Mathematical Modeling of Allelopathy. III. A Model for Curve-Fitting Allelochemical Dose Responses

Bioassay techniques are often used to study the effects of allelochemicals on plant processes, and it is generally observed that the processes are stimulated at low allelochemical concentrations and inhibited as the concentrations increase. A simple empirical model is presented to analyze this type of response. The stimulation-inhibition properties of allelochemical-dose responses can be described by the parameters in the model. The indices, p% reductions, are calculated to assess the allelochemical effects. The model is compared with experimental data for the response of lettuce seedling growth to Centaurepensin, the olfactory response of weevil larvae to alpha-terpineol, and the responses of annual ryegrass (Lolium multiflorum Lam.), creeping red fescue (Festuca rubra L., cv. Ensylva), Kentucky bluegrass (Poa pratensis L., cv. Kenblue), perennial ryegrass (L. perenne L., cv. Manhattan), and Rebel tall fescue (F. arundinacea Schreb) seedling growth to leachates of Rebel and Kentucky 31 tall fescue. The results show that the model gives a good description to observations and can be used to fit a wide range of dose responses. Assessments of the effects of leachates of Rebel and Kentucky 31 tall fescue clearly differentiate the properties of the allelopathic sources and the relative sensitivities of indicators such as the length of root and leaf.