Bayesian estimation of kinetic rate constants in a food-web model of polycyclic aromatic hydrocarbon bioaccumulation

Abstract Water, sediments, fish and other biota were sampled from fixed stations along bayous in the LaBranche Wetlands of Louisiana as part of an environmental contamination study in 1996 and 1997. In order to understand the biological fate of some of these contaminants, a spotted gar ( Lepisosteus oculatus ) food-web model was developed from site-specific data and established bioaccumulation modeling assumptions. Based on gut contents analysis, the gar were found to feed on terrestrial arthropods, a variety of small fish, aquatic insects, crayfish and grass shrimp. A Bayesian approach (a hierarchical model and Markov Chain Monte Carlo simulation) was used to estimate the kinetic rate constants of uptake from water, dietary uptake and total elimination for the food-web model using site-specific measurements of naphthalene, phenanthrene, and benzanthracene concentrations, reference literature inputs, and a hierarchical statistical model. This iterative simulation method resulted in a distribution of the parameters for each chemical comprised of the last 3000 values from four separate Markov Chains of length 15,000–25,000 iterations. The posterior parameter values were found to be consistent with rate constants published in the literature for various fish species, and were used to determine distributions of predicted gar PAH concentrations.