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Cited by 24Marine and fisheries researchMathematical and Theoretical Epidemiology and Ecology ModelsFish Ecology and Management Studies

Steepness is a slippery slope

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Miller, Timothy J., Brooks, Elizabeth N.·2021·Fish and Fisheries
DOI 10.1111/faf.12534
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Abstract

The Beverton–Holt and Ricker stock‐recruit functions were derived in terms of two pre‐recruit mortality parameters. Mace, & Doonan, (1988, A generalized bioeconomic simulation model for fish population dynamics) reparameterized the stock‐recruit function in terms of steepness, which combines pre‐recruit mortality with post‐recruit biological parameters defining unfished spawning biomass per recruit. Their parameterization explicitly assumes a stable age distribution at unexploited conditions, but also implicitly assumes that unexploited spawning biomass per recruit is time invariant. Temporal variation could occur in either pre‐recruit mortality rates or post‐recruit biological parameters, but different dynamics are produced. The former results in variation in both the stock‐recruit curve and the population equilibria, whereas variation in the latter only changes the points of equilibria on the curve. Thus, variation in either pre‐ or post‐recruit parameters will result in variation in steepness, maximum sustainable yield and associated management reference points. Empirical measures of components of post‐recruit productivity (maturity and mass at age, e.g.) are available for many managed fish stocks and often exhibit temporal variability. Yet use of the steepness parameterization requires an analyst to specify one set of post‐recruit biological parameters to define unexploited spawning biomass per recruit for the full time series. This misspecification leads to misperception of biological reference points and has implications for meta‐analyses of steepness, and interpretation of the dynamic concept. Returning to the original parameterization allows the isolation of any temporal or inter‐population variation in pre‐ and post‐recruit productivity and reduces the potential for mechanistic bias in stock‐recruit parameters.

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  • In the Beverton-Holt function, α is mainly linked to density-dependent mortality rates, whereas β pertains to mortality caused by external (density-independent) factors such as temperature, wind, currents, and food availability.

    “The parameters α and β are related to two types of mortality: α is mainly linked to density-dependent mortality rates, whereas β pertains to the mortality caused by external (or density-independent) factors, such as temperature, wind, currents, and food availability (Beverton and Holt, 1957; Miller and Brooks, 2021).”

    From Impacts of phytoplankton availability on bigeye tuna (Thunnus obesus) recruitment in the Indian Ocean (2024) · cites this paper as Miller and Brooks, 2021

    Section 2 assigns the mortality relationships in the opposite direction: the Beverton–Holt term governing recruitment at zero spawning biomass depends on density-independent mortality, while the second term includes density-dependent mortality and also depends on the first. The paper does not give temperature, wind, currents, or food availability as examples of factors governing β in this passage. Page numbers are unavailable in our copy. (LLM, conf=0.90)

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  • The Beverton-Holt stock-recruitment function describes the relationship between recruit abundance and spawning biomass of the stock.

    “The B–H stock–recruitment function describes the relationship between the recruit abundance and the spawning biomass of the stock (Miller and Brooks, 2021).”

    From Impacts of phytoplankton availability on bigeye tuna (Thunnus obesus) recruitment in the Indian Ocean (2024) · cites this paper as Miller and Brooks, 2021

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Research works printed but not linked: 39

