Skip to main content Accessibility help

Joint Action Analysis Utilizing Concentration Addition and Independent Action Models

  • Julie A. Abendroth (a1), Erin E. Blankenship (a2), Alex R. Martin (a3) and Fred W. Roeth (a3)


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−1 was 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 (EC x ) 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.

En la literatura de la ciencia de las malezas, modelos tales como el de adición de concentración, acción independiente, la suma de los efectos y la técnica de prueba de líneas paralelas se han usado para predecir y analizar la respuesta de toda la planta a la mezcla de herbicidas. Mientras que se necesita un modelo de acción conjunta de referencia para determinar si la mezcla de herbicida proporciona menos que (antagónico), igual a (cero interacción o aditivo) o mayor que (sinérgico) el control esperado, frecuentemente la selección del modelo se hace considerando poco las suposiciones biológicas subyacentes del modelo. Los modelos de acción conjunta de adición de concentración (CA) y acción independiente (IA) son los apropiados a considerar para los análisis de mezclas de herbicidas de dos componentes activos. El CA supone un efecto aditivo de dosis, con herbicidas que difieren solamente en potencia, mientras que IA supone un efecto multiplicativo en el que los herbicidas se comportan independientemente y secuencialmente dentro de la planta. Las respuestas de las mezclas predichas en los modelos CA e IA se computaron para una muestra de datos de una mezcla de mesotrione + atrazine. IA pronosticó respuestas a la mezcla más bajas que CA; por ejemplo, se estimó que mesotrione a 17.5 g/ha + atrazine a 140 g/ha proporcionaría un control de Amaranthus palmeri de 45% (IA) versus 53% (CA). Las predicciones de acción conjunta como sinergismo y antagonismo mostraron depender del modelo de referencia seleccionado. Mientras las combinaciones de mesotrione + atrazine resultaron ser sinérgicas, de acuerdo a las suposiciones IA, el análisis bajo las suposiciones CA indicó que mesotrione + atrazine sería sinérgico, aditivo y antagónico según el nivel de concentración efectiva (ECx) seleccionada y la proporción fija de mezcla utilizada. Debido a que no es posible determinar el modelo adecuado de acción conjunta basado en el ajuste de los datos pronosticados a los observados, se tomó en cuenta lo apropiado de las suposiciones biológicas subyacentes para el conjunto de datos muestra de la mezcla. Adicionalmente, los autores proporcionan criterios de decisión para ayudar a los investigadores en la selección de un modelo de acción conjunta de referencia apropiado.


Corresponding author

Corresponding author's E-mail:


