The usefulness of a mathematical model of exposure for environmental risk assessment

We respond to the Comment of Lang et al. [1] regarding our mathematical model [2] of exposure of non-target Lepidoptera to Bt-maize pollen expressing Cry1Ab within Europe. Lang et al. remark on the degree to which the model was subject to uncertainty. Perry et al. [2] did indeed emphasize precaution: they made four separate decisions to model worst-case scenarios; identified six distinct sources of variability to which their results might be sensitive; and emphasized six different bases for the uncertainty of predictions. Lang et al. rightly emphasize the importance of identifying to which parameters the results of a model are most sensitive; Perry et al. should perhaps have emphasized more that the parameter to which their estimates of mortality were most sensitive was undoubtedly the variable measuring the rate of change of mortality with concentration/dose of the Cry1Ab protein (i.e. the slope of the probit/logit regression line; see below). Regarding the relationship between the toxicity of MON810 and Bt176 pollen, Lang et al. imply that the relationship between mortality and dose may be nonlinear. Regressions from bioassay should always be checked for nonlinearity, but there was no evidence of this in any of the extensive number of regressions of Saeglitz et al. [3,4] upon which our slope estimate was based. Of course, the standard transformation of mortality to probits (or logits) and the logarithmic transformation of concentration [5,6] are designed to achieve a linear regression; both papers cited by Lang et al. use this method. Data from one of these papers [7] were tested for nonlinearity; none was found, and no disproportionally higher mortality at low Cry1Ab concentrations could be verified (figure 1). Lang et al. are correct that Perry et al. used the range of published [8,9] values (12.2 – 78.9) to derive an average of the ratio of the concentration of the Cry1Ab protein expressed in pollen of maize Bt176 relative to that in maize MON810 for which a 31.05-fold difference was assumed. This is already likely to be a worst-case underestimate because, as Sears et al. [8] noted, the value of expression for MON810 was near the current level of detection by immunoassay. We do not agree with Lang et al.'s interpretation of the data from Nguyen [10]: they compared the smallest Bt176 value from 2002 to the largest MON810 value from 2003. The within-year ratio of Bt176 : MON810 was 64.8 in 2002 and 30.5 in …