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

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

PeerJ ◽

10.7717/peerj.1623 ◽

2016 ◽

Vol 4 ◽

pp. e1623 ◽

Cited By ~ 6

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

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f98-035 ◽

1998 ◽

Vol 55 (6) ◽

pp. 1372-1377 ◽

Cited By ~ 118

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.

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

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f85-230 ◽

1985 ◽

Vol 42 (11) ◽

pp. 1833-1834 ◽

Cited By ~ 27

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.

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Peer Review #2 of "An explicit solution for calculating optimum spawning stock size from Ricker’s stock recruitment model (v0.1)"

10.7287/peerj.1623v0.1/reviews/2 ◽

2016 ◽

Author(s):

B Kennedy

Keyword(s):

Peer Review ◽

Explicit Solution ◽

Stock Size ◽

Spawning Stock ◽

Stock Recruitment ◽

Recruitment Model

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

10.7287/peerj.preprints.1394v1 ◽

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.

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