Hide All
Abendroth, J. A., Martin, A. R., and Roeth, F. W. 2006. Plant response to combinations of mesotrione and photosystem II inhibitors. Weed Technol. 20:267274.
Altenburger, R., Backhaus, T., Boedeker, W., Faust, M., Scholze, M., and Grimme, L. H. 2000. Predictability of the toxicity of multiple chemical mixtures to Vibrio fischero: mixtures composed of similarly acting chemicals. Environ. Tox. Chem. 19:23412347.
Altenburger, R., Bödeker, W., Faust, M., and Grimme, L. H. 1990. Evaluation of the isobologram method for the assessment of mixtures of chemicals. Ecotoxicol. Environ. Saf. 20:98114.
Armel, G. R., Rardon, P. L., McCormick, M. C., and Ferry, N. M. 2007. Differential response of several carotenoid biosynthesis inhibitors in mixtures with atrazine. Weed Technol. 21:947953.
Backhaus, T., Altenburger, R. A., Boedeker, W., Faust, M., Scholze, M., and Grimme, L. H. 2000. Predictability of the toxicity of a multiple mixture of dissimilarly acting chemicals to Vibrio fischeri . Environ. Tox. Chem. 19:23482356.
Backhaus, T., Faust, M., Scholze, M., Gramatica, P., Vighi, M., and Grimme, L. H. 2004. Joint algal toxicity of phenylurea herbicides is equally predictable by concentration addition and independent action. Environ. Tox. Chem. 23:258264.
Belden, J. B., Gilliom, R. J., and Lydy, M. J. 2007. How well can we predict the toxicity of pesticide mixtures to aquatic life? Integr. Environ. Assess. Manag. 3:364372.
Berenbaum, M. C. 1978. A method for testing for synergy with any number of agents. J. Infect. Dis. 137:122130.
Bliss, C. I. 1939. The toxicity of poisons applied jointly. Ann. Appl. Biol. 26:585615.
Bödeker, W., Altenburger, R., Faust, M., and Grimme, L. H. 1990. Methods for the assessment of mixtures of plant protection substances (pesticides): mathematical analysis of combination effects in phytopharmacology and ecotoxicology. Nachrbl. Dtsch. Pflanzenschutzd. 42:7078.
Bödeker, W., Altenburger, R., Faust, M., and Grimme, L. H. 1992. Synopsis of concepts and models for the quantitative analysis of combination effects: from biometrics to ecotoxicology. Arch. Complex Environ. Stud. 4:4553.
Boedeker, W., Drescher, K., Altenburger, R., Faust, M., and Grimme, L. H. 1993. Combined effects of toxicants: the need and soundness of assessment approaches in ecotoxicology. Sci. Total Environ. 134(Suppl. 2):931938.
Bradley, P. R., Johnson, W. G., and Smeda, R. J. 2000. Response of sorghum (Sorghum bicolor) to atrazine, ammonium sulfate, and glyphosate. Weed Technol. 14:1518.
Brommer, C. L., Shaw, D. R., Duke, S. O., Reddy, K. N., and Willeford, K. O. 2000. Antagonism of BAS 625 by selected broadleaf herbicides and the role of ethanol. Weed Sci. 48:181187.
Brown, D. W., Al-Khatib, K., Regehr, D. L., Stahlman, P. W., and Loughin, T. M. 2004. Safening grain sorghum injury from metsulfuron with growth regulator herbicides. Weed Sci. 52:319325.
Burke, I. C., Price, A. J., Wilcut, J. W., Jordan, D. L., Culpepper, A. S., and Tredaway-Ducar, J. 2004. Annual grass control in peanut (Arachis hypogaea) with clethodim and imazapic. Weed Technol. 18:8892.
Burke, I. C., Wilcut, J. W., and Porterfield, D. 2002. CGA-362622 antagonizes annual grass control with clethodim. Weed Technol. 16:749754.
Carter, W. H. Jr. 1995. Relating isobolograms to response surfaces. Toxicology 105:181188.
Cedergreen, N., Kudsk, P., Mathiassen, S. K., and Streibig, J. C. 2007. Combination effects of herbicides on plants and algae: do species and test systems matter? Pest Manag. Sci. 63:282295.
Colby, S. R. 1967. Calculating synergistic and antagonistic responses of herbicide combinations. Weeds 15:2022.
Crafts, A. S. and Cleary, C. W. 1936. Toxicity of arsenic, borax, chlorate, and their combinations in three California soils. Hilgardia 10:401413.
Drescher, K. and Boedeker, W. 1995. Assessment of the combined effects of substances: the relationship between concentration addition and independent action. Biometrics. 51:716730.
Faust, M., Altenburger, R., Backhaus, T., et al. 2003. Joint algal toxicity of 16 dissimilarly acting chemicals is predictable by the concept of independent action. Aquat. Toxicol. 63:4363.
