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CARD: curve-fitting allelochemical response data

De Li Liu1,2 and Min An2,3

1Wagga Wagga Agricultural Institute, NSW DPI, PMB, Wagga Wagga, NSW 2650, Australia,,
Wagga Wagga Agricultural Innovation Park, (CSU & NSW DPI), Wagga Wagga, NSW 2650, Australia
Environmental and Analytical Laboratories, Charles University, Wagga Wagga, NSW 2678,


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. Liu et al. (2003) developed a simple model to fit this type of allelochemical response data. Based on this model, CARD is developed as a Microsoft Windows based program that can be easily used to fit the stimulation-inhibition response data. The fitted parameters and statistical properties are output in text file or on the screen and the comparison between the fitted and observed values can be viewed graphically.

Key Words

Allelopathy, CARD, modelling, computer software, stimulation-inhibition response


Bioassay techniques are widely used for quantitative determination of biological responses to allelochemicals. Leather and Einhellig (1986, 1988) have extensively reviewed the nature and types of bioassay techniques used in studies of allelopathy. It is generally found that allelochemicals exhibit stimulation at low concentrations and inhibition at high concentrations (Lovett et al. 1989). The allelopathy dose-response relationship has, usually, an inverted U-shape but other kinds of response are also often found, such as absence of stimulation.

Several models have been proposed to describe allelochemical dose-response relationships. A log-logistic equation (Finney 1979) was used in studying the allelopathic potential of wheat (Triticum aestivum L.) to fit the root length of annual ryegrass (Lolium rigidum) to wheat sowing density (Wu et al. 2000). The log-logistic equation is widely used in herbicide dose response, but it does not feature stimulation at low doses. Brain and Cousens (1989) modified the log-logistic equation and presented a model that can account for the stimulative responses. An et al. (1993) presented a model, based on enzyme kinetics, which includes the feature of stimulation, but it is not possible to fit the observed data statistically. Dias (2001) used a Weibull function to fit allelochemical effects on germination process, but the Weibull function, like many other equations, does not possess the feature of stimulation. Liu et al. (2003) developed a highly flexible but simple equation for describing the general pattern of stimulation-inhibition in dose-responses of allelochemicals. Even though the equation is simple, the calculation is quite time-consuming as it involves the determination of the number of ln-transformation that gives the best fit of the model to observed data. This paper introduces the Windows based programm, CARD, that can be used to fit the stimulation-inhibition response curves, based on the model described by Liu et al. (2003).

The Software

CARD is written in Visual Basic 6. The input data file is a two-column text-format file. The first column (X-axis) is “dose” and the second column (Y-axis) is the corresponding observation for the response to the dose. The data files are named with an extension of *.ARD which can be selected by press button “Get Data File”, shown in Figure 1.

The statistical results are shown on screen and are written into a file named as *.TXT. The labels for axis can be input from text boxes, Graphical labels. CARD runs and determines the best number of ln-transformation. The best fitted coefficients, α and β are reported with standard errors and t-test for the statistical tests of the fitted parameters. Coefficient of determination (R2), F-test, root mean square error (RMSE) (Janssen and Heuberger 1995) and model efficiency (ME) (Nash and Sutcliffe 1970) are calculated. R2 and F-test are based on a multiple linear regression with the transformed data, while RMSE and ME are, respectively, defined as:


where O is the observed response value, P is the predicted response value. Ō is the mean of observed response values. It should be noted that the ME and R2 have identical values.

Figure 1. The input data is in a two-column text formatted file (top right) and the files are named as *.ARD (top left).

The maximum value of stimulation and the dose at which the maximum stimulation is researched are reported (Figure 2). The doses for p% reduction are also calculated. While p = 0, 50 and 100 are reported, user can select a p% from a dropdown menu for calculating the corresponding dose. The dose for 50% reduction is suggested as a measure of the inhibition potency of an allelochemical or the sensitivity of the testing organism to the allelochemical (Liu et al. 2003).

