Meta-analysis of intrinsic rates of increase and carrying capacity of populations affected by toxic and other stressors

Most of the thousands of substances and species that are of concern for environmental management will not be investigated empirically at ecologically relevant levels because of financial, practical, and ethical constraints. To allow risk assessment for these less well-known categories, we have developed a mechanistic model with classical equations from toxicology and ecology. The parameters are linked to well-known properties, such as the octanol-water partition ratio K-ow, acute lethal (body) concentrations, and organism size. This allows estimation of intrinsic rates of increase r and carrying capacity K over a wide range of substances and species. The model was calibrated with parameter values (mu +/- 95% confidence interval) obtained in reviews and validated by a meta-analysis with largely independent data from 200 laboratory experiments. For single substances, the 5 to 95% interval of the observations on intrinsic rates of increase overlapped with the range predicted by the model. Model and experiments independently indicated that population growth ceased below 1% of the acute median lethal concentration in about 5% of the cases. Exceptional values and possible explanations were identified. The reduction of the carrying capacity K was nearly proportional to the inhibition of the population growth r. Population-level effects of mixtures as estimated by concentration addition were confirmed by observations in the experiments. The impact of a toxicant and another stressor could generally be described by response multiplication, with the exception of cases with extreme stress. Data sets on population laboratory experiments are biased to metals and crustaceans. This field will benefit from empirical studies on chemicals, conditions, and species, identified as risky by the model. Other implications of the model for environmental management and research are discussed.