Reviews in Fish Biology and Fisheries

, Volume 22, Issue 3, pp 635–640 | Cite as

A technical note on seasonal growth models

  • Emili García-BerthouEmail author
  • Gerard Carmona-Catot
  • Roberto Merciai
  • Derek H. Ogle


The growth of many organisms is seasonal, with a dependence on variation in temperature, light, and food availability. A growth model proposed by Somers (Fishbyte 6:8–11, 1988) is one of the most widely used models to describe seasonal growth. We point out that three different formulae (beyond numerous typographical errors) have been used in the literature referring to Somers (Fishbyte 6:8–11, 1988). These formulae correspond to different curves and yield different parameter estimates with different biological interpretations. These inconsistencies have led to the wrong identification of the period of lowest growth rate (winter point) in some papers of the literature. We urge authors to carefully edit their formulae to assure use of the original definition in Somers (Fishbyte 6:8–11, 1988).


von Bertalanffy growth function Seasonality Temperature Fishery models Somers’ (1988) growth model 



We thank Luis A. Cubillos for sharing the anchoveta data and Professor Daniel Pauly and an anonymous reviewer for helpful comments. Financial support for this research was provided by the Spanish Ministry of Science (projects CGL2009-12877-C02-01 and Consolider-Ingenio 2010 CSD2009-00065). GCC and RM held doctoral fellowships, from the University of Girona (BR2010/10) and the Spanish Ministry of Education (AP2010-4025) respectively, during the preparation of the manuscript.

Supplementary material

11160_2012_9262_MOESM1_ESM.docx (17 kb)
Supplementary material 1 (DOCX 17 kb)


  1. Adolph SC, Porter WP (1996) Growth, seasonality, and lizard life histories: age and size at maturity. Oikos 77:267–278CrossRefGoogle Scholar
  2. Alcoverro T, Duarte CM, Romero J (1995) Annual growth dynamics of Posidonia oceanica: contribution of large-scale versus local factors to seasonality. Mar Ecol Prog Ser 120:203–210CrossRefGoogle Scholar
  3. Bayley PB (1988) Factors affecting growth rates of young tropical floodplain fishes: seasonality and density-dependence. Environ Biol Fish 21:127–142CrossRefGoogle Scholar
  4. Bellido JM, Pierce GJ, Romero JL, Millán M (2000) Use of frequency analysis methods to estimate growth of anchovy (Engraulis encrasicolus L. 1758) in the Gulf of Cádiz (SW Spain). Fish Res 48:107–115CrossRefGoogle Scholar
  5. Beverton RJH, Holt SJ (1957) On the dynamics of exploited fish populations. Fisheries Investigations (Series 2), vol 19. United Kingdom Ministry of Agriculture and Fisheries, LondonGoogle Scholar
  6. Bilgin S, Ozen O, Samsun O (2009a) Sexual seasonal growth variation and reproduction biology of the rock pool prawn, Palaemon elegans (Decapoda: Palaemonidae) in the southern Black Sea. Sci Mar 73:239–247CrossRefGoogle Scholar
  7. Bilgin S, Samsun O, Ozen O (2009b) Seasonal growth and reproduction biology of the Baltic prawn, Palaemon adspersus (Decapoda: Palaemonidae), in the southern Black Sea. J Mar Biol Assoc UK 89:509–519CrossRefGoogle Scholar
  8. Böhlenius H, Huang T, Charbonnel-Campaa L, Brunner AM, Jansson S, Strauss SH, Nilsson O (2006) CO/FT regulatory module controls timing of flowering and seasonal growth cessation in trees. Science 312:1040–1043PubMedCrossRefGoogle Scholar
  9. Botter-Carvalho ML, Santos PJP, Carvalho P (2007) Population dynamics of Callichirus major (Say, 1818) (Crustacea, Thalassinidea) on a beach in northeastern Brazil. Estuar Coast Shelf Sci 71:508–516CrossRefGoogle Scholar
  10. Chatzinikolaou E, Richardson CA (2008) Population dynamics and growth of Nassarius reticulatus (Gastropoda: Nassariidae) in Rhosneigr (Anglesey, UK). Mar Biol 153:605–619CrossRefGoogle Scholar
  11. Cloern JE, Nichols FH (1978) A von Bertalanffy growth model with a seasonally varying coefficient. J Fish Res Bd Can 35:1479–1482CrossRefGoogle Scholar
  12. Coma R, Ribes M, Gili JM, Zabala M (2000) Seasonality in coastal benthic ecosystems. Trends Ecol Evol 15:448–453PubMedCrossRefGoogle Scholar
  13. Contreras H, Jaramillo E, Duarte C, McLachlan A (2003) Population abundances, growth and natural mortality of the crustacean macroinfauna at two sand beach morphodynamic types in southern Chile. Rev Chil Hist Nat 76:543–561CrossRefGoogle Scholar
  14. Cubillos LA, Arcos DF, Bucarey DA, Canales MT (2001) Seasonal growth of small pelagic fish off Talcahuano, Chile (37°S, 73°W): a consequence of their reproductive strategy to seasonal upwelling? Aquat Living Resour 14:115–124CrossRefGoogle Scholar
  15. Defeo O, Arreguín-Sánchez F, Sánchez J (1992) Growth study of the yellow clam Mesodesma mactroides: a comparative analysis of three length-based methods. Sci Mar 56:53–59Google Scholar
  16. Deval MC (2009) Growth and reproduction of the wedge clam (Donax trunculus) in the Sea of Marmara, Turkey. J Appl Ichthyol 25:551–558CrossRefGoogle Scholar
  17. Deval MC, Göktürk D (2008) Population structure and dynamics of the cut trough shell Spisula subtruncata (da Costa) in the Sea of Marmara, Turkey. Fish Res 89:241–247CrossRefGoogle Scholar
  18. Etim L, King RP, Udo MT (2002) Breeding, growth, mortality and yield of the mudskipper Periophthalmus barbarus (Linneaus 1766)(Teleostei: Gobiidae) in the Imo River estuary, Nigeria. Fish Res 56:227–238CrossRefGoogle Scholar
  19. Fiori SM, Morsán EM (2004) Age and individual growth of Mesodesma mactroides (Bivalvia) in the southernmost range of its distribution. ICES J Mar Sci 61:1253–1259CrossRefGoogle Scholar
  20. Francis RICC (1988) Are growth parameters estimated from tagging and age-length data comparable? Can J Fish Aquat Sci 45:936–942CrossRefGoogle Scholar
  21. García CB, Duarte LO (2006) Length-based estimates of growth parameters and mortality rates of fish populations of the Caribbean Sea. J Appl Ichthyol 22:193–200CrossRefGoogle Scholar
  22. Gayanilo Jr FC, Sparre P, Pauly P (2005) FAO-ICLARM stock assessment tools (FiSAT II). Revised version. User’s manual. Food and Agriculture Organization of the United Nations, Rome. Available at
  23. Gayanilo FC Jr, Pauly D (1997) FAO-ICLARM Stock Assessment Tools (FiSAT) reference manual. Food and Agriculture Organization of the United Nations, RomeGoogle Scholar
  24. Hanumara RC, Ghedari S (1993) Interval estimation of parameters in models for seasonal growth in fishes. Fish Res 18:349–361CrossRefGoogle Scholar
  25. Herrmann M, Alfaya JEF, Lepore ML, Penchaszadeh PE, Arntz WE (2011) Population structure, growth and production of the yellow clam Mesodesma mactroides (Bivalvia: Mesodesmatidae) from a high-energy, temperate beach in northern Argentina. Helgoland Mar Res 65:285–297CrossRefGoogle Scholar
  26. Hoenig NA, Hanumara RC (1990) An empirical comparison of seasonal growth models. Fishbyte 8:32–34Google Scholar
  27. Martínez-Muñoz MA, Ortega-Salas AA (2010) Growth and mortality of the fish Citharichthys xanthostigma (Pleuronectiformes: Paralichthyidae) off the Western coast of Baja California, México. Rev Biol Trop 58:689–705PubMedGoogle Scholar
  28. Ogle DH (2011a) FSA: fisheries stock analysis. R package version 0.2-7. Available at
  29. Ogle DH (2011b) fishR Vignette - Von Bertalanffy Growth Model - Extra. Available at
  30. Pauly D (1990) Length-converted catch curves and the seasonal growth of fishes. Fishbyte 8:33–38Google Scholar
  31. Pauly D (1998) Beyond our original horizons: the tropicalization of Beverton and Holt. Rev Fish Biol Fisher 8:307–334CrossRefGoogle Scholar
  32. Pauly D, Gaschütz G (1979) A simple method for fitting oscillating length growth data, with a program for pocket calculators, ICES C.M. 1979/G:24Google Scholar
  33. Pauly D, Soriano-Bartz M, Moreau J, Jarre-Teichmann A (1992) A new model accounting for seasonal cessation of growth in fishes. Mar Freshw Res 43:1151–1156CrossRefGoogle Scholar
  34. Pitcher TJ, MacDonald PDM (1973) Two models for seasonal growth in fishes. J Appl Ecol 10:599–606CrossRefGoogle Scholar
  35. Porch CE, Wilson CA, Nieland DL (2002) A new growth model for red drum (Sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates. Fish Bull 100:149–152Google Scholar
  36. R Development Core Team (2011) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL
  37. Schnute J, Fournier D (1980) A new approach to length-frequency analysis: growth structure. Can J Fish Aquat Sci 37:1337–1351CrossRefGoogle Scholar
  38. Simpfendorfer CA, Poulakis GR, O’Donnell PM, Wiley TR (2008) Growth rates of juvenile smalltooth sawfish Pristis pectinata Latham in the western Atlantic. J Fish Biol 72:711–723CrossRefGoogle Scholar
  39. Somers IF (1988) On a seasonally oscillating growth function. Fishbyte 6:8–11Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Emili García-Berthou
    • 1
    Email author
  • Gerard Carmona-Catot
    • 1
  • Roberto Merciai
    • 1
  • Derek H. Ogle
    • 2
  1. 1.Institute of Aquatic EcologyUniversity of GironaGironaSpain
  2. 2.Northland CollegeAshlandUSA

Personalised recommendations