Faust, M., Altenburger, R., Boedeker, W., and Grimme, L. H. 1994. Algal toxicity of binary combinations of pesticides. Bull. Environ. Contam. Toxicol. 53:134141.
Gessner, P. K. 1995. Isobolographic analysis of interactions: an update on applications and utility. Toxicology 105:161179.
Gowing, D. P. 1960. Comments on tests of herbicide mixtures. Weeds 8:379391.
Green, J. M., Jensen, J. E., and Streibig, J. C. 1997. Defining and characterizing synergism and antagonism for xenobiotic mixtures. Pages 263274 in Hatzios, K. K., ed. Regulation of Enzymatic Systems Detoxifying Xenobiotics in Plants. Dordrecht, The Netherlands Kluwer Academic.
Hatzios, K. K. and Penner, D. 1985. Interaction of herbicides with other agrochemicals in higher plants. Rev. Weed Sci. 1:163.
Hollaway, K. L., Hallam, N. D., and Flynn, A. G. 1996. Synergistic joint action of MCPA ester and metsulfuron-methyl. Weed Res. 36:369374.
House, K. 1995. The consequences of assuming the wrong mode of action in the analysis of mixture experiments. Asp. Appl. Biol. 41:6976.
Hugie, J. A., Bollero, G. A., Tranel, P. J., and Riechers, D. E. 2008. Defining the rate requirements for synergism between mesotrione and atrazine in redroot pigweed (Amaranthus retroflexus). Weed Sci. 56:265270.
Jensen, K. I. N. and Caseley, J. C. 1990. Antagonistic effects of 2,4-D amine and bentazone on control of Avena fatua with tralkoxydim. Weed Res. 30:389395.
Jensen, P. K. and Kudsk, P. 1988. Prediction of herbicide activity. Weed Res. 28:473478.
Junghans, M., Backhaus, T., Faust, M., Scholze, M., and Grimme, L. H. 2003. Predictability of combined effects of eight chloroacetanilide herbicides on algal reproduction. Pest Manag. Sci. 59:11011110.
Kaushik, S., Inderjit, , Streibig, J. C., and Cedergreen, N. 2006. Activities of mixtures of soil-applied herbicides with different molecular targets. Pest Manag. Sci. 62:10921097.
Kelley, K. B., Wax, L. M., Hager, A. G., and Riechers, D. E. 2005. Soybean response to plant growth regulator herbicides is affected by other postemergence herbicides. Weed Sci. 53:101112.
Kelly, T. L. W. and Chapman, P. F. 1995. The design and analysis of mixture experiments to meet different objectives: a practical summary. Asp. Appl. Biol. 41:5159.
Koger, C. H., Burke, I. C., Miller, D. K., Kendig, J. A., Reddy, K. N., and Wilcut, J. W. 2007. MSMA antagonizes glyphosate and glufosinate efficacy on broadleaf and grass weeds. Weed Technol. 21:159165.
Koger, C. H., Price, A. J., and Reddy, K. N. 2005. Weed control and cotton response to combinations of glyphosate and trifloxysulfuron. Weed Technol. 19:113121.
Kosman, E. and Cohen, Y. 1996. Procedures for calculating and differentiating synergism and antagonism in action of fungicide mixtures. Am. Phytopathol. Soc. 86:12631272.
Kudsk, P. 1988. The influence of volume rates on the activity of glyphosate and difenzoquat assessed by a parallel-line assay technique. Pestic. Sci. 24:2129.
Kudsk, P. and Mathiassen, S. K. 1995. Joint action of tribenuron and other broadleaf herbicides. Asp. Appl. Biol. 41:95102.
Kudsk, P. and Mathiassen, S. K. 2004. Joint action of amino acid biosynthesis-inhibiting herbicides. Weed Res. 44:313322.
Lam, G. K. Y. 1994. A general formulation of the concept of independent action for the combined effects of agents. Bull. Math. Biol. 56:959980.
Lanclos, D. Y., Webster, E. P., and Zhang, W. 2002. Glufosinate tank-mix combinations in glufosinate-resistant rice (Oryza sativa). Weed Technol. 16:659663.
Liu, S. H., Quick, W. A., Hsiao, A. I., and Streibig, J. C. 1994. Effect of MCPA on the phytotoxicity of imazamethabenz-methyl applied to wild oats (Avena fatua L.). Weed Res. 34:425431.
Mathiassen, S. K. and Kudsk, P. 1993. Joint action of sulfonylurea herbicides and MCPA. Weed Res. 33:441447.
Mathiassen, S. K. and Kudsk, P. 1998. Influence of broad-leaved weed herbicides on the activity of fenoxaprop-P-ethyl. Weed Res. 38:283289.
Morse, P. M. 1978. Some comments on the assessment of joint action in herbicide mixtures. Weed Sci. 26:5871.
