Hierarchical non-linear mixed-effects models for estimating growth parameters of western Mediterranean solitary coral populations

•An alternative approach for estimating VBGF coral growth parameters is proposed.•HNLMMs allow to overcome limitations requested by methods currently employed.•Environmental information can be incorporate using the proposed HNLMMs.•The approach enables to model within-site correlation and variabilities at sites.

Marine biologists usually assess coral growth through the von Bertalanffy growth function (VBGF), a function of several biological parameters linked to age by a non-linear relationship. Coral growth parameters are then evaluated via ordinary least squares after a linear transformation of the VBGF. Current literature focuses on linearization techniques, but these methods are often used without considering a careful data examination and the presence of variability in coral of the same age or in coral of the same colony. For these reasons, a more thorough approach based on a hierarchical non-linear mixed-effects model is proposed. This model takes into account the influence of sites' characteristics to model heterogeneity between sites. Moreover, the contribution of environmental factors and all the reliable information that may influence coral growth can be suitably modelled. Two model specifications based on the standard and new VBGF parameterizations are introduced to analyse the growth of a solitary coral species Balanophyllia europaea. Results from the proposed modelling approach show the importance of including environmental conditions for species coral growth and support; furthermore, the results show the importance of the possibility of accounting for variability from different sources in terms of estimated growth curves.