A General Multivariate Dose–Response Model

This paper presents a general model for describing and predicting biological response to environmental factors. The theory embraces concepts and models used in earlier studies of the effects of toxicity on fish, and it extends these ideas in several directions. It can include an arbitrary number of factors, either detrimental or beneficial to the organism. Also, its statistical formulation allows (1) hypothesis testing to determine the relative importance of various factors and (2) calculation of critical factor levels that (with prescribed confidence) assure a community response no worse than a specified level. Our model is based on earlier work by Schnute and McKinnell, and, like theirs, its parameters have biologically meaningful interpretations. Our discussion includes an explanation of how the model relates specifically to toxicity studies. In a companion paper (Can. J. Fish. Aquat. Sci. 43: 1694–1709), we use our model to investigate salmonid response to gas supersaturation and ancillary factors.