Bulletin OEPP/EPPO Bulletin 16, 651-657 (1986)
`
`The joint action of fungicides in mixtures:
`comparison of t w o methods for synergy calculation
`
`by Y . LEVY, M. BENDERLY, Y. COHEN, U. GISI* and D. BASSAND*
`Bar-Ilan University, Ramat-Gan (Israel) and *Agrobiological Research Station, Sandoz,
`4108 Witterswil (Switzerland)
`
`Two methods for evaluating the joint action of fungicides in mixtures were analysed. In order
`to obtain a relatively rapid answer on the type of interaction between fungicides in a mixture
`(additivity, synergism or antagonism), one can apply the Abbott formula lo data on fungus
`survival. Tests with this method will not be accurate at high effective dose values. A more
`accurate determination of the joint action of fungicides can be made by the Wadley method,
`applied to data on effective doses. This involves more experimental work than the Abbott
`method. Optimization of mixing ratios of fungicides required a set of experimental data on
`effective doses with several mixing ratios.
`
`Introduction
`The mixing of chemicals offers many possibilities in the search for broader and more potent uses
`of pesticides. In all cases when pesticide mixtures are applied, the biological effect may be equal,
`greater or smaller than might be expected from the sum of the activities of the components when
`administered separately. These phenomena are defined as additivity, synergism and antagonism,
`respectively. The term synergism was first used in pharmacology to represent the unusual and
`greater combined effect of drugs (Macht, 1929), and the phenomenon has since been extensively
`studied with herbicides (Morse, 1978) and insecticides (Busvine, 1971). The expression of
`synergism in fungicide mixtures was reviewed by Scardavi (1 966).
`Use of fungicide mixtures has increased significantly during the last decade due to the
`evolution of phytopathogenic fungal genotypes resistant to site-specific fungicidcs. Mathcmati-
`cal models, as well as experimental studies, have shown that mixtures of site-specific and broad-
`spectrum fungicides can delay the build-up of resistant genotypes of foliar fungal plant
`pathogens (Delp, 1980; Levy et al., 1983; Staub & Sozzi, 1984).
`Prepacked mixtures are extensively used by growers in spite of the uncertainty in the
`evaluation of the joint action of their components. Synergistic interaction between the fungicides
`oxadixyl and mancozeb for control of Phytophthora infestans in tomatoes and potatoes and
`Plusmopora r:iticola in grapevine was reported by Gisi et a/. (1983, 1985) and between metalaxyl
`and mancozeb in controlling Pseudoperonospora cubensis in cucumbers by Samoucha & Cohen
`(1984). In uitro studies with the ‘crossed paper strip bioassay’ demonstrated synergism between
`fungicides against several fungal species (De Waard & Van Nistelrooy, 1982; De Waard, 1985;
`Katagiri & Uesugi, 1977). Differences in the evaluation of synergism have caused large variation
`in the results and interpretation of the joint action of pesticide mixtures (Sun &Johnson, 1960).
`There is voluminous literature on methodology for studying the joint action of insecticides and
`herbicides, but no attempt has been made to adapt and/or modify these methodologies to
`phytopathology. In this paper, we analyse the different concepts and calculation methods
`available for evaluating the interaction between components in mixtures, with the aim of making
`thcm easily available to plant pathologists. The interactions are measured as quanta1 rcsponsc of
`the target populations, which means that either mortality or survival are the variables, or else
`effective doses to obtain the same effect on a target population.
`65 1
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`SYNGENTA EXHIBIT 1014
`Syngenta v. UPL, PGR2023-00017
`
`

