Bayesian hierarchical nonlinear models for estimating coral growth parameters

In ecology, the standard tool for investigating the growth of marine speciesis the von Bertalanffy growth function (VBGF). The parameters of this func-tion are usually estimated by methods that might induce bias in the resultsbecause the VBGF neither distinguishes between the variability at individual orpopulation levels nor takes into account the contribution of site-specific environ-mental factors. A major problem arises when environmental measures are notdirectly linked to data because they are observed at different spatial locations,scales, or times. In this case, the association between site-specific environmentalfeatures and individual data might be forced. A Bayesian hierarchical nonlin-ear model (BHNLM) is proposed to provide reliable estimation of the VBGFparameters while taking into account biological information and site variabil-ity. We illustrate the advantages of the hierarchical structure that allow us tocapture the differences among species and sites when environmental informa-tion is ignored. The proposal is assessed through a case study concerning twoMediterranean corals,Balanophyllia europaeaandLeptopsammia pruvoti,improving both the statistical accuracy and the quantification of uncertaintiesaffecting marine species growth.