ESCROpath, a Bayesian mixing model to quantify diets and trophic flows in aquatic food webs

Food-web modelling is a key tool to provide a global and comprehensive knowledge on community structure, biodiversity and ecosystem processes and functioning. In particular, it allows computing integrative and holistic indices describing food web characteristics, topology and functioning. However, one of the main sources of uncertainty in most food-web models is the estimation of diet matrices. In the present work, we propose an innovative approach that combines (a) a Bayesian mixing model using both isotopes and contaminants as chemical tracers with (b) classical mass-balance equations. This dual approach allows the simultaneous estimation of diet composition, isotopic enrichment, contaminant biomagnification, and contaminants and biomass flows in the whole food web. This original model named ESCROpath also provides food-web indices derived from ecological network analysis (ENA). As a case study, the approach was implemented in the Gironde estuarine food web (SW France) for which isotopes, contaminants and trophic data exist. Two sets of priors were constructed accounting for more or less uncertainty in trophic parameter estimates. Outputs were compared with previous published Ecopath results. A constrained calibration led to very similar outputs as Ecopath (which shows that the method is able to find the initial set of parameters if it is forced to do so), whereas a free calibration led to slight differences in trophic parameters and ENA indice estimations (which shows that the Ecopath solution was not fully optimal). Quite different diet matrices and estimations of flows distribution within the food web can thus be obtained. ESCROpath is an original flexible food-web modelling tool that, for the first time, makes it possible to go from a model mainly built on an 'estimate' of the parameters based on expert knowledge (which constitutes the main criticism formulated against Ecopath) to a statistical Bayesian framework for the estimation of the trophic parameters. It thus provides a very integrated framework for food-web modelling by estimating simultaneously trophic parameters, diet compositions and trophic enrichment/magnification factors. By doing this, it notably provides reliable and robust uncertainty estimations for output parameters.