Merging the von Bertalanffy and Roff Models

Nigel Lester, Brian Shuter, and Peter Abrams showed how the mechanisms of the Roff model can lead to the von Bertalanffy growth equation by making a few specific assumptions. Based on empirical evidence from fish, Lester et al. assume that the scaling exponents for anabo-lism and catabolism are the same, that is, m1 = m2 = 2/3. This leads to linear length growth prior to maturation. As mature fish grows, however, surplus energy, which is proportional to W2/3, will increase, but not as much as the gonads, which are proportional to W . The model therefore predicts asymptotic growth after maturation because the proportion of available resources devoted to gonads and reproduction increases. The resultant postmaturation asymptotic growth curve now becomes

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