Growth functions that incorporate the cost of reproduction

• Biphasic growth models were reviewed and fit to Arctic lake trout datasets.
• Two new models were also proposed.
• Models that explicitly represent the reproductive process fitted the data best.
• Integrated estimation using size-at-age and maturity-at-age data was implemented.

As the commonly-used von Bertalanffy growth function (VB) does not explicitly incorporate changes in growth due to allocation of energy to reproduction, a more flexible function could be used when attempting to model juvenile and adult growth simultaneously. Here we review biphasic growth models, with emphasis on those that explicitly incorporate the cost of reproduction, and propose two new models: the von Bertalanffy logistic-L∞ (VB log-L∞) and the Cost of Reproduction (CoR) models. We fitted the models to eight data sets from males and females of four unfished or lightly-fished Arctic lake trout (Salvelinus namaycush) populations, and compared their fits to those of the commonly-used growth functions. In all cases, a biphasic growth model fitted the data better than simpler models such as the VB and the Richards models. Of the biphasic models, those that explicitly represent the reproductive process fitted the data best, particularly the Quince–Boukal model with the allometric exponent on the growth rate-weight relationship β = 0.8. The proposed models and the Quince–Boukal model provide a smooth transition between juvenile and adult growth by incorporating a logistic function with parameters dependent on the proportion of mature fish (or probability of being mature) at age. In addition to fitting growth models to the size-at-age data, we also attempted an integrated estimation for the three models that predict the age at maturity (the models are simultaneously fit to two data components, size at age and maturity at age.) The integrated estimation was the best compromise between modeling the two biological processes (growth and reproduction), but the separated estimation provided similar results in most cases, and may be easier to implement. We believe that taking the cost of reproduction into consideration is central for growth curves used in stock assessment models, as changes in growth trajectories may impact the perception of stock status. Future research should focus on the sensitivity of management advice to these growth curves for commercially-important fish stocks. For data-poor stocks, the models based on first principles, such as the Quince–Boukal model, can be used to produce management advice based on life history invariants, taking into account information on metabolic rates that can be obtained from other studies.

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