`

`652
`
`Y. Levy et al.
`
`Concepts
`Bliss (1939), and later Plackett & Hewlett (1952), put forward a biological classification of types
`of joint action, conceived originally for insecticides, which seems equally applicable for
`fungicides. Bliss (1939) defined three types of joint action: (a) independent joint action-the
`fungicides act independently and have different modes of action; (b) similar joint action-the
`fungicides produce similar but independent effects. so that one component can be substituted at
`a constant proportion for the other (Finney, 1971). The effectiveness of the mixture is then
`predictable directly from onc of the constituents if their rclative proportions are known; (c)
`synergistic or antagonistic action. One fungicide influences the biological activity of the other. In
`this case the effectiveness of a mixture cannot be assessed from that of the individual
`components. According to Bliss, a deviation from the expected efficacy of a mixture calculated
`from the activities of the individual components indicates syncrgism or antagonism. i.e. type (c)
`joint action.
`
`Independent joint action: the Abbott method
`If independent joint action of fungicides in mixture is assumed, the expected efficacy of a mixture
`can be predicted by the Abbott formula (Abbott, 1925) in terms of proportion ofthe population
`killed:
`(1)
`a+h-ah,
`E i e ~ p ) = a + ( l -a)b
`in which E(exp) is the expected control efficacy of a mixture, and a and b represent the
`proportion of the population controlled by fungicides A and B, respectively. The value ab
`represents the proportion of the population killed by A and B together. The value
`1 - [(a + 6 ) - ab] is therefore the proportion of the population which survived both fungicides.
`These survivors would contribute to synergism if it was operating. If efficacy is expressed in
`percent, equation 1 becomes:
`(2)
`E f e x p ) = n+b-(uh/100).
`For synergy calculation, the ratio (SF, synergy factor) between the observed experimental
`efficacy of the mixture Elobs) and the expected efficacy of the mixture is computed:
`SF = E(abs//E(exp).
`(3)
`A ratio Eiobs)/E(exp) greater or smaller than 1 indicates a dcviation from the hypothesis of
`independent action, which means that there is biological interaction between the fungicides. If
`SF > 1 , there is synergism; if SF < 1, thcre is antagonism.
`The most important advantage of this method is that it can evaluate, with no mathematical
`treatment, an interaction between two fungicides with only thrce test elements, i.e. the fungicides
`A and B alone and the mixture A+B. However, the accuracy of this method is doubtful at
`relatively high response levels of the components due to the rapid decrease of the maximal SF
`towards 1 .O with increasing response levels. Table 1 shows the maximal values of synergism that
`can be measured with the aid of the Abbott formula. It shows that the higher the response levels
`of the components, the smaller the synergy value that can be measured. Equation 3 calculates,
`therefore, the efficacy of a given mixture relative to the summed efficacies of its components.
`
`Similar joint action: the Wadley method
`The Wadley mcthod (Wadley, 1945, 1967) is based on the second hypothesis of Bliss, which
`assumes that one component can substitute at a constant proportion for the other. The expected
`effectiveness of a mixture is then directly predictable from the effectiveness of the constituents If
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`

