Fisheries Science

, Volume 83, Issue 3, pp 353–365 | Cite as

Incorporating accessibility limitation into the surplus production model

  • Shin-Ichiro Nakayama
  • Seiji Akimoto
  • Momoko Ichinokawa
  • Hiroshi Okamura
Original Article Fisheries


Limited access to aquatic populations hinders estimation of their status and establishment of effective management measures. We propose a modified surplus production model to cope with this problem. The model provides population parameters and biological reference points from a time series of annual accessible abundance data. Simulation tests showed that the model provided biological reference point estimates with little bias when sufficiently long time series were available. Even for short time series, we could obtain nearly unbiased estimates by providing information on the exploitation rate at the maximum sustainable yield (F MSY). As an application, we fit the modified surplus production model to 7-year accessible biomass estimates of a local population of Japanese spiky sea cucumber Apostichopus japonicus using a Bayesian approach. The results indicated that the stock in the area studied was likely to have experienced recent overfishing and had a high probability of being overfished in the future.


Limited accessibility Stock assessment Surplus production model DeLury method Stock assessment Apostichopus japonicus 



The Japan Science and Technology Agency’s Strategic Basic Research Programs (CREST) supported this work. The authors are grateful to Mitsutaku Makino and Takehiro Okuda for their valuable comments and advice. The authors are also grateful to the editor Kazuhiko Hiramatsu and two anonymous reviewers for their helpful suggestions to improve the paper.

Supplementary material

12562_2017_1078_MOESM1_ESM.doc (9.3 mb)
Supplementary material 1 (DOC 9549 kb)


