Bayesian hierarchical nonlinear models for estimating coral growth parameters

In ecology, the standard tool for investigating the growth of marine species is the von Bertalanffy growth function (VBGF). The parameters of this function are usually estimated by methods that might induce bias in the results because the VBGF neither distinguishes between the variability at individual or population levels nor takes into account the contribution of site-specific environmental factors. A major problem arises when environmental measures are not directly linked to data because they are observed at different spatial locations, scales, or times. In this case, the association between site-specific environmental features and individual data might be forced. A Bayesian hierarchical nonlinear model (BHNLM) is proposed to provide reliable estimation of the VBGF parameters while taking into account biological information and site variability. We illustrate the advantages of the hierarchical structure that allow us to capture the differences among species and sites when environmental information is ignored. The proposal is assessed through a case study concerning two Mediterranean corals, Balanophyllia europaea and Leptopsammia pruvoti, improving both the statistical accuracy and the quantification of uncertainties affecting marine species growth.