`

`Methods j o r fungicide synergy calculation
`653
`Table 1. Maximal synergy factor SF that can be computed with the aid of the Abbott formula at various
`responsc levels of fungicide mixtures
`Valeur maximale du coefficient de synergie (SF) qu’il est possible d’ttablir par utilisation de la fonnule
`d’Ahbott en fonction du niveau d’eficacite de deux fongicides et de leur mtlange
`
`Response level Response level Expected rcsponse level
`fungicide A
`fungicide B
`or the mixture*
`
`Maximal SF$
`
`~
`
`~~
`
`0.01
`0.05
`0.10
`0.15
`0.20
`0.25
`0.30
`0.35
`0.40
`0.45
`0.50
`0.55
`0.60
`0.65
`0.70
`0.75
`0.80
`0.85
`0.90
`0.95
`1 .0
`
`0.01
`0.05
`0.10
`0.15
`0.20
`0.25
`0.30
`0.35
`0.40
`0.45
`0.50
`0.55
`0.60
`0.65
`0.70
`0.75
`0.80
`0.85
`0.90
`0.95
`1 .o
`
`0.0199
`0.0975
`0.1900
`0.2775
`0.3600
`0.4375
`0.5100
`0.5775
`0.6400
`0.6975
`0.7500
`0.7975
`0.8400
`0.8775
`0.9100
`0.9375
`0.9600
`0.9775
`0.9900
`0.9975
`1 .OD00
`
`50.2512
`10.0256
`5.2631
`3.6036
`2.7777
`2.2988
`1.9607
`1.7316
`1.5625
`1.4336
`1.3333
`1.2539
`1.1904
`1.1396
`1.0989
`1.0666
`1.0416
`1.0230
`1.0101
`1.0025
`1 .0000
`
`* Calculated from equation (1).
`Calculated from equation (3), assuming that E(obs) = I
`
`their relative proportions are known. Wadlcy developed a short-cut graphic procedure to
`estimate the expected effectiveness of the mixture. Dose-response curves, obtained experinien-
`tally, are plottcd on log-probit paper (Finney, 1971) for cach ingredient and eye-fitted lines are
`drawn. A hypothetical dose-response curve is then drawn for the mixture based on the
`assumption that one ingredient can be substituted for the other. The experimental dose-
`response curve of the given mixture is also plotted and the ratio between corresponding equally
`effective doses (ED) of the observed and expected lines of the mixture is calculated. In addition to
`the graphic melhod, E D values can also be calculated by probit or logit analysis (Finney, 1971).
`Bascd on Sun & Johnson (1960), the formula used for the calculation of the hypothetical values
`(leading to equations 7 and 8) can be established as follows.
`The relative efficacy of two fungicides A and B is exprcssible by a single figurc, the ratio R of
`equally cffective doses, ED.& and EDB, respectively. The efficacy of the second component (B)
`relative to the first (A) is given by:
`
`(4)
`Since in case of similar joint action in a mixture each component can be substituted at a constant
`proportion for the other, the relative efficacy Re of a mixture can be expressed as:
`Re = EDA,/ED(exp) = n RA+b RB
`
`( 5 )
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`

`

`654
`
`Y. Levy et al.
`
`Table 2. Summary of differences between the Abbott and the Wadley methods for calculating interactions
`between fungicides in mixtures
`Rksumt des differences entre les mkthodes d’Abbott et de Wadley pour calculer les interactions entre
`fongicides uti1ist.s en mklange
`
`Abbott method
`
`Wadley method
`
`independent joint action
`% mortality (control)
`not required
`control efficacy observed
`control efficacy expected
`dependent on response
`level
`not possible
`
`similar joint action
`concentration
`rcquircd
`expected effective dose$
`observed effective dose
`not dependent on
`response level
`possible, isoboles
`
`Basic hypothesis*
`Variable measured
`Dose-response curves
`
`Synergism factor
`Reliability
`
`Optimization of
`mixing ratio
`
`* According to Bliss (1939).
`1 Usually 90%.
`
`where ED(exp) is the expected equally effective dose; a and b are the proportions of fungcides A
`and B in the mixture, and a +b= 1 .
`From equation 5 , ED(exp) can be expressed as follows:
`ED(exp) = ED*/(# RA + b RB)
`(6)
`or, after arithmetic transformation,
`(7)
`ED(expj = l/(a/EDA+b/EDB).
`In fact, ED(exp) is the harmonic mean of EDA and EDB weighted by their respective
`proportions a and bin the mixture. When a and b are not relative values but absolute amounts of
`the components in a mixture, equation 7 becomes:
`ED(exp) = (a + ~)/(u/EDA + b/EDe).
`(8)
`ED(exp) is compared with ED(obs) (the equally effective dose observed in experiment) in
`order to test the hypothesis of similar joint action. The measure for deviation from the
`hypothesis is again the synergy factor (SF):
`SF = ED(exp)/ED(obsj.
`(9)
`IfSF= 1, the hypothesis of similar joint action (or additivity) can be accepted; otherwise it will
`be rejected. If S F is greater than 1, there is synergistic action, while, if SF is smaller than 1, there is
`antagonistic interaction between the fungicides.
`Unlike the method based on the Abbott formula, the method of Wadley allows determination
`of synergy at any fungicide concentration. A summary of the differences between the two
`methods described is given in Table 2.
`
`Optimization of mixing ratios of fungicides by isobolograms
`One of the main objectives of studying synergy is to maximize the cost/benefit ratio of fungicides,
`i.e. to achieve highest control efficacy with minimal units of active ingredient of the components.
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`

