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 pop ulation-level effects of Chemicals in terms of the intrinsic rate of popula tion growth (r). Among the examined concentration-r functions, the power fu nction model, that is, r(x) = r(0)[1 - (x/alpha)(beta)], in which x is the exposure concentration and alpha and beta are parameters, performed with th e best fit to each data set. The power function model is characterized by t wo parameters representing the absolute Value of toxicity, alpha, and the c urvature of responses, beta. The bootstrap simulation, conducted on the ent ire data set consisting of all published data that we collected, indicated that the observed variance of beta among actual data sets could be mostly e xplained by the random error variation generated from the bootstrap resampl ings. The generic beta value, determined from the entire data set and expec ted to denote the best estimate of beta if the variability of beta was comp letely 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.