A generalized Dynamic Energy Budget model including 3D shape changes for modeling small pelagic fish growth

Understanding pelagic fish growth patterns from early life stages to adulthood is fundamental to accurately predict larval survival and predator-prey dynamics, which are influenced by individual size. Dynamic Energy Budget (DEB) models constitute useful tools to predict and explain these patterns in changing environments. In DEB models, fish individuals are usually assumed to grow either isomorphically, or to experience a metabolic acceleration phase between birth (b) and metamorphosis (j), during which the shape coefficient changes and both the maximum surface-area specific assimilation rate and the energy conductance are multiplied by a metabolic acceleration coefficient function of structural length. Here we propose a different growth model based on a Dynamic Energy Budget model (modified as in Maury, 2019 to properly account for the size-dependence of maintenance) that captures deviations from pure isomorphy, allowing length and width to grow non-proportionally. Our model represents the fish’s structural body as an ellipsoid and differentially allocates volumetric growth to length, height and width as a function of the distance between the current shape and characteristic stage-dependent shape attractors (expressed as width/length and height/width ratios). The resulting changes of the structural surface-to-volume ratios due to changing shape mechanistically explain the “metabolic acceleration” phenomenon that is often invoked to interpret early life growth patterns. We estimated model parameters for the European anchovy Engraulis encrasicolus, using data covering growth at all life-stages, observed shapes at early life stages, transitions between life-stages, and reproduction. The calibrated model accurately reproduces the observed deviations from isomorphy, with exponential length-dominated growth until metamorphosis, then a shift to height- and width-dominated growth (with a corresponding deceleration of growth in length) until the adult shape is reached, and finally isomorphic (characteristic von Bertalanffy) length growth. These deviations from the usual von Bertalanffy growth model could profoundly affect our understanding of larval survival, predator-prey and ecosystem-dynamics