Simplified Calculation of Optimum Spawning Stock Size from Ricker's Stock Recruitment Curve

1985 ◽  
Vol 42 (11) ◽  
pp. 1833-1834 ◽  
Author(s):  
Ray Hilborn
Keyword(s):  
Stochastic Variation ◽  
Simple Modification ◽  
Recruitment Curve ◽  
Stock Size ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Simplified Calculation

The optimum spawning stock size for a Ricker stock recruitment curve was shown to be accurately approximated by the equation Ps = Pr(0.5–0.07a) when 0 < a < 3. A simple modification was also shown to incorporate stochastic variation about the stock recruitment curve into calculations of optimum stock size.

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.

Improving the stock-recruitment relationship in Icelandic cod (Gadus morhua) by including age diversity of spawners

1998 ◽  
Vol 55 (6) ◽  
pp. 1372-1377 ◽  
Author(s):  
Gudrun Marteinsdottir ◽  
Kristjan Thorarinsson
Keyword(s):  
Gadus Morhua ◽  
Extended Period ◽  
Shannon Index ◽  
Age Composition ◽  
Stock Size ◽  
Age Diversity ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Mature Fish

The size of the Icelandic cod stock has been gradually declining since the middle of this century. Recruitment has been poor over an extended period of time and much below the long-term average since 1985. Except for the concurrent decrease in stock size and recruitment during this period, the stock size - recruitment relationship is weak. This relationship is improved by including the age composition of the spawning stock. Spawning stock age diversity in each year from 1955 to 1992 was estimated with the Shannon index using the number of mature fish in each age group. By including information on age composition, 31% of the total variation in recruitment was accounted for by the model with stock size, age diversity, and the interaction between the two, compared with less than 15% by single factor models of either age diversity or stock size. These results indicate that age diversity is an important component in stock-recruitment models and that one of the management goals for fish species should be to maintain high age diversity in the spawning stocks.

Effect of Assumptions about the Stock–Recruitment Relationship on a Lobster (Homarus gammarus) Stock Assessment

1986 ◽  
Vol 43 (11) ◽  
pp. 2353-2359 ◽  
Author(s):  
R. C. A. Bannister ◽  
J. T. Addison
Keyword(s):  
Carapace Length ◽  
Stock Assessment ◽  
Fishing Effort ◽  
Yield Curves ◽  
Recruitment Curve ◽  
Homarus Gammarus ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Yield Per Recruit ◽  
Marked Tendency

Stock assessment of the European lobster (Homarus gammarus) has involved yield per recruit analysis based on the established length cohort methodology of Jones (1974. ICES C.M. 1974/F:33; 1981. FAO Fish. Circ. 734) which assumes that recruitment to the fishery is independent of spawning stock. The Shepherd (1982. J. Cons. Int. Explor. Mer 40: 67–75) model has been used to simulate a range of assumed stock–recruitment relationships, and the resulting sensitivity analysis describes how these affect the relation between yield or biomass and four management variables, namely fishing mortality, minimum carapace length, maximum carapace length, and the capture or noncapture of egg-bearing females. Yield curves show a clear maximum with a marked tendency to stock collapse when fishing effort is high. For the range of simulations considered, the probability of an early recruit failure is greatest for asymptotic stock–recruitment curves, which generate yield curves with maxima at an effort substantially lower than the present level. Only with a highly overcompensatory stock–recruitment curve is there a case for increasing effort to maximise yield, but such a relationship tends to reduce the benefit of increasing minimum carapace length or of setting a maximum carapace length. The model predicts that the assumption made about the stock–recruitment relationship also has a marked effect on the results expected from a ban on the landing of egg-bearing females. Overall the results confirm the unsatisfactory prognosis of the yield per recruit model and emphasise the need to gain an understanding of the biological factors determining the shape of the lobster stock–recruitment curve.