Onofri, A., Carbonell, E. A., Piepho, H-P., Mortimer, A. M., and Cousens, R. D. 2010. Current statistical issues in Weed Research . Weed Res. 50:524.
Palmer, E. W., Shaw, D. R., and Holloway, J. C. Jr. 2000. Broadleaf weed control in soybean (Glycine max) with CGA-277476 and four postemergence herbicides. Weed Technol. 14:617623.
Paveley, N. D., Thomas, J. M., Vaughan, T. B., Havis, N. D., and Jones, D. R. 2003. Predicting effective doses for the joint action of two fungicide applications. Plant Pathol. 52:638647.
Pöch, G. 1991. Evaluation of combined effects with respect to independent action. Arch. Complex Environ. Stud, ACES 3:6574.
Pöch, G., Dittrich, P., and Holzmann, S. 1990a. Evaluation of combined effects in dose–response studies by statistical comparison with additive and independent interactions. J. Pharmacol. Meth. 24:311325.
Pöch, G., Reiffenstein, R. J., and Unkelbach, H. D. 1990b. Application of the isobologram technique for the analysis of combined effects with respect to additivity as well as independence. Can. J. Physiol. Pharmacol. 68:682688.
Ritz, C., Cedergreen, N., Jensen, J. E., and Streibig, J. C. 2006. Relative potency in nonsimilar dose–response curves. Weed Sci. 54:407412.
SAS. 2003. SAS/STAT. Version 9.1. Cary, NC SAS Institute.
Seefeldt, S. S., Jensen, J. E., and Fuerst, E. P. 1995. Log-logistic analysis of herbicide dose–response relationships. Weed Technol. 9:218227.
Shaw, D. R. and Arnold, J. C. 2002. Weed control from herbicide combinations with glyphosate. Weed Technol. 16:16.
Simpson, D. M. and Stoller, E. W. 1995. Response of sulfonylurea-tolerant soybean (Glycine max) and selected weed species to imazethapyr and thifensulfuron combinations. Weed Technol. 9:582586.
Simpson, D. M. and Stoller, E. W. 1996. Physiological mechanisms in the synergism between thifensulfuron and imazethapyr in sulfonylurea-tolerant soybean (Glycine max). Weed Sci. 44:209214.
Søbye, K. W., Streibig, J. C., and Cedergreen, N. 2010. Prediction of joint herbicide action by biomass and chlorophyll a fluorescence. Weed Res. 51:2332. DOI: 10.1111/j.1365-3180.2010.00824.x.
Streibig, J. C. 1984. Measurement of phytotoxicity of commercial and unformulated soil-applied herbicides. Weed Res. 24:327331.
Streibig, J. C. 2003. Assessment of Herbicide Effects. Accessed: April 18, 2010.
Streibig, J. C., Dayan, F. E., Rimando, A. M., and Duke, S. O. 1999. Joint action of natural and synthetic photosystem II inhibitors. Pestic. Sci. 55:137146.
Streibig, J. C. and Jensen, J. E. 2000. Actions of herbicides in mixtures. Pages 153180 in Cobb, A. H. and Kirkwood, R. C., eds. Herbicides and Their Mechanisms of Action. Boca Raton, FL Sheffield Academic.
Streibig, J. C., Kudsk, P., and Jensen, J. E. 1998. A general joint action model for herbicide mixtures. Pestic. Sci. 53:2128.
Streibig, J. C., Rudemo, M., and Jensen, J. E. 1993. Dose–response curves and statistical models. Pages 2955 in Streibig, J. C. and Kudsk, P., eds. Herbicide Bioassays. Boca Raton, FL CRC.
Sutton, P., Richards, C., Buren, L., and Glasglow, L. 2002. Activity of mesotrione on resistant weeds in maize. Pest Manag. Sci. 58:981984.
Vera, V., Gauvrit, C., and Cabanne, F. 2001. Efficacy and foliar absorption of flupyrsulfuron-methyl and prosulfocarb applied alone or in mixture on Lolium multiflorum and wheat. Agronomie 21:3343.
Wehtje, G. 2008. Synergism of dicamba with diflufenzopyr with respect to turfgrass weed control. Weed Technol. 22:679684.
Woodyard, A. J., Bollero, G. A., and Riechers, D. E. 2009. Broadleaf weed management in corn utilizing synergistic postemergence herbicide combinations. Weed Technol. 23:513518.
Woodyard, A. J., Hugie, J. A., and Riechers, D. E. 2009b. Interactions of mesotrione and atrazine in two weed species with different mechanisms for atrazine resistance. Weed Sci. 57:369378.


Joint Action Analysis Utilizing Concentration Addition and Independent Action Models

  • Julie A. Abendroth (a1), Erin E. Blankenship (a2), Alex R. Martin (a3) and Fred W. Roeth (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed