Modeling the Effect of Density-Dependent Chemical Interference upon Seed Germination

A mathematical model is presented to estimate the effects of phytochemicals on seed germination. According to the model, phytochemicals tend to prevent germination at low seed densities. The model predicts that at high seed densities they may increase the probability of seed germination and the number of germinating seeds. Hence, the effects are reminiscent of the density-dependent effects of allelochemicals on plant growth, but the involved variables are germination probability and seedling number. The results imply that it should be possible to bypass inhibitory effects of allelopathy in certain agricultural practices and to increase the efficiency of nature conservation in several plant communities.

Mathematical Modelling of Allelopathy: IV. Assessment of Contributions of Competition and Allelopathy to Interference by Barley

One of the main challenges to the research on allelopathy is technically the separation of allelopathic effect from competition, and quantitatively, the assessment of the contribution of each component to overall interference. A simple mathematical model is proposed to calculate the contribution of allelopathy and competition to interference. As an example of applying the quantitative model to interference by barley ( Hordeum vulgare cv. Triumph), the approach used was an addition of allelopathic effect, by an equivalent amount, to the environment of the test plant (white mustard, Sinapis alba), rather than elimination of competition. Experiments were conducted in glasshouse to determine the magnitude of the contributions of allelopathy and competition to interference by barley. The leachates of living barley roots significantly reduced the total dry weight of white mustard. The model involved the calculation of adjusted densities to an equivalent basis for modelling the contribution of allelopathy and competition to total interference. The results showed that allelopathy contributed 40%, 37% and 43% to interference by barley at 6, 12 and 18 white mustard pot−1. The consistency in magnitude of the calculated contribution of allelopathic effect by barley across various densities of receiver plant suggested that the adjusted equivalent density is effective and that the model is able to assess the contribution of each component of interference regardless of the density of receiver plant.

Implementation of Card: Curve-Fitting Allelochemical Response Data

Bioassay techniques are essential methods used to study the effects of allelochemicals on plant processes. It is often observed that the biological processes are stimulated at low allelochemical concentrations and inhibited as the concentrations increase. Liu et al., (2003) developed a simple model to fit this type of allelochemical response data. Based on the model, CARD (curve fitting allelochemical response data) was developed as a Windows based program that can be used to fit a stimulation-inhibition response data. An example of using CARD is given.

Whole-Range Assessment: A Simple Method for Analysing Allelopathic Dose-Response Data

Based on the typical biological responses of an organism to allelochemicals (hormesis), concepts of whole-range assessment and inhibition index were developed for improved analysis of allelopathic data. Examples of their application are presented using data drawn from the literature. The method is concise and comprehensive, and makes data grouping and multiple comparisons simple, logical, and possible. It improves data interpretation, enhances research outcomes, and is a statistically efficient summary of the plant response profiles.

Dose-Response—A Challenge for Allelopathy?

The response of an organism to a chemical depends, among other things, on the dose. Nonlinear dose-response relationships occur across a broad range of research fields, and are a well established tool to describe the basic mechanisms of phytotoxicity. The responses of plants to allelochemicals as biosynthesized phytotoxins, relate as well to nonlinearity and, thus, allelopathic effects can be adequately quantified by nonlinear mathematical modeling. The current paper applies the concept of nonlinearity to assorted aspects of allelopathy within several bioassays and reveals their analysis by nonlinear regression models. Procedures for a valid comparison of effective doses between different allelopathic interactions are presented for both, inhibitory and stimulatory effects. The dose-response applications measure and compare the responses produced by pure allelochemicals [scopoletin (7-hydroxy-6-methoxy-2 H-1-benzopyran-2-one); DIBOA (2,4-dihydroxy-2 H-1,4-benzoxaxin-3(4 H)-one); BOA (benzoxazolin-2(3 H)-one); MBOA (6-methoxy-benzoxazolin-2(3 H)-one)], involved in allelopathy of grain crops, to demonstrate how some general principles of dose responses also relate to allelopathy. Hereupon, dose-response applications with living donor plants demonstrate the validity of these principles for density-dependent phytotoxicity of allelochemicals produced and released by living plants ( Avena sativa L., Secale cereale L., Triticum L. spp.), and reveal the use of such experiments for initial considerations about basic principles of allelopathy. Results confirm that nonlinearity applies to allelopathy, and the study of allelopathic effects in dose-response experiments allows for new and challenging insights into allelopathic interactions.