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<br />106
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<br />D. W. BEYERS ET AL.
<br />
<br />that we used only two replicates per test concentration in ELS
<br />tests. Statistical power would have been increased had there
<br />been more replication, but other disadvantages of the hy-
<br />pothesis-testing approach (sensitivity to the selected level of
<br />significance, sensitivity to variability of data, and dependence
<br />on concentration interval) would not have been corrected.
<br />The influence of these factors has been thoroughly summa-
<br />rized by Stephan and Rogers [9J. Unlike regression analysis,
<br />hypothesis testing does not use concentration-response re-
<br />lations in toxicological data. Hypothesis testing uses a pair-
<br />wise comparison procedure to determine whether the
<br />difference between the mean response at a given concentration
<br />and the mean for the control is greater than the minimum sta-
<br />tistically significant difference. In contrast, linear-plateau
<br />regression uses all of the data to simultaneously estimate a
<br />threshold concentration. Regression analysis also has advan-
<br />tages of being designed to evaluate the relation between a de-
<br />pendent variable and a quantitative independent variable,
<br />and of providing parameter estimates for an equation that
<br />best describes the relation. The resulting equation can be used
<br />to interpolate effects to untested concentrations. Interpola-
<br />tion allows estimation of a concentration that corresponds
<br />to a specified magnitude of effect (e.g., concentration that
<br />produces a 50/0 reduction in growth) or the magnitude of ef-
<br />fect corresponding to a given concentration. The linear-pla-
<br />teau regression model is especially useful because it describes
<br />a concentration response and reflects that, for certain toxi-
<br />cants, there may be a threshold below which toxic effects are
<br />not observed.
<br />Justification for the linear-plateau regression model is
<br />based on the threshold concept [33,34J. A basic tenet of this
<br />concept is that toxic effects appear only when toxicant-
<br />induced changes in an organism exceed the ability of the or-
<br />ganism to compensate by homeostatic mechanisms. A variety
<br />of protective mechanisms have been identified in fish: me-
<br />tallothionein [35,36J, nonmetallothionein metal-binding pro-
<br />teins [37], induction of mixed-function oxidase system [38],
<br />and mucus barriers [39J. These mechanisms decrease toxic
<br />effects by sequestering, eliminating, or reducing absorption
<br />of toxicants; but they may be overwhelmed by high concen-
<br />trations or long-term exposure.
<br />In reality, a threshold model may not correctly represent
<br />the toxicology of carbaryl and malathion. A curvilinear
<br />model may be more appropriate, but aquatic toxicology data
<br />are often inadequate to describe higher order relationships.
<br />Given a mechanistic basis, a more complicated model may
<br />be justified; lacking this, a parsimonious model is preferred.
<br />Even if the concentration-response relation is higher order,
<br />a linear-plateau model may provide a relatively close approx-
<br />imation of the level of effect at any given concentration while
<br />providing an estimate of the concentration at which toxic ef-
<br />fects are first manifested.
<br />Nonlinear regression models are typically more difficult
<br />to specify and estimate than linear models. Recent improve-
<br />ments in statistical packages have increased the efficiency of
<br />nonlinear regression. We used the NUN procedure in SAS@
<br />[20]. A derivative-free approach called multivariate-secant
<br />or false-position method was especially useful because it did
<br />not require specification of partial derivatives of the model
<br />
<br />with respect to each parameter [4OJ. Other factors that prob-
<br />ably contributed to the success of our analyses were (a) use
<br />of a relatively simple regression model and (b) analysis of
<br />data that were distributed such that at least two treatment
<br />responses characterized plateau and concentration-response
<br />lines.
<br />Linear-plateau regression performed well for analysis of
<br />toxic effects on survival and growth of Colorado squawfish
<br />and bony tail. Linear-plateau regression models were in close
<br />agreement with the observed concentration response and ex-
<br />plained a significant amount of total experimental variation.
<br />There is evidence to support application of the threshold con-
<br />cept for study of toxic effects in fishes. Linear-plateau regres-
<br />sion is an alternative statistical method that is consistent with
<br />the threshold concept and has advantages of regression anal-
<br />ysis for study of concentration-response relations.
<br />
<br />Acknowledgement- We thank Peter J. Sikoski for his help through-
<br />out this study. DelWayne Nimmo, John D. Tessari, and James R.
<br />ZumBrunnen provided technical advice and assistance. Heidi T. Best-
<br />gen, William H. Clements, Peter M. Kiffney, and two anonymous
<br />reviewers provided comments that improved the manuscript. This
<br />study was supported by a cooperative agreement with the Grasshop-
<br />per Integrated Pest Management Project of the U.S. Department of
<br />Agriculture-Animal and Plant Health Inspection Service, Lowell
<br />C. McEwen, principal investigator.
<br />
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