`

`k rethods for fungicide synergy calculation
`
`655
`
`ED90,
`! 00
`
`80
`
`60
`
`40
`
`20
`
`0
`
`I
`5
`
`I
`10
`
`15
`
`20
`
`ED90,
`
`Fig. 1. Isobologram for the two fungicides A (oxadixyl) and B (mancozeb) active against Phytophthura
`infestans on potato plants, giving a theoretical (ANB) and an experimental (AMB) isobole for A + B
`mixtures with ratios between 1 + 1 and 1 + 32. The level of synergy can he measured by the ratio R =ONjOM
`which is maximal for the mixture A + B = 1 + 7.
`Isobologramme des dcux fongicidcs oxadixyl (A) et mancozebe (B) pour leur activitt contre Phytophthora
`in?‘p,rtans sur pomme dc tcrrc. L‘isobole ANB represente la courbe theorique en I’absence de synergic;
`l’isobole AMB donne les resultats d’un essai utilisant differcnts melanges (1 : I jusqu’i 1 : 32). Le rapport
`R = ONIOM sert d. ncsure du coefficient de synergie; il est maximal pour 1e melange 1 : 7 de A ct B.
`
`The Wadley method is applied using mixture of components at different ratios in order to
`obtain a fixed control efficacy for each mixture, e.g. ED90. A so-called isobole is then plotted
`along the dose pairs of points producing these control efficacies. A theoretical isobole (straight
`line between A and B) is plotted according to the Wadley method for each mixture. Various
`possible syncrgistic interactions are represented by experimental isoboles falling within triangle
`ABO (Fig. 1).
`The ratio ON,’OM serves as a measure of SF (Fig. I). This ratio is maximal where the distance
`between the points M and N is largest, representing the highest level of synergistic interactions of
`the components in the mixture; thus, the ratio of the components in the mixture is optimal (De
`Waard, 1985; Plackett & Hewlett, 1948; Tammes, 1964). For the highest value of ON/OM, the
`point M is given by the intersection of the experimental isobole with the tangent parallel to the
`straight line between A and B. If EDA and EDB are plotted on the axis using the same scale, the
`isobologram is in most cases asymmetric, making the plotting difficult. In practice, the distances
`OA and OB should be made equally long (symmetric isobologram, as in Fig. 1) so that triangle
`ABO is bisected by the line ON into two symmetric triangles A N 0 and BNO. In case of
`synergistic interactions of the components A and B, any dose pair of points for a single mixture is
`in one of those areas; it is then easy to decide in what direction one has to optimize the mixing
`ratio.
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`

