Model selection and parameterization of the concentration-response functions for population-level effects

As concentration–response functions for chronic population‐level effects of pollutant chemicals, three mathematical models were presented and examined for goodness of fit to published toxicological data that estimated the population‐level effects of chemicals in terms of the intrinsic rate of population growth (r). Among the examined concentration–r functions, the power function model, that is, r(x) = r(0)[1 – (x/a)β], in which x is the exposure concentration and α and β are parameters, performed with the best fit to each data set. The power function model is characterized by two parameters representing the absolute value of toxicity, α, and the curvature of responses, β. The bootstrap simulation, conducted on the entire data set consisting of all published data that we collected, indicated that the observed variance of β among actual data sets could be mostly explained by the random error variation generated from the bootstrap resamplings. The generic β value, determined from the entire data set and expected to denote the best estimate of β if the variability of β was completely due to random sampling error, was estimated as 1.84. It was implied that the response of the intrinsic rate of natural increase (r) to chemical exposure was nearly quadratic in many cases.