Estimating Trophic Levels and Trophic Magnification Factors Using Bayesian Inference

Abstract

Food web biomagnification is increasingly assessed by estimating trophic magnification factors (TMF) where solvent (often lipid) normalized contaminant concentration is regressed onto the trophic level, and TMFs are represented by the slope of the relationship. In TMF regressions, the uncertainty in the contaminant concentrations is appreciated, whereas the trophic levels are assumed independent and not associated with variability or uncertainty pertaining to e.g. quantification. In reality, the trophic levels may vary due to measurement error in stable isotopes of nitrogen (δ(15)N) of each sample, in δ(15)N in selected reference baseline trophic level, and in the enrichment factor of δ(15)N between two trophic levels (ΔN), which are all needed to calculate trophic levels. The present study used a Markov Chain Monte Carlo method, with knowledge about the food web structure, which resulted in a dramatic increase in the precision in the TMF estimates. This also lead to a better understanding of the uncertainties in bioaccumulation measures; instead of using point estimates of TMF, the uncertainty can be quantified (i.e., TMF >1, namely positive biomagnification, with an estimated X % probability).