Impact of time-varying productivity on estimated stock–recruitment parameters and biological reference points

Models with time-varying parameters are increasingly being considered in the assessment of fish stocks, but their reliability when used to derive biological reference points or benchmarks has not been thoroughly evaluated. Here, we evaluated stock–recruitment models with and without time-varying productivity in a simulation framework for sockeye salmon (Oncorhynchus nerka) under different scenarios of productivity and exploitation. Ignoring trends in productivity led to overestimates of productivity and underestimates of capacity when both exploitation rates and productivity declined over time, resulting in an underestimation on average of benchmarks of biological status. Despite being less biased, time-varying models had relatively poor fit based on AICc and BIC model selection criteria. Our simulation results were compared with empirical analyses of 12 Fraser River sockeye salmon stocks in British Columbia, Canada. Although benchmarks were less biased when based on time-varying models, underlying true benchmarks based on spawner abundances at maximum sustainable yield, SMSY, trend downwards when productivity declines, which may not be aligned with conservation objectives. We conclude with best practices when adapting biological benchmarks to time-varying productivity.

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

ICES Journal of Marine Science ◽

10.1093/icesjms/fsu022 ◽

2014 ◽

Vol 72 (1) ◽

pp. 111-116 ◽

Cited By ~ 14

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.

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

ICES Journal of Marine Science ◽

10.1093/icesjms/fst105 ◽

2013 ◽

Vol 70 (6) ◽

pp. 1075-1080 ◽

Cited By ~ 6

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.

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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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Optimal F0.1 Criteria and Their Relationship to Maximum Sustainable Yield

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f87-335 ◽

1987 ◽

Vol 44 (S2) ◽

pp. s339-s348 ◽

Cited By ~ 56

Author(s):

R. B. Deriso

Keyword(s):

Quantitative Relationship ◽

Maximum Sustainable Yield ◽

Sustainable Yield ◽

Fish Stocks ◽

Pacific Halibut ◽

Western Lake ◽

Gadus Macrocephalus ◽

Hippoglossus Stenolepis ◽

Stock Recruitment ◽

Yield Per Recruit

There is a unique size of entry into the fishable population that maximizes yield per recruit when an F0.1 fishing criterion is applied to the simple theory of fishing developed by Beverton and Holt in 1957. I define such a pair of parameters (size of entry, F0.1 value) to be the optimal F0.1 criteria and show that they are characterized by the single quantity M/K. A quantitative relationship is established between maximum sustainable yield and the optimal F0.1 criteria for a model population where recruitment is governed by a Ricker stock–recruitment function. This new theory is applied to three fish stocks: Pacific halibut (Hippoglossus stenolepis), western Lake Erie walleye (Stizostedion vitreum vitreum), and Bering Sea Pacific cod (Gadus macrocephalus).

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Incorporating natural variability in biological reference points and population dynamics into management of Atlantic salmon (Salmo salar L.) stocks returning to home waters

ICES Journal of Marine Science ◽

10.1093/icesjms/fsw015 ◽

2016 ◽

Vol 73 (6) ◽

pp. 1513-1524 ◽

Cited By ~ 4

Author(s):

Jonathan White ◽

Niall Ó Maoiléidigh ◽

Paddy Gargan ◽

Elvira de Eyto ◽

Gerald Chaput ◽

...

Keyword(s):

