John Wiley & Sons, Ltd.

Mathematical relationships between metrics of chemical bioaccumulation in fish

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Five widely used metrics of bioaccumulation in fish are defined and discussed, namely the octanol‐water partition coefficient (KOW), bioconcentration factor (BCF), bioaccumulation factor (BAF), biomagnification factor (BMF) and trophic magnification factor (TMF). Algebraic relationships between these metrics are developed and discussed using conventional expressions for chemical uptake from water and food and first order losses by respiration, egestion, biotransformation and growth dilution. It is shown that twoBCFs may be defined, namelyas an equilibrium partition coefficient KFW or as a non‐equilibrium BCFK in which egestion losses are included. BAFs are shown to be the product of the BCFK and a novel “equilibrium multiplier” M containing two ratios, namely the diet to water concentration ratio and the ratio of uptake rate constants for respiration and dietary uptake. BMFs are shown to be proportional to the lipid normalized ratio of the predator/prey values of BCFK and the ratio of the equilibrium multipliers. Relationships with TMFs are also discussed. The effects of chemical hydrophobicity, biotransformation and growth are evaluated by applying the relationships to a range of illustrative chemicals of varying KOW in a linear four trophic level food web with typical values for uptake and loss rate constants. The roles of respiratory and dietary intakes are demonstrated and it is shown thateven slow rates of biotransformation and growth can significantly affect bioaccumulation. BCFKs and the values of M can be regarded as the fundamental determinants of bioaccumulation and biomagnification in aquatic food webs. Analyzing data from food webs can be enhanced by plotting logarithmic lipid normalized concentrations or fugacities as a linear function of trophic level to deduce TMFs. Implications for determining bioaccumulation by laboratory tests for regulatory purposes are discussed. Environ. Toxicol. Chem. © 2013 SETAC

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