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Oecologia

, Volume 172, Issue 3, pp 631–643 | Cite as

Estimating age at maturation and energy-based life-history traits from individual growth trajectories with nonlinear mixed-effects models

  • Thomas BrunelEmail author
  • Bruno Ernande
  • Fabian M. Mollet
  • Adriaan D. Rijnsdorp
Methods

Abstract

A new method is presented to estimate individuals’ (1) age at maturation, (2) energy acquisition rate, (3) energy expenditure for body maintenance, and (4) reproductive investment, and the multivariate distribution of these traits in a population. The method relies on adjusting a conceptual energy allocation model to individual growth curves using nonlinear mixed-effects modelling. The method’s performance was tested using simulated growth curves for a range of life-history types. Individual age at maturation, energy acquisition rate and the sum of maintenance and reproductive investment rates, and their multivariate distribution, were accurately estimated. For the estimation of maintenance and reproductive investment rates separately, biases were observed for life-histories with a large imbalance between these traits. For low reproductive investment rates and high maintenance rates, reproductive investment rate estimates were strongly biased whereas maintenance rate estimates were not, the reverse holding in the opposite situation. The method was applied to individual growth curves back-calculated from otoliths of North Sea plaice (Pleuronectes platessa) and from scales of Norwegian spring spawning herring (Clupea harengus). For plaice, maturity ogives derived from our individual estimates of age at maturation were almost identical to the maturity ogives based on gonad observation in catch samples. For herring, we observed 51.5 % of agreement between our individual estimates and those directly obtained from scale reading, with a difference lower than 1 year in 97 % of cases. We conclude that the method is a powerful tool to estimate the distribution of correlated life-history traits for any species for which individual growth curves are available.

Keywords

Bioenergetics growth model Individual growth trajectory Life-history trade-offs Energy acquisition Maintenance Reproductive investment Sexual maturation 

Notes

Acknowledgments

The authors would like to thank the Institute of Marine Research (Bergen, Norway) for providing the data on NSSH. We are also grateful to Mikko Heino and two anonymous reviewers for their critical comments which greatly helped in improving the manuscript. This study was supported by the European research training network FishACE and the strategic research program “Sustainable spatial development of ecosystems, landscapes, seas and regions” funded by the Dutch Ministry of Agriculture, Nature Conservation and Food Quality.

Supplementary material

442_2012_2527_MOESM1_ESM.pdf (26 kb)
Supplementary material 1 (PDF 26 kb)
442_2012_2527_MOESM2_ESM.pdf (33 kb)
Supplementary material 2 (PDF 33 kb)