Atlantic Salmon ◽

Sampling Error ◽

Specific Weight ◽

Maximum Sustainable Yield ◽

Natural Variability ◽

Reference Points ◽

Major Development ◽

Stock Assessments ◽

Population Structures ◽

Stock Recruitment

Following advice from the International Council for the Exploration of the Seas and North Atlantic Salmon Conservation Organization, Irish salmon stocks have been managed on a river-by-river basis since 2007 with biological reference points (BRPs) based on maximum sustainable yield (MSY). A method for estimating BRPs at the river scale and the associated variability arising from observed variability in population structures and fecundities is presented here. Calculations of BRPs (referred to as conservation limits, CLs) were updated and their natural variability was included. Angling logbooks provided new river-specific weight data to give sea age and fecundity ranges, and improved estimates of river-wetted areas, to account for available nursery habitat for juveniles and river-specific carrying capacities, were introduced. To transport BRPs, Bayesian stock–recruitment analysis was re-run with an updated list of monitored rivers and smolt ages. Results were converted to salmon numbers per river in Monte Carlo simulations incorporating the variability in sea ages and fecundities. Minimum sample size rules were implemented to reduce sampling error effects. Results showed that average total CL increased by 7%, average one sea-winter (1SW) CL decreased by 5% and average multi-sea-winter (MSW) CL increased by 157%. Differences were attributed to increases in wetted areas, MSW proportions, and changes in both 1SW and MSW fecundities. While some changes were large, we believe that these updated CLs provide more accurate estimates and with associated confidence limits they are more robust, river-specific, and readily incorporated into stock assessments. As a significant improvement on their predecessors, they represent a major development for the conservation and management of salmon stocks. Additionally, the approach described is portable across stocks and has the potential to be implemented in other jurisdictions to improve the management of Atlantic salmon. Finally, this method of incorporating variation has application for the development of BRPs and management of other species.

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Use of the Kalman filter to reconstruct historical trends in productivity of Bristol Bay sockeye salmon (Oncorhynchus nerka)

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f03-069 ◽

2003 ◽

Vol 60 (7) ◽

pp. 809-824 ◽

Cited By ~ 58

Author(s):

Randall M Peterman ◽

Brian J Pyper ◽

Brice W MacGregor

Keyword(s):

Kalman Filter ◽

Sockeye Salmon ◽

Oncorhynchus Nerka ◽

Time Varying ◽

Historical Trends ◽

Bristol Bay ◽

Fish Stocks ◽

The Past ◽

Better Than

Fisheries scientists and managers are concerned about potential long-term, persistent changes in productivity of fish stocks that might result from future climatic changes or other alterations in aquatic systems. However, because of large natural variability and measurement error in fisheries data, such changes are usually difficult to detect until long after they occur. Previous research using numerous Monte Carlo simulation trials showed that a Kalman filter performed better than standard estimation techniques in detecting such trends in a timely manner. Therefore, we used historical data along with a Kalman filter that included a time-varying Ricker a parameter to reconstruct changes in productivity (recruits per spawner at a given spawner abundance) of eight Bristol Bay, Alaska, sockeye salmon (Oncorhynchus nerka) stocks over the past 40 years. Productivity generally increased for most stocks but varied widely for others and dramatically decreased in another. Such large changes in productivity are important for management. They greatly affected optimal spawner abundances and optimal exploitation rates, suggesting that in the future, scientists should consider using models with time-varying productivity parameters.

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Challenges to fisheries advice and management due to stock recovery

ICES Journal of Marine Science ◽

10.1093/icesjms/fsy084 ◽

2018 ◽

Vol 75 (6) ◽

pp. 1864-1870 ◽

Cited By ~ 7

Author(s):

Rob van Gemert ◽

Ken H Andersen

Keyword(s):

Maximum Sustainable Yield ◽

Reference Points ◽

Forage Fish ◽

Fish Stocks ◽

Density Dependent ◽

Piscivorous Fish ◽

Predation Mortality ◽

Management Procedures ◽

Dependent Growth ◽

New Situation

Abstract During the 20th century, many large-bodied fish stocks suffered from unsustainable fishing pressure. Now, signs of recovery are appearing among previously overfished large-bodied fish stocks. This new situation raises the question of whether current fisheries advice and management procedures, which were devised and optimized for depleted stocks, are well-suited for the management of recovered stocks. We highlight two challenges for fisheries advice and management: First, recovered stocks are more likely to show density-dependent growth. We show how the appearance of density-dependent growth will make reference points calculated with current procedures inaccurate. Optimal exploitation of recovered large-bodied fish stocks will therefore require accounting for density-dependent growth. Second, we show how a biomass increase of large-bodied piscivorous fish will lead to a reverse trophic cascade, where their increased predation mortality on forage fish reduces forage fish productivity and abundance. The resulting decrease in maximum sustainable yield of forage fish stocks could lead to conflicts between forage and large-piscivore fisheries. Avoiding such conflicts requires that choices are made between the exploitation of interacting fish stocks. Failure to account for the changed ecological state of recovered stocks risks creating new obstacles to sustainable fisheries management.