  1. 1.
    Hilborn R, Branch TA (2013) Does catch reflect abundance? No, it is misleading. Nature 494:303–306CrossRefPubMedGoogle Scholar
  2. 2.
    Methot RD, Wetzel CR (2013) Stock synthesis: a biological and statistical framework for fish stock assessment and fishery management. Fish Res 142:86–99CrossRefGoogle Scholar
  3. 3.
    Hilborn R, Walters CJ (1992) Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Chapman and Hall, New YorkCrossRefGoogle Scholar
  4. 4.
    Walters CJ, Martell SJD (2004) Fisheries ecology and management. Princeton University Press, PrincetonGoogle Scholar
  5. 5.
    Punt AE, Butterworth DS, Penny AJ (1995) Stock assessment and risk analysis for the South Atlantic population of Albacore Thunnus alalunga using an age-structured production model. S Afr J Mar Sci 16:287–310CrossRefGoogle Scholar
  6. 6.
    Punt AE, Pribac F, Walker TI, Taylor BL, Prince JD (2000) Stock assessment of school shark, Galeorhinus galeus, based on a spatially explicit population dynamics model. Mar Freshw Res 51:205–220CrossRefGoogle Scholar
  7. 7.
    Purcell SW (2010) Managing sea cucumber fisheries with an ecosystem approach. FAO Fisheries and Aquaculture Technical Paper 520Google Scholar
  8. 8.
    Ohashi H, Yamamoto M, Fujimura H, Shiraki N (1990) Local product cultivation techniques (echinoderms). Bulletin of Yamaguchi Prefectural Naikai Fisheries Experiment Station 19:192 (in Japanese) Google Scholar
  9. 9.
    Makino M (2011) A theory of the management options for sea cucumber fisheries in Japan: a simulation analysis with management objectives and area characteristics. Jpn J Fish Econ 55:149–165Google Scholar
  10. 10.
    Yamana Y, Hamano T (2006) A new size measurement for the Japanese sea cucumber Apostichopus japonicus (Stichopodidae) estimated from the body length and body breadth. Fish Sci 72:585–589CrossRefGoogle Scholar
  11. 11.
    Woodby DA, Kruse GH, Larson RC (1993) A conservative application of a surplus production model to the sea cucumber fishery in southeast Alaska. In: Proceedings of the international symposium on management strategies for exploited fish populations. Alaska Sea Grant College Program Report 93: 191–202Google Scholar
  12. 12.
    Fournier D, Archibald CP (1982) A general theory for analyzing catch at age data. Can J Fish Aquat Sci 39:1195–1207CrossRefGoogle Scholar
  13. 13.
    Polacheck T, Hilborn R, Punt AE (1993) Fitting surplus production models: comparing methods and measuring uncertainty. Can J Fish Aquat Sci 50:2597–2607CrossRefGoogle Scholar
  14. 14.
    Butterworth DS, Ianelli JN, Hilborn R (2003) A statistical model for stock assessment of southern bluefin tuna with temporal changes in selectivity. Afr J Mar Sci 25:331–361CrossRefGoogle Scholar
  15. 15.
    Quinn TJ, Deriso RB (1999) Quantitative fish dynamics. Oxford University Press, OxfordGoogle Scholar
  16. 16.
    Williams BK, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic, New YorkGoogle Scholar
  17. 17.
    Fournier DA, Skaug HJ, Ancheta J, Ianelli J, Magnusson A, Maunder MN, Nielsen A, Sibert J (2012) AD model builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optim Method Softw 27:233–249CrossRefGoogle Scholar
  18. 18.
    Yang HS, Yuan XT, Zhou Y, Mao YZ, Zhang T, Liu Y (2005) Effects of body size and water temperature on food consumption and growth in the sea cucumber Apostichopus japonicus (Selenka) with special reference to aestivation. Aquac Res 36:1085–1092CrossRefGoogle Scholar
  19. 19.
    DeLury DB (1947) On the estimation of biological populations. Biometrics 3:145–167CrossRefPubMedGoogle Scholar
  20. 20.
    Kirihara S (2008) Stock management and ecology of sea cucumbers. News letter, Aquaculture Institute, Aomori Prefectural Fisheries Research Center 113:1–2 (in Japanese) Google Scholar
  21. 21.
    Mitsukuri K (1903) Notes on the habits and life-history of Stichopus japonicus Selenka. Annot Zool Japon 5:1–21Google Scholar
  22. 22.
    Matsumiya Y (1984) Analysis of the sea cucumber population in Omura Bay, Nagasaki Prefecture. News letter, Faculty of fisheries, Nagasaki University 55:1–8 (in Japanese) Google Scholar
  23. 23.
    Pawitan Y (2001) In all likelihood: statistical modeling and inference using likelihood. Oxford Science, OxfordGoogle Scholar
  24. 24.
    Plummer M. (2003) JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing 124:125Google Scholar
  25. 25.
    Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409CrossRefGoogle Scholar
  26. 26.
    Agnew DJ, Gutierrez NL, Stern-Pirlot A, Smith ADM, Zimmermann C, Sainsbury K (2012) Rebuttal to Froese and Proelss “evaluation and legal assessment of certified seafood”. Mar Policy 38:551–553CrossRefGoogle Scholar
  27. 27.
    Thorson JT, Branch TA, Jensen OP (2012) Using model-based inference to evaluate global fisheries status from landings, location, and life history data. Can J Fish Aquat Sci 69:645–655CrossRefGoogle Scholar
  28. 28.
    Myers RA, Barrowman NJ, Hutchings JA, Rosenberg AA (1995) Population dynamics of exploited fish stocks at low population levels. Science 269:1106–1108CrossRefPubMedGoogle Scholar
  29. 29.
    Thorson JT, Jensen OP, Zipkin EF (2014) How variable is recruitment for exploited marine fishes? A hierarchical model for testing life history theory. Can J Fish Aquat Sci 71:973–983CrossRefGoogle Scholar
  30. 30.
    González-Yáñez AA, Millán RP, León ME, Cruz-Font L, Wolff M (2006) Modified DeLury depletion model applied to spiny lobster, Panulirus argus (Latreille, 1804) stock, in the southwest of the Cuban Shelf. Fish Res 79:155–161CrossRefGoogle Scholar
  31. 31.
    Roa-Ureta RH (2012) Modeling in-season pulses of recruitment and hyperstability-hyperdepletion in the Loligo gahi fishery around the Falkland Islands with generalized depletion models. ICES J Mar Sci 69:1403–1415CrossRefGoogle Scholar
  32. 32.
    Pella JJ, Tomlinson PK (1969) A generalized stock production model. Inter Am Trop Tuna Comm Bull 13:416–497Google Scholar
  33. 33.
    Thorson JT, Cope JM, Branch TA, Jensen OP (2012) Spawning biomass reference points for exploited marine fishes, incorporating taxonomic and body size information. Can J Fish Aquat Sci 69:1–13CrossRefGoogle Scholar

Copyright information

© Japanese Society of Fisheries Science 2017

Authors and Affiliations

  • Shin-Ichiro Nakayama
    • 1
  • Seiji Akimoto
    • 2
  • Momoko Ichinokawa
    • 1
  • Hiroshi Okamura
    • 1
  1. 1.National Research Institute of Fisheries ScienceFisheries Research Agency, JapanKanazawa, YokohamaJapan
  2. 2.Kanagawa Prefectural Fisheries Technology CenterMiuraJapan

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