Environmental Biology of Fishes

, Volume 77, Issue 3–4, pp 293–300 | Cite as

Evidence of two-phase growth in elasmobranchs



It is often assumed that the von Bertalanffy growth model (VBGM) is appropriate to describe growth in length-at-age of elasmobranchs. However, a review of the literature suggests that a two-phase growth model could better describe growth in elasmobranchs. We compare the two-phase growth model (TPGM) with the VBGM for 18 data sets of elasmobranch species, by fitting the models to 36 age-length-at-age data pairs available. The Akaike Information Criteria (AIC) and the difference in AIC between both models revealed that in 23 cases the probability that the TPGM was true ≥50%. The VBGM tends to estimate larger L values than the two-phase growth model, while the k parameter tends to be underestimated. The growth rate in length-at-age appears tends to decrease near the age at first maturity in several species of elasmobranch. The importance of the TPGM lies in that it may better describe this aspect of the life history of many elasmobranchs. In this context, we conclude that the TPGM should be used along with other growth models in order to precisely estimate elasmobranch life history parameters.


Elasmobranchs von Bertalanffy Two-phase growth Sharks Skates 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to thank Enric Cortés and Terry Walker for commentaries and revision of the manuscript. In addition, we would like to thank the authors who facilitated their information to us to conduct the analyses and to two anonymous referees for reviewing the manuscript. We would particularly like to thank the California Sea Grant for providing funding to travel to the meeting and present the results of this study.


