Abstract.A new hypothesis, the Climax Hypothesis, is proposed to describe how the ratios of individual chemicals influence the joint effects of chemical mixtures. This hypothesis is derived from a generalized approach using ''isobolograms.'' With this hypothesis, one can predict that for a given mixture, a curvilinear correlation exists between the joint effects and the ratios of individual chemicals and that this curve has a climax at the equitoxic ratio. This prediction is supported by the observed toxicity to Vibrio fischeri of 18 mixtures (12 binary mixtures, 4 ternary mixtures, and 2 quaternary mixtures). With this prediction, the Climax Hypothesis has some promising applications such as controlling the discharge of effluents in environmental science, maximizing detoxifying effects in medicine, and optimizing combined pesticides in agriculture.Increasing concern over the usual exposure to multiple rather than to single chemicals has promoted investigations into the joint effects of chemical mixtures. Because of the flood of chemical pollutants, it is not feasible to test the toxicity of all mixtures at all ratios. Understanding of the rules for joint toxic effects is therefore necessary.As is well known, the joint effects of chemical mixtures can be qualitatively described as simple addition, synergism, antagonism, or independent action (Placket and Hewlett 1967; Xu and Nirmalakhandan 1998) as follows: (1) simple addition: ideal additive effects are observed when the joint toxic response is equal to the sum of the individual chemical toxicities; (2) synergism: more than addition, the combined effect is greater than the sum of the toxicities of the individual chemicals; (3) antagonism: less than addition, the overall toxic effect is less than the sum of the toxicities of the individual chemicals; and (4) independent action: the joint toxic effect is equal to that caused by the individual chemical with the greatest toxicity. To further quantitatively assess the degree of joint effect, three indicators have been proposed by toxicologists: toxic units (TU); the additive index (AI); and the mixture toxicity index (MTI) (Sprague and Ramsay 1965;Marking 1977;Kçnemann 1981). Definitions and uses of these concepts are listed in Table 1 As pointed out by toxicologists (Chen and Huang 1996), the joint effect depends on both the slopes and the ratios of the individual toxicants. The influence of the slopes for the individual toxicants on the joint effect was demonstrated by Chen and Huang (1996). Based on the slope, they successfully derived some criteria to qualitatively predict the likelihood of occurrence of joint effects in mixture toxicity. However, these criteria cannot provide quantitative predictions of the degree of joint effect (Chen and Huang 1996). As for the ratio of individual chemicals, many studies have found that this did influence the joint effect of a chemical mixture (Dong and Feng 1994). However, it remains unclear how the ratio influences the joint effect and whether its influence is quantitative....