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Status and targets for rebuilding the three major fish stocks in Lake Victoria

10.1101/2020.10.26.354639 ◽

2020 ◽

Author(s):

Laban Musinguzi ◽

Mark Olokotum ◽

Vianny Natugonza

Keyword(s):

Fisheries Management ◽

Nile Tilapia ◽

Lake Victoria ◽

Maximum Sustainable Yield ◽

Reference Points ◽

Nile Perch ◽

Fish Stocks ◽

Illegal Fishing ◽

Stock Status ◽

Low Levels

AbstractWe determined fisheries management reference points for three major fish stocks in Lake Victoria (Nile tilapia, Nile perch and Dagaa) for Uganda and the whole lake. The aim was to ascertain stock status and define reasonable objectives and targets for rebuilding to sustainable levels. Dagaa was found to be healthy in Uganda and the whole lake but tending to overfished status. In Uganda, the stock status of Nile tilapia and Nile perch was recruitment impaired but tending more towards collapsed and overfished status respectively. In the whole lake, the stock status of Nile tilapia and Nile perch was collapsed and overfished respectively with the latter tending more towards recruitment impaired. Estimates of maximum sustainable yield (MSY) showed that catches could be increased under good management. Rebuilding the Nile tilapia and Nile perch stock biomasses to MSY level (Bmsy) could respectively increase the catches above the current level by 9.2% and 29.5% in Uganda and by 72.8% and 15.1% in the whole lake. The immediate objective for fisheries management should be to rebuild biomass for the Nile tilapia and Nile perch stocks to Bmsy. Elimination of illegal fishing practices has proved to be effective. In addition, management needs to keep catches at low levels until biomass for the stocks is ≥Bmsy for at least three consecutive years.

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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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Implications of late-in-life density-dependent growth for fishery size-at-entry leading to maximum sustainable yield

ICES Journal of Marine Science ◽

10.1093/icesjms/fsx236 ◽

2018 ◽

Vol 75 (4) ◽

pp. 1296-1305 ◽

Cited By ~ 8

Author(s):

Rob van Gemert ◽

Ken H Andersen

Keyword(s):

Density Dependence ◽

Maximum Sustainable Yield ◽

Sustainable Yield ◽

Fish Stocks ◽

Density Dependent ◽

Large Size ◽

Adult Growth ◽

Stock Assessments ◽

Stock Recruitment ◽

Dependent Growth

Abstract Currently applied fisheries models and stock assessments rely on the assumption that density-dependent regulation only affects processes early in life, as described by stock–recruitment relationships. However, many fish stocks also experience density-dependent processes late in life, such as density-dependent adult growth. Theoretical studies have found that, for stocks which experience strong late-in-life density dependence, maximum sustainable yield (MSY) is obtained with a small fishery size-at-entry that also targets juveniles. This goes against common fisheries advice, which dictates that primarily adults should be fished. This study aims to examine whether the strength of density-dependent growth in actual fish stocks is sufficiently strong to reduce optimal fishery size-at-entry to below size-at-maturity. A size-structured model is fitted to three stocks that have shown indications of late-in-life density-dependent growth: North Sea plaice (Pleuronectes platessa), Northeast Atlantic (NEA) mackerel (Scomber scombrus), and Baltic sprat (Sprattus sprattus balticus). For all stocks, the model predicts exploitation at MSY with a large size-at-entry into the fishery, indicating that late-in-life density dependence in fish stocks is generally not strong enough to warrant the targeting of juveniles. This result lends credibility to the practise of predominantly targeting adults in spite of the presence of late-in-life density-dependent growth.

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