  1. Avsar D (2001) Age, growth, reproduction and feeding of the spurdog (Squalus acanthias Linnaeus, 1758) in the South-eastern Black sea. Estuar Coast Shelf Sc 52:269–278CrossRefGoogle Scholar
  2. Brown CA, Gruber SH (1988) Age assessment of the lemon shark, Negaprion brevirostris, using tetracycline validated vertebral central. Copeia 1988:747–753CrossRefGoogle Scholar
  3. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach 2 ed Springer-Verlag, New York, NYGoogle Scholar
  4. Cailliet GM, Martin LK, Harvey JK, Kusher D, Welden BA (1983) Preliminary studies on the age and growth of blue, Prionace glauca, common thesher, Alopias vulpinus, and shortfin mako, Isurus oxyrinchus, sharks from California waters. In: Proceedings of the international workshop on age determination of oceanic pelagic fishes: tunas, billfishes, and sharks. pp 179–188. In: Prince ED, Pulos LM (eds) NOAA Tech. Rep. NMFS 8, U.S. Dept. Comm., Washington, DCGoogle Scholar
  5. Cailliet GM, Mollet HF, Pittenger GG, Bedford D, Natanson LJ (1992) Growth and demography of the pacific angel shark (Squatina californica), based upon tag returns off California. Aust J Mar Freshw Res 43:1313–1330CrossRefGoogle Scholar
  6. Cailliet GM, Goldman KJ (2004) Age Determination and Validation in Chondrichthyan Fishes. In: Carrier JC, Musick JA, Heithaus MR (eds), Biology of sharks and their relatives. CRC Press, Boca Raton, FL, pp 399–446Google Scholar
  7. Cailliet GM, Smith WD, Mollet HF, Goldman KJ (2006). Chondrichthyan growth studies: an updated review, stressing terminology, sample size sufficiency, validation, and curve fitting. pp. 000–000. In: Carlson JK, Goldman KJ (eds), Special volume from symposium of the American Elasmobranch Society. Google Scholar
  8. Clarke MW, Connolly PL, Bracken JJ (2002) Catch, discarding, age estimation, growth and maturity of the squalid shark Deania calceus west and north of Ireland. Fish Res 56:139–153CrossRefGoogle Scholar
  9. Cortés E (2000) Life history patterns and correlations in sharks. Rev Fish Sci 8:299–344Google Scholar
  10. Cowley PD (1997) Age and growth of the blue stingray Dasyatis chrysonota chrysonota from the south-east ern cape coast of South Africa. S Afr J Mar Sci 18:31–38Google Scholar
  11. Cruz-Martínez A, Chiappa-Carrara X, Arenas-Fuentes V (2002) Age and growth of the bull shark Carcharhinus leucas from the southern Gulf of Mexico. NAFO SCR Doc. 02/88, 1–11Google Scholar
  12. Day T, Taylor PD (1997) von Bertalanffy´s growth equation should not be used to model age and size at maturity. Am Nat 149:381–393CrossRefGoogle Scholar
  13. Du Buit MH (1976) Age et croissance de Raja batis et de Raja naevus en Mer Celtique. J Cons Per Int Expl Mer 37:261–265Google Scholar
  14. Francis MP, Francis RICC (1992) Growth rate estimates for New Zealand rig (Mustelus lenticulatus). Aust J Mar Freshw Res 43: 1157–1176CrossRefGoogle Scholar
  15. Froese R, Pauly D (eds) (2004) FishBase-world wide web electronic publication. www.fishbase.org, version (03/2004)Google Scholar
  16. Goosen AJJ, Smale MJ (1997) A preliminary study of age and growth of the smooth-hound shark Mustelus mustelus (Triakidae). S Afr J Mar Sci 18:85–91Google Scholar
  17. Haddon M (2001) Modelling and Quantitative Methods in Fisheries. Chapman & Hall/CRC, Boca Raton, FL. p 406Google Scholar
  18. Holden MJ (1972) The growth rates of Raja brachyura, R. clavata and R. montagui as determined from tagging data. J Cons Per Int Expl Mer 34:161–168Google Scholar
  19. Jensen AL (1985) Relations among net reproductive rate and life history parameters for lake Whitefish (Coregonus clupeaformis). Can J Fish Aquat Sci 42:164–168CrossRefGoogle Scholar
  20. Kusher DI, Smith SE, Cailliet GM (1992) Validated age and growth of the leopard shark, Triakis semifasciata, with comments on reproduction. Environ Biol Fish 35:187–203CrossRefGoogle Scholar
  21. Motulsky H, Christopoulos A (2003) Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. GraphPad Sofware Inc., San Diego CA, www.graphpad.comGoogle Scholar
  22. Musick JA (1999) Life in the slow lane: ecology and conservation of long-lived marine animals. American fisheries society symposium 23, Bethesda, MarylandGoogle Scholar
  23. Natanson LJ, Cailliet GM (1990) Vertebral growth zone deposition in Pacific Angel sharks. Copeia 1990:1133–1145CrossRefGoogle Scholar
  24. Natanson LJ, Casey JG, Kohler NE (1995) Age and growth estimates for the dusky shark, Carcharhinus obscurus, in the western North Atlantic Ocean. Fish Bull 93:116–126Google Scholar
  25. Natanson LJ, Kohler NE (1996) A preliminary estimate of age and growth of the dusky shark Carcharhinus obscurus from the South-West Indian Ocean, with comparisons to the Western North Atlantic population. S Afr J Mar Sci 17:217–224Google Scholar
  26. Natanson LJ, Mello JJ, Campana SE (2002) Validated age and growth of the porbeagle shark (Lamna nasus) in the western North Atlantic Ocean. Fish Bull 100:266–278Google Scholar
  27. Pauly D (1981) The relationships between gill surface area and growth performance in fish: a generalization of von Bertalanffy´s theory of growth. Meeresforschung 28:251–282Google Scholar
  28. Pratt HL, Casey JG (1990) Shark reproductive strategies as a limiting factor in directed fisheries, with a review of Holden’s method of estimating growth parameters. NOAA Tech. Rep. NMFS 90: 97–109Google Scholar
  29. Ricker WR (1979) Growth rates and models. In: Hoar WS, Randall DJ, Brett JR (eds) Fish physiology. Acad. Press, New York, NY, pp 677–743Google Scholar
  30. Schnute J (1981) A versatile growth model with statistically stable parameters. Can J Fish Aquat Sci 38:1128–1140CrossRefGoogle Scholar
  31. Skomal GB, Natanson LJ (2003) Age and growth of the blue shark (Prionace glauca) in the North Atlantic Ocean. Fish Bull 101:627–639Google Scholar
  32. Sminkey TS, Musick JA (1995) Age and growth of the sandbar shark, Carcharhinus plumbeus, before and after population depletion. Copeia 1995:871–883CrossRefGoogle Scholar
  33. Soriano M, Moreau J, Hoenig JM, Pauly D (1992) New functions for the analysis of two-phase growth of juvenile and adult fishes, with application to nile perch. Trans Am Fish Soc 121:486–493CrossRefGoogle Scholar
  34. Sulikowski JA, Morin MD, Suk SH, Howell WH (2003) Age and growth estimates of the winter skate (Leucoraja ocellata) in the western Gulf of Maine. Fish Bull 101:405–413Google Scholar
  35. Timmons M, Bray RN (1997) Age, growth, and sexual maturity of shovelnose guitarfish, Rhinobatos productus (Ayres). Fish Bull 95: 349–359Google Scholar
  36. von Bertalanffy L (1938) A quantitative theory of organic growth. Hum Biol 10:181–213Google Scholar
  37. Walker TI (1998) Can shark resources be harvested sustainably? A question revisited with a review of shark fisheries. Mar Freshw Res 49:553–572CrossRefGoogle Scholar
  38. Walker TI, Taylor BL, Hudson RJ, Cottier JP (1998) The phenomenon of apparent change of growth rate in gummy shark (Mustelus antarcticus) harvested off southern Australia. Fish Res 39:139–163CrossRefGoogle Scholar
  39. Wang Y-G, Thomas MR, Somers IF (1995) A maximum likelihood approach for estimating growth from tag-recapture data. Can J Fish Aquat Sci 52:252–259Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Departamento de Ciencias del MarUniversidad Arturo PratIquiqueChile
  2. 2.Departamento de Oceanografía, Facultad de Ciencias Naturales y OceanográficasUniversidad de ConcepciónConcepciónChile

Personalised recommendations