Modelling length-at-age relationships in fish: A simpler and more flexible alternative to the 'typical' von...

The von Bertalanffy growth model (VBGM) is undoubtedly the most frequently used by fisheries biologists to describe length-at-age relationships. Its widespread application, often achieved in an ordinary least-squares non-linear regression framework such as with the commonly used FSA package in R, allows to estimate the length-at-infinity (L_inf) that is useful for the assessment of stock status. However, under potentially indeterminate growth, the estimation of a 'model-driven' growth curve with a notional L_inf, including the commonly used Gompertz and logistic growth models, and that of Richards to a lower extent, may negatively affect the shape of their respective predicted length-at-age relationship. Here, using a 'data-driven' approach based on shape-constrained additive models (SCAMs), 21 publicly available length-at-age fish datasets were analysed and compared under the two general modelling approaches according to two penalised measures of fit to identify a preferred model each time. Given that a model must respect its underlying assumptions to be of practical use, new helper functions for the hnp package were first used to test whether all competing models were sufficiently adequate. Although the VBGM was found to perform generally well, the SCAM framework yielded the top-ranking models in most instances and also allowed for accommodating biphasic growth, that is, an analytically detectable curvature change that may result from a trade-off between growth and reproduction. The SCAM framework thus appears innately well-suited to describe the large observed diversity of growth trajectories across fish species and may also act as a useful complement to assess the appropriateness of the estimated L_inf when relying on the VBGM.