  1. A'mar, Z. T., Punt, A. E., & Dorn, M. W. (2009). The evaluation of two management strategies for the Gulf of Alaska walleye pollock fishery under climate change. ICES Journal of Marine Science, 66(7), 1614- 1632. https://doi.org/10.1093/icesj ms/fsp044 · DOI
  2. Barneche, D. R., Robertson, D. R., White, C. R., & Marshall, D. J. (2018). Fish reproductive energy output increases disproportionately with body size. Science, 360, 642-645. https://doi.org/10.1126/scien ce.aao6868 · DOI
  3. Berger, A. M. (2019). Character of temporal variability in stock productiv- ity inuences the utility of dynamic reference points. Fisheries Research, 217, 185-197. https://doi.org/10.1016/j.fishr es.2018.11.028 · DOI
  4. Brooks, E. N. (2013). Effects of variable reproductive potential on refer- ence points for fisheries management. Fisheries Research, 138, 152- 158. https://doi.org/10.1016/j.fishr es.2012.06.003 · DOI
  5. Brooks, E. N., & Deroba, J. J. (2015). When \data" are not data: The pit- falls of post-hoc analyses that use stock assessment model output. Canadian Journal of Fisheries and Aquatic Sciences, 72(4), 634-641. https://doi.org/10.1139/cjfas -2014-0231 · DOI
  6. Brooks, E. N., & Powers, J. E. (2007). Generalized compensation in stock- recruit functions: Properties and implications for management. ICES Journal of Marine Science, 64(3), 413-424. https://doi.org/10.1093/ icesj ms/fsl046 · DOI
  7. Brooks, E. N., Thorson, J. T., Shertzer, K. W., Nash, R. D., Brodziak, J. K., Johnson, K. F., Klibansky, N., Wells, B. K., & White, J. (2019). Paulik revisited: Statistical framework and estimation perfor- mance of multistage recruitment functions. Fisheries Research, 217, 58-70.recruitment: Theory, Estimation, and Application in Fishery Stock Assessment Models. https://doi.org/10.1016/j.fishr es.2018.06.018 · DOI
  8. de Valpine, P., & Hastings, A. (2002). Fitting population models incorporat- ing process noise and observation error. Ecological Monographs, 72(1), 57-76. https://doi.org/10.1890/0012-9615(2002)072[0057:FPMIP N]2.0.CO;2 · DOI
  9. Dorn, M. W. (2002). Advice on west coast rock fish harvest rates from bayesian meta-analysis of stock{recruit relationships. North American Journal of Fisheries Management, 22(1), 280-300. https://doi. org/10.1577/1548-8675(2002)022<0280:AOWCR H>2.0.CO;2 · DOI
  10. Forrest, R. E., McAllister, M. K., Dorn, M. W., Martell, S. J. D., & Stanley, R. D. (2010). Hierarchical Bayesian estimation of recruitment param- eters and reference points for Pacific rockfishes (Sebastes spp.) under alternative assumptions about the stock-recruit function. Canadian Journal of Fisheries and Aquatic Sciences, 67(10), 1611-1634. https:// doi.org/10.1139/F10-077 · DOI
  11. Francis, R. I. C. C. (1992). Use of risk analysis to assess fishery manage- ment strategies: A case study using orange roughy (Hoplostethus atlanticus) on the Chatham Rise, New Zealand. Canadian Journal of Fisheries and Aquatic Sciences, 49(5), 922-930. https://doi. org/10.1139/f92-102 · DOI
  12. Green, B. S. (2008). Maternal effects in fish populations. Advances in Marine Biology, 54(489), 1-105.
  13. Hixon, M. A., Johnson, D. W., & Sogard, S. M. (2014). BOFFFFs: On the importance of conserving old-growth age structure in fishery popu- lations. ICES Journal of Marine Science, 71(8), 2171-2185. https://doi. org/10.1093/icesj ms/fst200 · DOI
  14. Lee, H.-H., Maunder, M. N., Piner, K. R., & Methot, R. D. (2012). Can steepness of the stockrecruitment relationship be estimated in fishery stock assessment models? Fisheries Research, 125-126(1), 254-261. https://doi.org/10.1016/j.fishr es.2012.03.001 · DOI
