters from Ricker’s model.

scholarly journals An explicit solution for calculating optimum spawning stock size from Ricker's stock recruitment curve

2015 ◽  
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

Ricker’s stock recruitment model is widely used to describe the spawner-offspring relationship for fishes. After model fitting, the spawning stock size that produces the maximum sustainable yield (SMSY), 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 both SMSY and UMSY in terms of the productivity and density-dependent parameters from Ricker’s model.

The estimation and robustness of FMSY and alternative fishing mortality reference points associated with high long-term yield

2012 ◽  
Vol 69 (9) ◽  
pp. 1468-1480 ◽  
Author(s):  
Jan Horbowy ◽  
Anna Luzeńczyk
Keyword(s):  
Total Yield ◽  
Reference Points ◽  
Superior Performance ◽  
Equilibrium Yield ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Yield Per Recruit ◽  
Different Sources ◽  
Recruitment Model

Equations for equilibrium yield and biomass are presented and used to derive FMSY and alternative reference points (ARPs). ARPs are analogues of the traditional points based on yield-per-recruit (YPR) or spawning stock-per-recruit (SPR) (F0.1, F40%, F50%), but refer to the equilibrium total yield or biomass. The method combines YPR and SPR analysis with stock–recruitment relationships. The sensitivity of FMSY and ARPs to the range of available stock–recruitment data, recruitment variance, various steepness levels in the stock–recruitment models, assessment variance, and bias are tested. The analysis showed that in most cases, F40%B and F50%B, defined by the equilibrium biomass (B), were the most robust relative to the different sources of uncertainty. However, in the case of the misspecification of the stock–recruitment relationship, FMSY showed superior performance. F40%B for the Beverton and Holt stock–recruitment model and F50%B for the Ricker recruitment model can be recommended as conservative fishing mortalities associated with high long-term yield. For the considered steepness, they produced yield up to 5%–10% lower than yield at FMSY.

scholarly journals Fitting a non-parametric stock–recruitment model in R that is useful for deriving MSY reference points and accounting for model uncertainty

2012 ◽  
Vol 70 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Noel G. Cadigan
Keyword(s):  
Confidence Intervals ◽  
Model Uncertainty ◽  
Fishery Management ◽  
Reference Points ◽  
Parametric Models ◽  
Parametric Approach ◽  
Stock Size ◽  
Stock Recruitment ◽  
Recruitment Model ◽  
Non Parametric

Abstract Cadigan, N. G. 2013. Fitting a non-parametric stock–recruitment model in R that is useful for deriving MSY reference points and accounting for model uncertainty. – ICES Journal of Marine Science, 70:56–67. Modelling the relationship between parental stock size and subsequent recruitment of fish to a fishery is often required when deriving reference points, which are a fundamental component of fishery management. A non-parametric approach to estimate stock–recruitment relationships is illustrated using a simulated example and nine case studies. The approach preserves compensatory density dependence in which the recruitment rate monotonically decreases as stock size increases, which is a basic assumption of commonly used parametric stock–recruitment models. The implications of the non-parametric estimates on maximum sustainable yield (MSY) reference points are illustrated. The approach is used to provide non-parametric bootstrapped confidence intervals for reference points. The efficacy of the approach is investigated using simulations. The results demonstrate that the non-parametric approach can provide a more realistic estimation of the stock–recruitment relationship when informative data are available compared with common parametric models. Also, bootstrap confidence intervals for MSY reference points based on different parametric stock–recruitment models often do not overlap. The confidence intervals based on the non-parametric approach tend to be much wider, and reflect better uncertainty due to stock–recruit model choice.

scholarly journals Quirky patterns in time-series of estimates of recruitment could be artefacts

2014 ◽  
Vol 72 (1) ◽  
pp. 111-116 ◽  
Author(s):  
M. Dickey-Collas ◽  
N. T. Hintzen ◽  
R. D. M. Nash ◽  
P-J. Schön ◽  
M. R. Payne
Keyword(s):  
Time Series ◽  
Stock Assessment ◽  
Meta Analysis ◽  
Reference Points ◽  
Fish Stocks ◽  
Stock Recruitment ◽  
Modelling Assumptions ◽  
Meta Analyses ◽  
Recruitment Model ◽  
Recruitment Time

Abstract The accessibility of databases of global or regional stock assessment outputs is leading to an increase in meta-analysis of the dynamics of fish stocks. In most of these analyses, each of the time-series is generally assumed to be directly comparable. However, the approach to stock assessment employed, and the associated modelling assumptions, can have an important influence on the characteristics of each time-series. We explore this idea by investigating recruitment time-series with three different recruitment parameterizations: a stock–recruitment model, a random-walk time-series model, and non-parametric “free” estimation of recruitment. We show that the recruitment time-series is sensitive to model assumptions and this can impact reference points in management, the perception of variability in recruitment and thus undermine meta-analyses. The assumption of the direct comparability of recruitment time-series in databases is therefore not consistent across or within species and stocks. Caution is therefore required as perhaps the characteristics of the time-series of stock dynamics may be determined by the model used to generate them, rather than underlying ecological phenomena. This is especially true when information about cohort abundance is noisy or lacking.

scholarly journals Can stock–recruitment points determine which spawning potential ratio is the best proxy for maximum sustainable yield reference points?

