Statistical Tests for Hormesis and Effective Dosages in Herbicide Dose Response

The log-logistic model is a popular candidate for modeling dose response in agronomy. One of its limitations is monotonicity: the response is either continuously increasing or decreasing with changes in dosage. In herbicide dose response investigations, authors have previously noted an increase in biomass or growth for subinhibitory dosages. This hormetic effect, if ignored, can lead to substantial bias in estimates of effective dosages and can distort inferences about the differential effects of experimental treatments. We present an extension of a model capable of modeling hormetic effects that allows inference about effective dosages. Furthermore, the model can be used to compare effective dosages among different treatments if hormetic effects are present for some and absent for others and provides appropriate estimates of rates of change. In a designed experiment where velvetleaf (Abutilon theophrasti Medikus) and barnyardgrass [Echinochloa crus-galli (L.) P. Beauv.] were treated with glyphosate [isopropylamine salt of N-(phosphonomethyl)glycine] + (NH 4 ) 2 SO 4 or glufosinate [2-amino-4-(hydroxymethylphosphinyl)butanoic acid] (NH 4 ) 2 SO 4 at various rates, hormetic effects were found for barnyardgrass treated with glyphosate but not with glufosinate. Procedures for a valid comparison of effective dosages between the two herbicides are presented. Software code to perform the analyses is given in an appendix.