Marine Biology

, 165:76 | Cite as

The growth cessation model: a growth model for species showing a near cessation in growth with application to bigeye tuna (Thunnus obesus)

  • Mark N. Maunder
  • Richard B. Deriso
  • Kurt M. Schaefer
  • Daniel W. Fuller
  • Alexandre M. Aires-da-Silva
  • Carolina V. Minte-Vera
  • Steven E. Campana
Method

Abstract

We present the growth cessation model, which is designed for species, such as some tropical tunas, that have an apparent linear relationship between length and age, followed by a marked reduction of growth after the onset of sexual maturity. The growth curve simply assumes linear growth for the youngest individuals and then uses a logistic function to model how the growth rate falls to zero at greater ages. One characteristic of the model is that, as t → 0, the model converges to a linear regression. The range of ages for which a linear regression adequately represents the mean length at age depends on when the logistic function becomes influential. A beneficial characteristic of this model is that, unlike other growth models, a preponderance of younger fish may not overwhelm the information from older fish, which biases the estimates of mean length at age for older fish. We apply the growth curve to bigeye tuna (Thunnus obesus) data from the eastern Pacific Ocean, obtained from otolith daily increment counts and tagging experiments, and compare the results with those from the von Bertalanffy and Richards growth curves. The growth cessation model fits the eastern Pacific Ocean bigeye tuna data better than do the von Bertalanffy and Richards growth curves. These results support the use of the growth cessation model for bigeye tuna in the eastern Pacific Ocean, and since many species have growth curves that flatten out to the point where growth is almost undetectable, this indicates that the growth cessation model may be widely applicable.

Notes

Compliance with ethical standards

Conflict of interest

Mark Maunder declares that he has no conflict of interest. Richard Deriso declares that he has no conflict of interest. Kurt Schaefer declares that he has no conflict of interest. Dan Fuller declares that he has no conflict of interest. Alexandre Aire-da-Silva declares that he has no conflict of interest. Carolina Minte-Vera declares that she has no conflict of interest. Steven Campana declares that he has no conflict of interest.

Ethical approval

All applicable international, national, and institutional guidelines for the care and use of animals were followed.