The user can view the graphics showing the observed and predicted values with both actual doses and transformed doses (g(D), see Liu et al. 2003). While at the default, the predictions at the best fitted ln-transformation are plotted and the user can view the predicted and observed values with a given number of ln-transformations.

The predictions with various values of doses are also calculated and listed on screen and in the output file.

Results and Discussion

CARD is a simple but useful program, for example, if one wants to fit dose-response data to the model described by Liu et al. (2003). The data of Selander et al. (1974) are used for an example (Figure 2). R2 and ME reached the highest value of 0.99 at the 4th ln-transformations. CARD calculates additional 4 ln-transformations after the best number of transformations is determined. At the best number of transformations the RMSE is the smallest, while the value of R2, ME and F-test are the highest. Further increase in ln-transformation will increase RMSE and decrease R2, ME and F-test. The criterion for determination of the best number of ln-transformations was detailed by Liu et al. (2003).

While allelochemicals possess the nature of stimulation and inhibition, depending on concentrations, the shape of curves for stimulation-inhibition behaviour varies, depending on the nature of allelochemicals and the biological activities of receivers. The most important feature of the model described by Liu et al. (2003) is that the ln(D+1) cumulative transformations gave various sharps and at any number of cumulative ln-transformations the control remains the value of zero, where D is doses. In addition, after each ln-transformation, the model remains a simple quadratic equation, which can be fitted by a standard multiple linear regression. Because of this feature, CARD can be developed to fit the nonlinear relationship by a linear least squares regression.

Figure 2. The observed and fitted values are compared, statistical results are shown and options can be selected in CARD.

CARD on a CD Rom is available from “CARD Request, NSW DPI, Wagga Wagga Agricultural Institute, PMB, Wagga Wagga, NSW 2650, Australia” at the cost of $15 for material, postaage and handing, or email to the author for a free electronic copy. The setup for installation is simple and easy to use.


An M, Johnson IR, and Lovett JV. 1993. Mathematical modelling of allelopathy: Biological response to allelochemicals and its interpretation. Journal of Chemical Ecology 19, 2379-2388.

Brain P, and Cousens R. 1989. An equation to describe dose responses where there is stimulation of growth at low doses. Weed Res 29:93-96.

Dias L. 2001. Describing phytotoxic effects on cumulative germination. Journal of Chemical Ecology 27, 411-418.

Finney Y. 1979. Bioassay and the practice of statistical inference. Int. Statistical Review 47, 1-12.

Janssen, P.H.M. and Heuberger, P.S.C., 1995. Calibration of process-oriented models. Ecological Modelling 83, 55-66.

Leather G.R. and Einhellig F.A. 1986. Bioassay in the study of allelopathy. In: Putnam AR and Tang CS (ed), The Science of Allelopathy, pp 133-145. John Wiley and Sons, New York.

Leather GR, and Einhellig FA. 1988. Bioassay of naturally occurring allelochemicals for phytotoxicity. Journal of Chemical Ecology 14, 1821-1828.

Liu, D.L., M. An, I.R. Johnson and J.V. Lovett. 2003. Mathematical modelling of allelopathy. III. A model for curve-fitting allelochemical dose responses. Nonlinearity in Biology, Toxicology, and medicine: 1(1), 37-50.

Lovett JV, Ryuntyu MY, and Liu DL. 1989. Allelopathy, chemical communication, and plant defense. Journal of Chemical Ecology 15, 1193-1201.

Nash, J.E., and Sutcliffe, J.V., 1970. Rever flow forecasting through conceptual models. Part I. A discussion of principles. Journal of Hydrology 10, 282-290.

Selander, J. Kalo, P. Kangas, E. and Pertunnen, V. 1974. Olfactory behaviours of Hylobium abietis L. (Col., Curculionidae). I. Response to several terpenoid fractions isolated from Scots pine phloem. Ann. Entom. Fenn. 40, 108-115.

Wu H, Pratley J, Lemerle D, and Haig T. 2000. Laboratory screening for allelopathic potential of wheat (Triticum aestivum) accessions against annual ryegrass (Lolium rigidum). Australian Journal of Agricultural Research 51, 259-266.

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