  15. Legault, C. M., & Palmer, M. C. (2016). In what direction should the fish- ing mortality target change when natural mortality increases within an assessment? Canadian Journal of Fisheries and Aquatic Sciences, 73(3), 349-357. https://doi.org/10.1139/cjfas -2015-0232 · DOI
  16. Liermann, M., & Hilborn, R. (1997). Depensation in fish stocks: A hier- archical Baysian meta-analysis. Canadian Journal of Fisheries and Aquatic Sciences, 54(9), 1976-1984. https://doi.org/10.1139/f97-105 · DOI
  17. MacCall, A. D., Klingbeil, R. A., & Methot, R. D. (1985). Recent increased abundance and potential productivity of Pacific mackerel (Scomber ja- ponicas). CalCOFI Report 26, La Jolla, CA, pp. 119-129.
  18. Mantzouni, I., Sørensen, H., O'Hara, R. B., & MacKenzie, B. R. (2010). Hierarchical modelling of temperature and habitat size effects on population dynamics of North Atlantic cod. ICES Journal of Marine Science, 67(5), 833-855. https://doi.org/10.1093/icesj ms/fsp291 · DOI
  19. Marshall, D. J., Allen, R. M., & Crean, A. J. (2008). The ecological and evo- lutionary importance of maternal effects in the sea. Oceanography and Marine Biology: An Annual Review, 46, 203-350.
  20. Methot, R. D., & Wetzel, C. R. (2013). Stock synthesis: A biological and statistical framework for fish stock assessment and fishery manage- ment. Fisheries Research, 142, 86-99. https://doi.org/10.1016/j.fishr es.2012.10.012 · DOI
  21. Michielsens, C. G. J., & McAllister, M. K. (2004). A Bayesian hierarchical analysis of stock recruit data: Quantifying structural and parame- ter uncertainties. Canadian Journal of Fisheries and Aquatic Sciences, 61(6), 1032-1047. https://doi.org/10.1139/f04-048 · DOI
  22. Miller, T. J., Hare, J. A., & Alade, L. (2016). A state-space approach to incor- porating environmental effects on recruitment in an age-structured assessment model with an application to Southern New England yellowtail ounder. Canadian Journal of Fisheries and Aquatic Sciences, 73(8), 1261-1270. https://doi.org/10.1139/cjfas -2015-0339 · DOI · Paper page
  23. Miller, T. J., O'Brien, L., & Fratantoni, P. S. (2018). Temporal and envi- ronmental variation in growth and maturity and effects on man- agement reference points of Georges Bank Atlantic cod. Canadian Journal of Fisheries and Aquatic Sciences, 75(12), 2159-2171. https:// doi.org/10.1139/cjfas -2017-0124 · DOI
  24. Myers, R. A. (2001). Stock and recruitment: Generalizations about max- imum reproductive rate, density dependence, and variability using meta-analytic approaches. ICES Journal of Marine Science, 58(5), 937- 951. https://doi.org/10.1006/jmsc.2001.1109 · DOI
  25. Myers, R. A., & Barrowman, N. J. (1996). Is fish recruitment related to spawner abundance? Fishery Bulletin, 94(4), 707-724.
  26. Myers, R. A., Bowen, K. G., & Barrowman, N. J. (1999). Maximum re- productive rate of fish at low population sizes. Canadian Journal of Fisheries and Aquatic Sciences, 56(12), 2404-2419. https://doi. org/10.1139/f99-201 · DOI
  27. Needle, C. L. (2001). Recruitment models: Diagnosis and progno- sis. Reviews in Fish Biology and Fisheries, 11(2), 95-111. https://doi. org/10.1023/A:10152 08017674 · DOI
  28. O'Leary, C. A., Thorson, J. T., Miller, T. J., & Nye, J. A. (2020). Comparison of multiple approaches to calculate time-varying biological reference points in climate-linked population-dynamics models. ICES Journal of Marine Science, 77(3), 930-941. https://doi.org/10.1093/icesj ms/ fsz215 · DOI