`

`656
`
`Y. Levy et al.
`
`Conclusion
`In order to get a relatively rapid answer on whether two (or more) fungicides act synergistically,
`one can use the Abbott method. Tests with this method should be conducted with fungicide
`concentrations not exceeding the ED50 values for each. An accurate determination of synergy
`magnitude can be made with the Wadley method which involves more experimental work than
`the Abbott method. Optimization of mixing ratios of fungicides requires a set of experimental
`data with several mixing ratios. and the various data sets should be plotted as isobolograms.
`
`Activite de melanges de fongicides
`
`Deux methodes pour I’tvaluation de I’activite des fongicides utilisks en melange sont analysees.
`Afin d’obtenir assez rapidement une reponse sur le type d’interactions entre fongicides dans un
`melange (effet simplement additif, synergisme ou antagonisme), il est possible d’appliquer la
`formule d’Abbott i des donnees sur la mortalitt des champignons, ceci ayant neanmoins pour
`inconvtnient une diminution de la precision lorsque les dosages augmentent. Une determination
`plus juste de l’activite des melanges de fongicidcs peut &trc faitc g r k e a la methode de Wadley,
`appliquee a des doses effectives. Ceci demande un surcroit important de travail experimental par
`rapport a la methode d’Abbott. L’optimisation des proportions de fongicides dans un mtlange
`necessite I’obtention de donnees experimentales sur les doses effectives de melanges en
`differentes proportions.
`
`References
`ASBOTT, W.S. (1925) A method of compuling the effectiveness of an insecticide. Journal of Economic
`Entomohgy 18, 265-267.
`BLISS, C.I. (1939) The toxicity of poisons applied jointly. Annuls uf Applied Biology 26, 585-615.
`BUSVINE, J .R. (197 I) A Critirul Rer:iew of the Techniques.for Testing Insecticides, 2nd ed. Commoiiwcalth
`Agricultural Bureaux, Slough.
`DLLP, C.J. (1980) Coping with resistance to plant disease control agents. Plant Diseuse 64, 652-657.
`DE WAARD, M A . (1 985) Fungicide synergism and antagonism. In Fungicidesfor Crop Prorection. BCPC
`Monograph no. 31, pp. 89-95. BCPC, Croydon.
`
`DE WAARD, M.A. & VAN NISTELROOY, J.G.M. (19x2) Antagonistic and synergistic activities of various
`chemicals on the toxicity of fenarimol to Aspergillzts nitluims. Pesticide Science 13, 279 286.
`Fi”m, D.L. (1971) Probit Analysis, 3rd ed. Cambridge University Press, Cambridge.
`CIS[, U., HARK, J., SANDMEIER, R. & WIEDMER, H. (1983) A ncw systemic oxazolidinone fungicide (SAN 371
`F) against diseases caused by Pcronosporales. Mededelingen m n cle Faaculteit Landbouu,M;eien.schappen,
`Rijksuniversiteit Grni 48, 541-549.
`GISI, U., BINDER, H. & RIMBACH, E. (1985) Synergistic interactions of fungicides with different modes of
`action. Transaction.7 of the British Mycological Socieij, 85, 299 306.
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`

`

`Methodsfor fungicide .synergy calculation
`
`657
`
`KATAGIRI, M. & UESIXI, Y. (1977) Similarities between the fungicidal action of isoprothiolane and
`organophosphorus fungicides. Phytopathology 67, 141 5-1417.
`LEVY, Y., LEVI, R. & COHF?;, Y. (1983) Buildup of a pathogen subpopulation resistant to a systemic fungicide
`under various control strategies: a flexible simulation model. Phytopathology 73, 1475-1480.
`MACHT, D.I. (1929) Pharmacological synergism of stereoisomers. Proceedings of'the Nutionul Academy of
`Science.7 15, 63-70.
`MORSE, P.M. (1978) Somc comments on the assessment ofjoint action in herbicide mixtures. Weed Science
`26, 58-7 1.
`PLACKETT, R.L. & HEWLEI'T, P.S. (1948) Statistical aspects of the independent joint action of poisons,
`particularly insecticides. 1. The toxicity of a mixture of poisons. Annals ofAppljedBioloXj1 35, 347-358.
`PLACKETT, R.L. & HEWLETT, P.S. (1952) Quanta1 responses to mixtures of poisons. Journal of
`th? Royal
`Statisficd Socict.y B 14, 141-163.
`SAMOUCIIA, Y . & COHEN, Y . (1984) Synergy between mctalaxyl and mancozeb in controlling downy mildew
`in cucumbers. Phytopafhology 14, 1434-1435.
`SCARDAVI, A. (1966) Synergism among fungicides. Annual Reciew of Phytoputhology 4, 335-348.
`STAUB, T. & Sozzr, D. (1984) Fungicide resistance: a continuing challenge. PIunt Disease 68, 102&1031.
`SUN, Y.P. & JOHNSON, E.R. (1960) Analysis ofjoint action of insecticides against housc flies. Journal of
`Economic Entomology 53, 887-892.
`TAMMES, P.M.L. (1 964) Isoboles, a graphic representation of synergism in pesticides. Netherlands Journal of
`Plant Pathology 70, 73-80.
`WADLEY, F.M. (1945) The evidence required to show synergistic action of insecticides and a short cut in
`analysis. US Department of Agriculture, Bureau of' Entomology and Plant Quarantine no. ET-223.
`WADLLY, F.M. (1967) Experimental Statistics in Entomology. Graduate School Press, Washington.
`
` 13652338, 1986, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2338.1986.tb00338.x by San Jose State University, Wiley Online Library on [22/01/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
`
`