, 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


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.


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



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)


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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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