  29. Powers, J. E. (2014). Age-specific natural mortality rates in stock as- sessments: Size based vs. density-dependent. ICES Journal of Marine Science, 71(7), 1629-1637. https://doi.org/10.1093/icesj ms/fst226 · DOI
  30. Pulkkinen, H., & Mantyniemi, S. (2013). Maximum survival of eggs as the key parameter of stock-recruit meta-analysis: Accounting for parameter and structural uncertainty. Canadian Journal of Fisheries and Aquatic Sciences, 70(4), 527-533. https://doi.org/10.1139/cjfas -2012-0268 · DOI
  31. Punt, A. E., Smith, D. C., & Smith, A. D. M. (2011). Among-stock com- parisons for improving stock assessments of data-poor stocks: The \Robin Hood" approach. ICES Journal of Marine Science, 68(5), 972- 981. https://doi.org/10.1093/icesj ms/fsr039 · DOI
  32. Quinn, T. J., & Deriso, R. B. (1999). Quantitative Fish Dynamics (p. 542). Oxford University Press.
  33. Ricker, W. E. (1954). Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11(5), 559-623. https://doi.org/10.1139/ f54-039 · DOI
  34. Ricker, W. E. (1975). Computation and interpretation of biological sta- tistics of fish populations. Bulletin of the Fisheries Research Board of Canada, Number 119, 382 p.
  35. Stock, B. C., Miller, T. J. (In review). The Woods Hole assessment model (WHAM): A general state-space assessment framework that incor- porates time-and age-varying processes via random effects and links to environmental covariates. Fisheries Research.
  36. Szuwalski, C. S., Vert-Pre, K. A., Punt, A. E., Branch, T. A., & Hilborn, R. (2015). Examining common assumptions about recruitment: A meta- analysis of recruitment dynamics for worldwide marine fisheries. Fish and Fisheries, 16(4), 633-648. https://doi.org/10.1111/faf.12083 · DOI
  37. Thorson, J. T., Cope, J. M., Kleisner, K. M., Samhouri, J. F., Shelton, A. O., & Ward, E. J. (2015). Giants' shoulders 15 years later: Lessons, chal- lenges and guidelines in fisheries meta-analysis. Fish and Fisheries, 16(2), 342-361. https://doi.org/10.1111/faf.12061 · DOI
  38. Trippel, E. A., Kjesbu, O. S., & Solemdal, P. (1997). Effects of adult age and size structure on reproductive output in marine fishes (pp. 31-62). Springer.
  39. Xu, H., Miller, T. J., Hameed, S., Alade, L. A., & Nye, J. A. (2018). Evaluating the utility of the Gulf Stream Index for predicting recruitment of Southern New England-Mid Atlantic yellowtail ounder. Fisheries Oceanography, 27(1), 85-95. https://doi.org/10.1111/fog.12236 · DOI

Cited by

Sorted by citations

Authors
Miller, T. J., & Brooks, E. N.
Affiliations
NOAA National Marine Fisheries Service (US)
Corresponding author
Miller, Timothy J.
ORCID
Venue
Fish and Fisheries
Publisher
Wiley
Published
2021-02-08
Volume
22
Issue
3
Pages
634-645
ISSN
  • 1467-2960 (ISSN-L)
  • 1467-2979
DOI
10.1111/faf.12534
OpenAlex
W3128916945
Cited by
24
References
0
Citations by year
2026: 5 · 2025: 4 · 2024: 6 · 2023: 4 · 2022: 5
FWCI
1.54
Type
journal article
Language
en
Open access
Licence
Locations
  • Fish and Fisheries (publishedVersion, cc-by)
  • NOAA Institutional Repository (submittedVersion)
Topics
  • Physical Sciences › Environmental Science › Global and Planetary Change › Marine and fisheries research
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
  • Physical Sciences › Environmental Science › Nature and Landscape Conservation › Fish Ecology and Management Studies
Keywords
Beverton-Holt model, Ricker model, maximum sustainable yield, fish population dynamics, temporal variation

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