2013 ◽  
Vol 70 (6) ◽  
pp. 1075-1080 ◽  
Author(s):  
Christopher M. Legault ◽  
Elizabeth N. Brooks
Keyword(s):  
Life History ◽  
Mortality Rate ◽  
Maximum Sustainable Yield ◽  
Reference Points ◽  
Sustainable Yield ◽  
Marine Science ◽  
Fishing Mortality ◽  
Scatter Plots ◽  
Stock Recruitment ◽  
Spawning Potential Ratio

Abstract Legault, C. M., and Brooks, E. N. 2013. Can stock–recruitment points determine which spawning potential ratio is the best proxy for maximum sustainable yield reference points? – ICES Journal of Marine Science, 70: 1075–1080. The approach of examining scatter plots of stock–recruitment (S–R) estimates to determine appropriate spawning potential ratio (SPR)-based proxies for FMSY was investigated through simulation. As originally proposed, the approach assumed that points above a replacement line indicate year classes that produced a surplus of spawners, while points below that line failed to achieve replacement. In practice, this has been implemented by determining Fmed, the fishing mortality rate that produces a replacement line with 50% of the points above and 50% below the line. A new variation on this approach suggests FMSY proxies can be determined by examining the distribution of S–R points that are above or below replacement lines associated with specific SPRs. Through both analytical calculations and stochastic results, we demonstrate that this approach is fundamentally flawed and that in some cases the inference is diametrically opposed to the method's intended purpose. We reject this approach as a tool for determining FMSY proxies. We recommend that the current proxy of F40% be maintained as appropriate for a typical groundfish life history.

Recruitment variation in abalone: Its importance to fisheries management

1995 ◽  
Vol 46 (3) ◽  
pp. 555 ◽  
Author(s):  
PE McShane
Keyword(s):  
Egg Production ◽  
Field Experiments ◽  
Stock Assessment ◽  
Reference Points ◽  
High Fecundity ◽  
Spatial And Temporal Scales ◽  
Recruitment Failure ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Many Sources

Recruitment failure has been implicated in the decline of several abalone fisheries. Traditionally, fisheries scientists invoke theoretical stock-recruitment relationships to predict trends in abundance of an exploited stock under various harvest regimes. The empirical evidence in support of a positive relationship between spawning stock and recruits is not strong. A further problem in interpretation of such relationships is that both 'stock' and 'recruitment' have various definitions in fisheries and ecological literature. The definition of a stock for abalone is not clear. As emphasized in this review, which considers each stage in the life history of abalone, the abundance of spawners is one of many sources of variation in recruitment. The evidence for invertebrates, particularly those with high fecundity, is that recruitment varies independently of the abundance of spawners. This is also the case for abalone, where recruits have been measured as the density of immediate post-settlement individuals, juveniles, or as adults entering the exploitable stock. A problem with stock-recruitment hypotheses is that they have intuitive appeal. It is considered 'dangerous' to manage fisheries under the assumption that a reduction in the number of spawners by fishing will not affect recruitment. Such danger to abalone stocks has been more recently assessed by egg-per-recruit analyses, whereby various harvest strategies are examined relative to reference points for egg production. These studies are reviewed and assessed relative to the often conflicting aims of managers and scientists. This review of studies of recruitment variation in abalone emphasizes the need for a more rigorous, autecological approach to stock assessment in which field experiments are conducted over realistic spatial and temporal scales, permitting robust testing of hypotheses.

scholarly journals Delay in fishery management: diminished yield, longer rebuilding, and increased probability of stock collapse1

2006 ◽  
Vol 64 (1) ◽  
pp. 149-159 ◽  
Author(s):  
Kyle W. Shertzer ◽  
Michael H. Prager
Keyword(s):  
Fishery Management ◽  
Economic Loss ◽  
Maximum Sustainable Yield ◽  
Sustainable Yield ◽  
Short Term ◽  
Stock Status ◽  
Stock Biomass ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Stock Collapse

Abstract Shertzer, K. W., and Prager, M. H. 2007. Delay in fishery management: diminished yield, longer rebuilding, and increased probability of stock collapse. ICES Journal of Marine Science, 64: 149–159. When a stock is depleted, catch reductions are in order, but typically they are implemented only after considerable delay. Delay occurs because fishery management is political, and stricter management, which involves short-term economic loss, is unpopular. Informed of stock decline, managers often hesitate, perhaps pondering the uncertainty of scientific advice, perhaps hoping that a good year class will render action moot. However, management delay itself can have significant costs, when it exacerbates stock decline. To examine the biological consequences of delay, we simulated a spectrum of fisheries under various degrees of delay in management. Increased delay required larger catch reductions, for more years, to recover benchmark stock status (here, spawning-stock biomass at maximum sustainable yield). Management delay caused stock collapse most often under two conditions: (1) when the stock–recruitment relationship was depensatory, or (2) when catchability, unknown to the assessment, was density-dependent and fishing took juveniles. In contrast, prompt management resulted in quicker recoveries and higher cumulative yields from simulated fisheries. Benefits to stock biomass and fishery yield can be high from implementing management promptly.

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