Aspects of spawner-recruit relationships, with particular reference to crustacean stocks: A review

1993 ◽  
Vol 44 (4) ◽  
pp. 589 ◽  
Author(s):  
N Caputi
Keyword(s):  
Fisheries Management ◽  
Environmental Variables ◽  
Short Term ◽  
Stochastic Variation ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
The Impact ◽  
Western Australian ◽  
Crustacean Fisheries

The fundamental biological issue for fisheries management is undoubtedly the prevention of recruitment overfishing, i.e. to prevent the spawning stock from being depleted by fishing to a level where it significantly reduces the abundance of recruits. However, for many important fisheries, particularly crustacean fisheries, the stock-recruitment relationship (SRR) is not known. In many cases, research on recruitment has concentrated on short-term studies of recruitment processes to the exclusion of research into the SRR which requires development of long term databases. This paper examines techniques required to model the SRR, using case studies from Western Australian crustacean fisheries. Outlines of potential problems such as errors and biases in the measurement of stock and recruitment indices, the time series nature of the data, and lack of stationarity in the data, are given with possible solutions. Environmental effects, which can greatly influence the abundance of recruits, may need to be determined before the underlying SRR can be seen. Some of the advantages and possible disadvantages of incorporating environmental variables in the SRR are examined. A thorough assessment of SRRs also involves a study of the impact of fishing on the stock and the effect of stochastic variation using simulations. The evaluation of the SRR requires a multi-disciplinary approach which includes the fields of biology, environment, economics, population dynamics and statistics.

scholarly journals Extending process and understanding for the development of complex ecosystem models, with application to the Chatham Rise Atlantis model

2021 ◽  
Author(s):  
◽  
Vidette McGregor
Keyword(s):  
Population Dynamics ◽  
New Zealand ◽  
Species Interactions ◽  
Initial Conditions ◽  
Ecosystem Models ◽  
Recruitment Curve ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Species Groups ◽  
Oceanographic Variables

<p>The Chatham Rise is a highly productive deep-sea ecosystem that supports numerous substantial commercial fisheries, and is therefore a likely candidate for an ecosystem based approach to fisheries management in New Zealand. This thesis describes model construction, calibration and validation, for the first end-to-end ecosystem model of the Chatham Rise, New Zealand. The work extends beyond what has previously been done for validating such models, and explores uncertainty analyses through bootstrapping the oceanographic variables, perturbing the model's initial conditions, and analysing species interaction effects, with the results further analysed with respect to known data gaps. This enables the inclusion of uncertainty in simulated scenarios using the Chatham Rise Atlantis model, thus providing an envelope of results with which to analyse and understand the likely responses of the Chatham Rise ecosystem. The model was designed with 24 dynamic polygons, 5 water column depth bins, 55 species functional groups, and used 12-hour timesteps. The transfer of energy was tracked throughout the system using nitrogen as the model's main currency. The model simulated the system from 1900–2015, preceded by a 35 year burn-in period. The model produced very similar biomass trajectories in response to historical fishing to corresponding fisheries stock assessment models for key fisheries species. Population dynamics and system interactions were considered realistic with respect to growth rates, mortality rates, diets and species group interactions. The model was found to be generally stable under perturbations to the initial conditions, with lower trophic level species groups having the most variability. The specification of the Spawning Stock Recruitment curve was explored, as it relates to the multi-species and ecosystem models within which it is now applied. Close attention needs to be given to population dynamics specific to multi-species interactions such as predation-release, in particular the Spawning Stock Recruitment curve. Potentially misleading dynamics under predation-release were identified, and the simple solution of applying a cap to recruitment when biomass exceeds virgin levels was explored. The population dynamics of myctophids under fishing induced predation release were analysed with and without limiting recruitment to virgin levels. The effects were evident in several ecosystem indicators, suggesting unintentional mis-specification could lead to erroneous model results. It raises several questions around the specification of the Spawning Stock Recruitment relationship for multispecies models, and more generally, whether the concept of ‘virgin’ (or ‘unfished’) biomass should be reconsidered to reflect dynamic natural mortality and potentially changing unfished states. The model components that had knowledge gaps and were found to most likely to influence model results were the initial conditions, oceanographic variables, and the aggregate species groups ‘seabird’ and ‘cetacean other’. It is recommended that applications of the model, such as forecasting biomasses under various fishing regimes, should include alternatives that vary these components, and present appropriate levels of uncertainty in results. Initial conditions should be perturbed, with greater variability applied to species groups modelled as biomass-pools, and age-structured species groups that have little data available from the literature.</p>

Extending process and understanding for the development of complex ecosystem models, with application to the Chatham Rise Atlantis model

2021 ◽  
Author(s):  
◽  
Vidette McGregor
Keyword(s):  
Population Dynamics ◽  
New Zealand ◽  
Species Interactions ◽  
Initial Conditions ◽  
Ecosystem Models ◽  
Recruitment Curve ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Species Groups ◽  
Oceanographic Variables

