Temporal variability and ignorance in Monte Carlo contaminant bioaccumulation models: a case study with selenium in...

Although the parameters for contaminant bioaccumulation models most likely vary over time, lack of data makes it impossible to quantify this variability. As a consequence, Monte Carlo models of contaminant bioaccumulation often treat all parameters as having fixed true values that are unknown. This can lead to biased distributions of predicted contaminant concentrations. This article demonstrates this phenomenon with a case study of selenium accumulation in the mussel Mytilus edulis in San Francisco Bay. "Ignorance-only" simulations (in which phytoplankton and bioavailable selenium concentrations are constant over time, but sampled from distributions of field measurements taken at different times), which an analyst might be forced to use due to lack of data, were compared with "variability and ignorance" simulations (sampling phytoplankton and bioavailable selenium concentrations each month). It was found that ignorance-only simulations may underestimate or overestimate the median predicted contaminant concentration at any time, relative to variability and ignorance simulations. However, over a long enough time period (such as the complete seasonal cycle in a seasonal model), treating temporal variability as if it were ignorance at least gave a range of predicted concentrations that enclosed the range predicted by explicit treatment of temporal variability. Comparing the temporal variability in field data with that predicted by simulations may indicate whether the right amount of temporal variability is being included in input variables. Sensitivity analysis combined with biological knowledge suggests which parameters might make important contributions to temporal variability. Temporal variability is potentially more complicated to deal with than other types of stochastic variability, because of the range of time scales over which parameters may vary.