#### Abstract

Crop scientists and government regulators are interested in mediating pollen flow from transgenic crops to other crops and weed species. To this end, a multi-year, multilocation series of experiments was conducted in eastern Colorado by the Department of Soil and Crop Sciences at Colorado State University. These experiments were done to estimate the distance required between plots of transgenic corn and wheat and plots of the respective non-transgenic crop to obtain at most a regulated limit of cross-pollination. The experiments involved planting a rectangle of transgenic crop in the middle of a non-transgenic field and measuring the proportion of cross-pollinated crop at various distances along transects radiating in multiple directions. Gene flow to the non-transgenic crop was evaluated in wheat using herbicide tolerance and in corn using kernel color. An initial Generalized Linear Mixed Model with binomial response and logit link was estimated with independent variables: a square root transformation of distance, an additional covariate, and a random location effect. For corn, the additional covariate was transect orientation; for wheat, it was the relative heading time of the recipient variety. An enhanced model that included additional sources of variation was also examined. The analysis for both of these assumed models addresses two problems: 1) an Upper Tolerance Limit on the binomial probability of cross-pollination, which includes 100c% of the locations with 100d% confidence, at set values of the independent variables; and 2) an Upper Tolerance Limit on the distance at which 100c% of the locations will have binomial probability of cross-pollination less than a specified value, with 100d% confidence, at set values of the other independent variables. The problems are addressed using Frequentist and Bayesian methods.

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TOLERANCE INTERVALS FOR GENE FLOW RATES FROM TRANSGENIC TO NON-TRANSGENIC WHEAT AND CORN USING A LOGISTIC REGRESSION MODEL WITH RANDOM LOCATION EFFECTS

Crop scientists and government regulators are interested in mediating pollen flow from transgenic crops to other crops and weed species. To this end, a multi-year, multilocation series of experiments was conducted in eastern Colorado by the Department of Soil and Crop Sciences at Colorado State University. These experiments were done to estimate the distance required between plots of transgenic corn and wheat and plots of the respective non-transgenic crop to obtain at most a regulated limit of cross-pollination. The experiments involved planting a rectangle of transgenic crop in the middle of a non-transgenic field and measuring the proportion of cross-pollinated crop at various distances along transects radiating in multiple directions. Gene flow to the non-transgenic crop was evaluated in wheat using herbicide tolerance and in corn using kernel color. An initial Generalized Linear Mixed Model with binomial response and logit link was estimated with independent variables: a square root transformation of distance, an additional covariate, and a random location effect. For corn, the additional covariate was transect orientation; for wheat, it was the relative heading time of the recipient variety. An enhanced model that included additional sources of variation was also examined. The analysis for both of these assumed models addresses two problems: 1) an Upper Tolerance Limit on the binomial probability of cross-pollination, which includes 100c% of the locations with 100d% confidence, at set values of the independent variables; and 2) an Upper Tolerance Limit on the distance at which 100c% of the locations will have binomial probability of cross-pollination less than a specified value, with 100d% confidence, at set values of the other independent variables. The problems are addressed using Frequentist and Bayesian methods.