<p>The Chatham Rise is a highly productive deep-sea ecosystem that supports numerous substantial commercial fisheries, and is therefore a likely candidate for an ecosystem based approach to fisheries management in New Zealand. This thesis describes model construction, calibration and validation, for the first end-to-end ecosystem model of the Chatham Rise, New Zealand. The work extends beyond what has previously been done for validating such models, and explores uncertainty analyses through bootstrapping the oceanographic variables, perturbing the model's initial conditions, and analysing species interaction effects, with the results further analysed with respect to known data gaps. This enables the inclusion of uncertainty in simulated scenarios using the Chatham Rise Atlantis model, thus providing an envelope of results with which to analyse and understand the likely responses of the Chatham Rise ecosystem. The model was designed with 24 dynamic polygons, 5 water column depth bins, 55 species functional groups, and used 12-hour timesteps. The transfer of energy was tracked throughout the system using nitrogen as the model's main currency. The model simulated the system from 1900–2015, preceded by a 35 year burn-in period. The model produced very similar biomass trajectories in response to historical fishing to corresponding fisheries stock assessment models for key fisheries species. Population dynamics and system interactions were considered realistic with respect to growth rates, mortality rates, diets and species group interactions. The model was found to be generally stable under perturbations to the initial conditions, with lower trophic level species groups having the most variability. The specification of the Spawning Stock Recruitment curve was explored, as it relates to the multi-species and ecosystem models within which it is now applied. Close attention needs to be given to population dynamics specific to multi-species interactions such as predation-release, in particular the Spawning Stock Recruitment curve. Potentially misleading dynamics under predation-release were identified, and the simple solution of applying a cap to recruitment when biomass exceeds virgin levels was explored. The population dynamics of myctophids under fishing induced predation release were analysed with and without limiting recruitment to virgin levels. The effects were evident in several ecosystem indicators, suggesting unintentional mis-specification could lead to erroneous model results. It raises several questions around the specification of the Spawning Stock Recruitment relationship for multispecies models, and more generally, whether the concept of ‘virgin’ (or ‘unfished’) biomass should be reconsidered to reflect dynamic natural mortality and potentially changing unfished states. The model components that had knowledge gaps and were found to most likely to influence model results were the initial conditions, oceanographic variables, and the aggregate species groups ‘seabird’ and ‘cetacean other’. It is recommended that applications of the model, such as forecasting biomasses under various fishing regimes, should include alternatives that vary these components, and present appropriate levels of uncertainty in results. Initial conditions should be perturbed, with greater variability applied to species groups modelled as biomass-pools, and age-structured species groups that have little data available from the literature.</p>

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.

Influence of Stream Flows and Stock Size on Recruitment of Arctic Grayling (Thymallus arcticus) in the Chena River, Alaska

1992 ◽  
Vol 49 (5) ◽  
pp. 1027-1034 ◽  
Author(s):  
Robert A. Clark
Keyword(s):  
Population Data ◽  
Time Frame ◽  
Alternative Analysis ◽  
Stream Flows ◽  
Stock Size ◽  
Theoretical Contribution ◽  
Arctic Grayling ◽  
Spawning Stock ◽  
Stock Recruitment ◽  
Thymallus Arcticus

The hypothesis that recruitment of Arctic grayling (Thymallus arcticus) in the Chena River is influenced by stream flows and stock size was tested using population data collected from 1976 through 1990. Recruitment may be influenced by stream flows during the initial weeks of life of Arctic grayling, namely during spawning, emergence, and the larval stage. Using correlation and regression analyses, stream flow during the time-frame was found to be a significant descriptor of variability in recruitment (r = −0.751, P = 0.005). Although stream flows were implicated in recruitment variation, creation of an environment-dependent, stock–recruitment model was not possible because estimates of measurement error were lacking, because of bias due to the relation between residuals and subsequent stock size, and because of the presumed autocorrelation of stock size. An alternative analysis was conducted to investigate the influence of stock size on recruitment when stream flows were thought to minimally affect recruitment. Using an estimate of natural mortality rate and assuming no fishing mortality, the theoretical contribution of recruits to the spawning stock exceeded the maximum observed stock size. I concluded that the maximum observed stock size failed to negatively influence recruitment, and the level of stock size that might influence recruitment is greater than the maximum observed stock size.

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