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Analysis of Synergistic and Antagonistic Effects of Herbicides Using Nonlinear Mixed-Model Methodology1

When herbicides are applied in mixture, and infestation by weeds is less than expected compared with when herbicides are applied alone, a synergistic effect is said to exist. The inverse response is described as being antagonistic. However, if the expected response is defined as a multiplicative, nonlinear function of the means for the herbicides when applied alone, then standard linear model methodology for tests of hypotheses does not apply directly. Consequently, nonlinear mixed-model methodology was explored using the nonlinear mixed-model procedure (PROC NLMIXED) of SAS System®. Generality of the methodology is illustrated using data from a randomized block design with repeated measures in time. Nonlinear mixed-model estimates and tests of synergistic and antagonistic effects were more sensitive in detecting significance, and PROC NLMIXED was a versatile tool for implementation. Additional index words: Least significant difference, linear mixed models, repeated measures, tank mixture. Abbreviations: DAT, days after treatment; GH, glufosinate plus mixture herbicide; GHD, glufosinate plus mixture herbicide by DAT; ML, maximum likelihood; MSE, mean square error; Rep, replication.