A Bayesian mixture model for estimating intergeneration chronic toxicity

Environ Sci Technol. 2008 Nov 1;42(21):8108-14. doi: 10.1021/es801030t.


Understanding toxic effects on biological populations across generations is crucial for determining the long-term consequences of chemical pollution in aquatic environments. As a consequence, there is considerable demand for suitable statistical methods to analyze complex multigeneration experimental data. We demonstrate the application of a Bayesian mixture model (with random-effects) to assess the effect of intergeneration copper (Cu) exposure on the reproductive output of the copepod, Tigriopus japonicus, using experimental data across three generations. The model allowed us to appropriately specify the nonstandard statistical distribution of the data and account for correlations among data points. The approach ensured more robust inferences than standard statistical methods and, because of the model's mechanistic formulation, enabled us to test more subtle hypotheses. We demonstrate intergeneration Cu exposure effects on both components of reproductive output (1) the ovisac maturation rate, and (2) the number of nauplii per ovisac. Current and parent generation Cu exposures negatively affected current generation reproductive output However, in terms of reproductive output, there was also some evidence for adaptation to parental Cu exposures, but with an associated cost under Cu concentrations different from the parental exposure. Bayesian mixture and random-effects models present a robust framework for analyzing data of this kind and for better understanding chemical toxicity.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Bayes Theorem
  • Copepoda / drug effects
  • Copper / toxicity
  • Electricity
  • Models, Biological*
  • Reproduction / drug effects
  • Toxicity Tests, Chronic*


  • Copper