In all experiments, mortality was tallied after 48 hr. Control mortality was <5%. Average control mortality was 2.7%. At least 6 doses of each pesticide plus a control (water only) were tested in each replication per pesticide per bee species. Each replication included a total of 60–135 bees of each species depending on species' availability. Dose-mortality regressions were estimated assuming the normal distribution (i.e., probit model) with the computer program PoloPlus [47] as described by Robertson et al. [48] . We used a two-step procedure to analyze data for each chemical. In the first step, we examined plots of standardized residuals for outliers, which were then eliminated from the data sets. The second and final probit analysis was done to test hypotheses of parallelism (slopes not significantly different) and equality (slopes and intercepts not significantly different) with likelihood ratio tests [48] . PoloPlus also calculated lethal dose ratios (LDR's) of the most toxic chemical compared with all other chemicals for each species. An LDR provides a means to test whether two LD's are significantly different (i.e., when the 95% CI for the LDR did not include the value 1.0 [47] , [48] ).
For tests with a mixture, at least 5 doses of the mixture that bracketed 5–95% mortality were tested concurrently with experiments with at least 5 doses of individual mixture components. As before, 60–135 bees of each species were tested depending on species' availability. To test the hypothesis of independent joint action of fenbuconazole with acetamiprid or imidacloprid, we used the computer program PoloMix [49] . Assuming independent joint action of two mixture chemicals, test subjects can die of three possible causes. The first cause is natural mortality, with a probability po (a constant). The other two causes of mortality are the probabilities of mortalities for chemical 1 or chemical 2. For the first chemical, the probability of response (p1) is a function of dose D1. Usually, the probit or logit of dose X of chemical 1 is log(D1) (i.e., X1 = log[D1]). For the second chemical, the probability of response (p2) is a function of dose D2. If these three causes of mortality are independent, the probability of death (p) is p = p0+(1−p0)p1+(1−p0)(1−p1) p2. When each “+” sign means “or” and each product means “and,” this equation means that the total probability of death equals death from natural causes (p0), or no death from natural causes (1−p0) and death from the first chemical [e.g., (1−p0)p1], or no death from natural causes or from the first chemical [i.e., (1−p0)(1−p1)], but death from the second chemical [i.e., (1−p0)(1−p1) p2]. The χ2 statistic produced by PoloMix [49] was used to test the hypothesis of independent joint action. This test statistic is calculated by obtaining an estimate for the probability of mortality (p) for several dose levels of the two components and then comparing (the estimate of p) with the observed proportion killed at the corresponding dose levels. The three contributions to p are estimated separately. First, p0 is calculated as the proportional mortality observed in the control group. Next, p1 and p2 are estimated from bioassays of chemical 1 and chemical 2, with test statistics estimated from PoloPlus [47] .
For tests with a mixture, at least 5 doses of the mixture that bracketed 5–95% mortality were tested concurrently with experiments with at least 5 doses of individual mixture components. As before, 60–135 bees of each species were tested depending on species' availability. To test the hypothesis of independent joint action of fenbuconazole with acetamiprid or imidacloprid, we used the computer program PoloMix [49] . Assuming independent joint action of two mixture chemicals, test subjects can die of three possible causes. The first cause is natural mortality, with a probability po (a constant). The other two causes of mortality are the probabilities of mortalities for chemical 1 or chemical 2. For the first chemical, the probability of response (p1) is a function of dose D1. Usually, the probit or logit of dose X of chemical 1 is log(D1) (i.e., X1 = log[D1]). For the second chemical, the probability of response (p2) is a function of dose D2. If these three causes of mortality are independent, the probability of death (p) is p = p0+(1−p0)p1+(1−p0)(1−p1) p2. When each “+” sign means “or” and each product means “and,” this equation means that the total probability of death equals death from natural causes (p0), or no death from natural causes (1−p0) and death from the first chemical [e.g., (1−p0)p1], or no death from natural causes or from the first chemical [i.e., (1−p0)(1−p1)], but death from the second chemical [i.e., (1−p0)(1−p1) p2]. The χ2 statistic produced by PoloMix [49] was used to test the hypothesis of independent joint action. This test statistic is calculated by obtaining an estimate for the probability of mortality (p) for several dose levels of the two components and then comparing (the estimate of p) with the observed proportion killed at the corresponding dose levels. The three contributions to p are estimated separately. First, p0 is calculated as the proportional mortality observed in the control group. Next, p1 and p2 are estimated from bioassays of chemical 1 and chemical 2, with test statistics estimated from PoloPlus [47] .
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