The study of a Daphnia population model suggests that sublethal effects of nonpolar narcotics on growth of individual organisms can result in ultimate extinction of the population at chronic chemical concentrations near the effect concentration that leads to a 50% reduction in individual growth (the 16-d EC50 for growth). A quantitative dose-response relationship (QDRR)--a population extinction threshold, relating the minimal chronic chemical concentration that yields population persistence and the octanol/water partition coefficient (K(ow))--is generated from numerical simulation studies of a Daphnia population model. The transition from population persistence to extinction is examined in terms of density functions in the lipid, structure, and age variables associated with models of individual daphnids. The densities of populations undergoing transition from persistence to extinction due to increased toxicity suggest that critically stressed populations are age-bimodal with a component of old, large individuals and a component of small, nonreproductive individuals. The populations that persist near the threshold for extinction are unexpectedly diverse in age density and consist of relatively small individuals. (Copyright (c) 1993 SETAC.)