References

  1. Aires-da-Silva AM, Maunder MN, Schaefer KM, Fuller DW (2015) Improved growth estimates from integrated analysis of direct aging and tag–recapture data: an illustration with bigeye tuna (Thunnus obesus) of the eastern Pacific Ocean with implications for management. Fish Res 163:119–126CrossRefGoogle Scholar
  2. Andrews AH, DeMartini EE, Brodziak J, Nichols RS, Humphreys RL (2012) A long-lived life history for a tropical, deepwater snapper (Pristipomoides filamentosus): bomb radiocarbon and lead–radium dating as extensions of daily increment analyses in otoliths. Can J Fish Aquat Sci 69:1850–1869CrossRefGoogle Scholar
  3. Barrowman NJ, Myers RA (2000) Still more spawner-recruitment curves: the hockey stick and its generalizations. Can J Fish Aquat Sci 57:665–676CrossRefGoogle Scholar
  4. Campana SE, Valentin AE, MacLellan SE, Groot JB (2016) Image-enhanced burnt otoliths, bomb radiocarbon and the growth dynamics of redfish (Sebastes mentella and S. fasciatus) off the eastern coast of Canada. Mar Freshw Res 67:925–936CrossRefGoogle Scholar
  5. Dortel E, Sardenne F, Bousquet N, Rivot E, Million J, Le Croizier G, Chassot E (2015) An integrated Bayesian modeling approach for the growth of Indian Ocean yellowfin tuna. Fish Res 163:69–84CrossRefGoogle Scholar
  6. Eveson JP, Laslett GM, Polacheck T (2004) An integrated model for growth incorporating tag–recapture, length-frequency, and direct aging data. Can J Fish Aquat Sci 61:292–306CrossRefGoogle Scholar
  7. Ewing GP, Lyle JM, Murphy RJ, Kalish JM, Ziegler PE (2007) Validation of age and growth in a long-lived temperate reef fish using otolith structure, oxytetracycline and bomb radiocarbon methods. Mar Freshw Res 58:944–955CrossRefGoogle Scholar
  8. Farley JH, Clear NP, Leroy B, Davis TLO, McPherson G (2006) Age, growth and preliminary estimates of maturity of bigeye tuna, Thunnus obesus, in the Australian region. Mar Freshw Res 57:713–724CrossRefGoogle Scholar
  9. Fournier DA, Hampton J, Sibert JR (1998) MULTIFAN-CL: a length-based, age-structured model for fisheries stock assessment, with application to South Pacific albacore, Thunnus alalunga. Can J Fish Aquat Sci 57:1002–1010Google Scholar
  10. Francis C (2016) Growth in age-structured stock assessment models. Fish Res 180:77–86CrossRefGoogle Scholar
  11. Francis MP, Campana SE, Jones CM (2007) Age under-estimation in New Zealand porbeagle sharks (Lamna nasus): is there an upper limit to ages that can be determined from shark vertebrae? Mar Freshw Res 58:10–23CrossRefGoogle Scholar
  12. Francis C, Aires-da-Silva A, Maunder MN, Schaefer KM, Fuller DW (2016) Estimating fish growth for stock assessments using both age–length and tagging-increment data. Fish Res 180:113–118CrossRefGoogle Scholar
  13. Gunn JS, Clear NP, Carter TI, Rees AJ, Stanley CA, Farley JH, Kalish JM (2008) Age and growth in southern bluefin tuna, Thunnus maccoyii (Castelnau): direct estimation from otoliths, scales and vertebrae. Fish Res 92:207–220CrossRefGoogle Scholar
  14. Heino M, Kaitala V (1999) Evolution of resource allocation between growth and reproduction in animals with indeterminate growth. J Evol Biol 12:423–429CrossRefGoogle Scholar
  15. Karkach A (2006) Trajectories and models of individual growth. Demogr Res 15:347–400CrossRefGoogle Scholar
  16. Kolody DS, Eveson JP, Hillary RM (2016) Modelling growth in tuna RFMO stock assessments: current approaches and challenges. Fish Res 180:177–193CrossRefGoogle Scholar
  17. Laslett GM, Eveson JP, Polacheck T (2002) A flexible maximum likelihood approach for fitting growth curves to tag–recapture data. Can J Fish Aquat Sci 59:976–986CrossRefGoogle Scholar
  18. Lopez S, France J, Gerrits WJ, Dhanoa MS, Humphries DJ, Dijkstra J (2000) A generalized Michaelis–Menten equation for the analysis of growth. J Anim Sci 78:1816–1828CrossRefPubMedGoogle Scholar
  19. Maunder MN, Piner KR (2015) Contemporary fisheries stock assessment: many issues still remain. ICES J Mar Sci 72:7–18CrossRefGoogle Scholar
  20. Maunder MN, Watters GM (2003) A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the Eastern Pacific Ocean. Inter-Am Trop Tuna Comm Bull 22:433–582Google Scholar
  21. Maunder MN, Crone PR, Punt AE, Valero JL, Semmens BX (2016) Growth: theory, estimation, and application in fishery stock assessment models. Fish Res 180:1–3CrossRefGoogle Scholar
  22. Minte-Vera CV, Maunder MN, Casselman JM, Campana SE (2016) Growth functions that incorporate the cost of reproduction. Fish Res 180:31–44CrossRefGoogle Scholar
  23. Morsán E, Ciocco NF (2004) Age and growth model for the southern geoduck, Panopea abbreviata, off Puerto Lobos (Patagonia, Argentina). Fish Res 69:343–348CrossRefGoogle Scholar
  24. Natanson LJ, Skomal GB (2015) Age and growth of the white shark, Carcharodon carcharias, in the western North Atlantic Ocean. Mar Freshw Res 66:387–398CrossRefGoogle Scholar
  25. Parham JF, Zug GR (1997) Age and growth of loggerhead sea turtles (Caretta caretta) of coastal Georgia: an assessment of skeletochronological age-estimates. Bull Mar Sci 61:287–304Google Scholar
  26. Punt AE, Haddon M, McGarvey R (2016) Estimating growth within size-structured fishery stock assessments: what is the state of the art and what does the future look like? Fish Res 180:147–160CrossRefGoogle Scholar
  27. Restrepo VR, Diaz GA, Walter JF, Neilson JD, Campana SE, Secor D, Wingate R (2010) Updated estimate of the growth curve of Western Atlantic bluefin tuna. Aquat Living Resour 23:335–342CrossRefGoogle Scholar
  28. Richards FJ (1959) A flexible growth function for empirical use. J Exp Bot 10:290–301CrossRefGoogle Scholar
  29. Schaefer KM, Fuller DW (2006) Estimates of age and growth of bigeye tuna (Thunnus obesus) in the eastern Pacific Ocean, based on otolith increments and tagging data. Inter-Am Trop Tuna Comm Bull 23:32–76Google Scholar
  30. Sebens K (1987) The ecology of indeterminate growth in animals. Annu Rev Ecol Syst 18:371–407CrossRefGoogle Scholar
  31. Wang Y-G (1998) Growth curves with explanatory variables and estimation of the effect of tagging. Aust NZ J Stat 40:299–304CrossRefGoogle Scholar
  32. Zhu J, Maunder MN, Aires-da-Silva AM, Chen Y (2016) Estimation of growth within stock synthesis models: management implications when using length-composition data. Fish Res 180:87–91CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Mark N. Maunder
    • 1
    • 2
  • Richard B. Deriso
    • 1
  • Kurt M. Schaefer
    • 1
  • Daniel W. Fuller
    • 1
  • Alexandre M. Aires-da-Silva
    • 1
  • Carolina V. Minte-Vera
    • 1
  • Steven E. Campana
    • 3
  1. 1.Inter-American Tropical Tuna CommissionLa JollaUSA
  2. 2.Center for the Advancement of Population Assessment MethodologyLa JollaUSA
  3. 3.Life and Environmental SciencesUniversity of IcelandReykjavíkIceland

Personalised recommendations