Joint Action Analysis Utilizing Concentration Addition and Independent Action Models

Abstract

In weed science literature, models such as concentration addition, independent action, effect summation, and the parallel line assay technique have been used to predict and analyze whole-plant response to herbicide mixtures. Although a joint action reference model is necessary for determining whether the herbicide mixture provides less than (antagonistic), equal to (zero-interaction or additive), or greater than (synergistic) expected control, model selection often occurs with little regard to the model's underlying biological assumptions. The joint action models of concentration addition (CA) and independent action (IA) are the appropriate models to consider for analysis of herbicide mixtures of two active components. CA assumes additivity of dose, with herbicides differing only in potency, whereas IA assumes multiplicativity of effects, in which herbicides behave independently and sequentially within the plant. CA and IA predicted mixture responses were computed for a sample mixture data set of mesotrione plus atrazine. IA predicted lower mixture responses than CA; for example, mesotrione at 17.5 g ha−1+ atrazine at 140 g ha−1was predicted to provide 45% (IA) compared with 53% (CA) control of Palmer amaranth. Joint action claims of synergism and antagonism were shown to be dependent on the reference model selected. Although mesotrione plus atrazine combinations were synergistic under IA assumptions, analysis under CA assumptions indicated mesotrione plus atrazine to be synergistic, additive, and antagonistic according to the selected effective concentration (ECx) level and fixed-ratio mixture. Because it is not possible to determine the appropriate joint action model on the basis of fit of predicted to observed mixture data, the appropriateness of underlying biological assumptions was considered for the sample mixture data set. Additionally, we provide decision criteria to aid researchers in their selection of an appropriate joint action reference model.