Flexible von Bertalanffy growth models incorporating Bayesian splines

•A flexible class of growth models based on the von Bertalanffy is described.•The models are subject to only very mild parametric assumptions.•A southern bluefin tuna dataset is fitted as well as the best parametric model.•Growth trajectory as a function of age may highlight changes in life stage.

Understanding the growth rates of fish is vital for effective fisheries management. Historically a three-parameter von Bertalanffy growth model (VBGM) has most often been used to describe the somatic growth of fish. However, increasingly, populations are identified with patterns of growth that are not adequately described by the standard VBGM. We describe a more flexible growth model obtained by replacing the normally constant von Bertalanffy growth coefficient, k, with a piecewise constant function, K, of age. In principle this allows arbitrary monotonic growth to be approximated within a generalized von Bertalanffy structure. Posterior distributions of model parameters are approximated by the method of Hamiltonian Monte Carlo using the Stan software package. Spline smoothing of the K function is achieved by specifying a hierarchical random walk prior. We compare fits achieved using this new approach to observations of length-at-age of southern bluefin tuna (Thunnus maccoyii) with a range of existing growth models.