References

  1. Atkinson D (1994) Temperature and organism size—a biological law for ectotherms. Adv Ecol Res 25:1–58CrossRefGoogle Scholar
  2. Baulier L, Heino M (2008) Norwegian spring-spawning herring as the test case of piecewise linear regression method for detecting maturation from growth patterns. J Fish Biol 73:2452–2467CrossRefGoogle Scholar
  3. Bernardo J (1993) Determinants of maturation in animals. Trends Ecol Evol 8:166–173PubMedCrossRefGoogle Scholar
  4. Bernardo J (1994) Experimental analysis of allocation in two divergent, natural salamander populations. Am Nat 143:14–38CrossRefGoogle Scholar
  5. Berrigan D, Charnov EL (1994) Reaction norms for age and size at maturity in response to temperature—a puzzle for life historians. Oikos 70:474–478CrossRefGoogle Scholar
  6. Brander KM (1995) The effect of temperature on growth of Atlantic cod (Gadus morhua L.). ICES J Mar Sci 52:1–10CrossRefGoogle Scholar
  7. Campana SE (2001) Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J Fish Biol 59:197–242CrossRefGoogle Scholar
  8. Dhillon RS, Fox MG (2004) Growth-independent effects of temperature on age and size at maturity in Japanese medaka (Oryzias latipes). Copeia 2004:37–45CrossRefGoogle Scholar
  9. Engelhard GH, Heino M (2004) Maturity changes in Norwegian spring-spawning herring Clupea harengus: compensatory or evolutionary responses? Mar Ecol Prog Ser 272:245–256CrossRefGoogle Scholar
  10. Engelhard GH, Dieckmann U, Godø OR (2003) Age at maturation predicted from routine scale measurements in Norwegian spring-spawning herring (Clupea harengus) using discriminant and neural network analyses. ICES J Mar Sci 60:304–313CrossRefGoogle Scholar
  11. Fablet R, Le Josse N (2004) Automated fish age estimation from otolith images using statistical learning. Fish Res 72:279–290CrossRefGoogle Scholar
  12. Jennings S, Beverton RJH (1991) Intraspecific variation in the life history tactics of Atlantic herring (Clupea harengus L.) stocks. ICES J Mar Sci 48:117–125CrossRefGoogle Scholar
  13. Johnson JB (2001) Adaptive life-history evolution in the live bearing fish Brachyrhaphis rhabdophora: genetic basis for parallel divergence in age and size at maturity and a test of predator-induced plasticity. Evolution 55:1486–1491PubMedGoogle Scholar
  14. Kooijman SALM (2000) Dynamics energy and mass budgets in biological systems. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  15. Kuparinen A, O’Hara RB, Merilä J (2008) The role of growth history in determining the age and size at maturation. Fish Fish 9:201–207CrossRefGoogle Scholar
  16. Kuparinen A, Cano J, Loehr J, Herczeg G, Gonda A, Merila J (2011) Fish age at maturation is influenced by temperature independently of growth. Oecol Aquat 167:435–443CrossRefGoogle Scholar
  17. Mollet FM, Ernande B, Brunel T, Rijnsdorp AD (2010) Multiple growth-related life history traits estimated simultaneously in individuals. Oikos 119:10–26CrossRefGoogle Scholar
  18. Mollmann C, Kornilovs G, Fetter M, Koster FW (2005) Climate, zooplankton, and pelagic fish growth in the central Baltic Sea. ICES J Mar Sci 62:1270–1280CrossRefGoogle Scholar
  19. Pinheiro JC, Bates DM (2000) Mixed effects models in S and S-plus. Springer, New YorkCrossRefGoogle Scholar
  20. Pinheiro JC, Bates DM, DebRoy S, Sarkar D, the R Core Team (2007) nlme: linear and nonlinear mixed effects models. R package version 3.1-86Google Scholar
  21. R Development Core Team (2006) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  22. Reznick DN (1990) Plasticity in age and size at maturity in male guppies (Poecilia reticulata)—an experimental evaluation of alternative models of development. J Evol Biol 3:185–203CrossRefGoogle Scholar
  23. Ricklefs RE (2003) Is rate of ontogenetic growth constrained by resource supply or tissue growth potential? A comment on West et al.’s model? Funct Ecol 17:384–393CrossRefGoogle Scholar
  24. Rijnsdorp AD (1990) The mecanism of energy allocation over reproduction and somatic growth in the female North Sea plaice, Pleuronectes platessa L. Neth J Sea Res 25:279–290CrossRefGoogle Scholar
  25. Rijnsdorp AD, Storbeck F (1995) Determining the onset of sexual maturity from otoliths of individual female North Sea plaice, Pleuronectes platessa L. In: Secor D, Dean J, Campana S (eds) Recent developments in fish otolith research. University of South Carolina Press, Columbia, pp 581–598Google Scholar
  26. Rijnsdorp AD, Van Leeuwen PI (1992) Density dependent and independent changes in somatic growth of female North Sea plaice Pleuronectes platessa between 1930 and 1985 as revealed by back-calculation of otoliths. Mar Ecol Prog Ser 88:19–32CrossRefGoogle Scholar
  27. Rijnsdorp AD, van Leeuwen PI, Visser TAM (1990) On the validity and precision of back-calculation of growth form otoliths of the plaice, Pleuronectes platessa L. Fish Res 9:97–117CrossRefGoogle Scholar
  28. Roff DA (1983) An allocation model of growth and reproduction in fish. Can J Fish Aquat Sci 40:1395–1404CrossRefGoogle Scholar
  29. Runnström S (1936) A study on the life history and migrations of the Norwegian spring-spawning herring based on the analysis of the winter rings and summer zones of the scales. Fiskeridir Skr Ser Havunders 5:1–103Google Scholar
  30. Scott RD, Heikkonen J (2012) Estimating age at first maturity in fish from change-points in growth rate. Mar Ecol Prog Ser 450:147–157CrossRefGoogle Scholar
  31. Stearns SC (1984) The effects of size and phylogeny on patterns of covariation in the life history traits of lizards and snakes. Am Nat 123:56–72CrossRefGoogle Scholar
  32. Stearns SC, Hoekstra RJ (2005) Evolution, 2nd edn. Oxford University Press, New YorkGoogle Scholar
  33. Stearns SC, Koella JC (1986) The evolution of phenotypic plasticity in life-history traits: predictions of reaction norms for age and size at maturity. Evolution 40:893–913CrossRefGoogle Scholar
  34. West GB, Brown JH, Enquist BJ (2001) A general model for ontogenetic growth. Nature 413:628–631PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas Brunel
    • 1
    Email author
  • Bruno Ernande
    • 2
  • Fabian M. Mollet
    • 1
    • 3
  • Adriaan D. Rijnsdorp
    • 1
    • 4
  1. 1.Wageningen IMARESIJmuidenThe Netherlands
  2. 2.IFREMER, Laboratoire Ressources HalieutiquesBoulogne-sur-MerFrance
  3. 3.Blueyou Consulting Ltd.ZürichSwitzerland
  4. 4.Aquaculture and Fisheries GroupWageningen UniversityWageningenThe Netherlands

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