'ATE PLANT BOARD
UtMEK 0Bft3X =KA 9 MI O AGBICULTMB
Agricultural Researoh Admalnistration
ureau of ontology and Plant Quarantine
E T 0 53W SISoSIoIC ACTION OF I CTICIDMs
AID A SOWT CT IN ANALIBIS
By F K. M.Vadley, statistical consultant
he purse of this paper i1 threefold: (1) To restate definitions
of Joint action of insecticides, (2) to show what is required for clear-
cut recognition of synergisma, and (3) to indicate a workable abshort cut in
Synengm between insecticides m be defined as a joint action of
two materials, such that the total effect is greater than the sum of the
two effects when each is used alone. Cox (2) restricts the application
of the tera "aynergism" to mixtures of insecticidal materials, each of
which has some toxicity when used alone. He thus excludes the case
where a substance without toxicity of its own i mproves the action of an
insecticide. Such a substance Is called simply an activator. The proof
of activation is less oaoUlex than that of synergism; a significant
added percentage 6f kill shown in replicated trials should be sufficient.
To u terstad syInergism it is necessary to consider possible types
of action of Bmixtures of poisons. The subject has been discussed clearly
by Bliss (_) a inn ) ad touched upon by the writer (2). Bliss
discusses three types of action of two poisons in a mixture- independent
joint action, similar joint action, and synergistic action. Both Bliss
and Finney mention the possibility of negative synergisma, or antagonism,
and both suggest methods for analysis of data on toxic action. The
methods discussed may be extended to mixtures of more than two poisons.
Iaen action can be defined as action in a different way by
each poison, a different physiological activity or vital system being
affected.. There my be more or less correlation in susceptibility,
since the Individuals susceptible to one action um tend also to be
susceptible to the other. If there is a marked positive correlation of
this sort, both poisons will tend to work on the sow group of insects,
and we will get little or no increase in kill by the mixture over the
mortality that would be caused, by the stronger insecticide used alone.
AUG 1 3 9
If there is little or no correlation, there will be no kill by each
substance and seom overlapping, of the sort indicated by Abbott's
forila for am mortality in the presence of another. In that case
the total kill will be higher than it would be with correlation. The
possibility of negative correlation, that is, the individuals suscep-
"tible to one poison being resistant to the other, might also be con-
sidered. Zach poison would kill the group susceptible to it with little
or no overlapping, and the total kill would be still higher. This aon-
dition seem unlikely. Finney defines expected independent action vith-
out allowance for correlation. This is equivalent to the concept of
Abbott's formula. Suppose, for instance, that a certain concentration
of poison A kills 80 percent and one of B 60 percent. If the two poe-
sons are independent in action, we would expect a kill of 80 percent + 60
percent-(60 percent of 80 percent), or 92 percent. It seemS probable that
soe positive correlation often occurs. Action significantly less than
independent action indicates antagonism.
Similar Joint effect is produced by two or more poisons acting
similarly, and affecting the same organs or processes in the indivldnal.
It Implies that one insecticide could be substituted for the other at a
constant rate. If this rate is known, equivalence can also be determined.
It is recognized that the soundest method of comparing two itsecticides
is to ovare concentrations needed for a given effect, and this mthod
has a special application here.
Suppose, for instance, that a concentration of 1 unit of insecti-
cide A is required to give 50 percent kill of an insect species, and
that 2 units of insecticide B are required for the sam result. Than A
is twice as effective as B. A mixture of 1/2 unit of A and 1 unit of
B will produce the ano result as either 1 unit "of A o- 2 of B, if
similar Joint effect occurs. If action is independent, there will be
som overlapping, and the =ixture will have somavwhat less effect. On
the basis of similar Joint effect, 1 unit of A and 1 of B will be
equivalent to 1 1/2 units of A alone.
It can readily be shown, by the nature of dosage-mortality curves
involved and the slopes they usually show, that similar Joint effect
is greater then independent effect, either with or without correlation.
The greatest effect of a mixture, which could be predicted from idi-
vidual action of its ingredients, would be similar Joint effect. If
the effect of the combination can be shown to exceed sianflioantly the
action expected froa similar Joint effect, synergism is strongly in-
The Determination of Synergism
The determination of synergism will require (1) sam estimate of
similar Joint effect inferred from the action of each ingredient used
alone, and (2) the determination of significance of erperiority in re-
sults, if any, over this similar effect.
To estimate the similar Joint effect we need dosage-mrtality
curves for each poison alone, so that equlvalecoe n.t a given mortality
can be calculated by interpolation. The log-;rotl transf zamtic- is
convenient for this purpose, since it usually gives linearity between
40 and 95 percent mortality, and since special log-probability paper
can be obtained for rapid graphic interpolation. As a matter of fact,
between 25 and 70 percent the untransformed dosage-mortality curve is
near enough linearity for rough interpolation, but above 70 percent
the transformation ie an improvement. When the estimate of equiv-
alence has been obtained., the concentration of the mixture can be
calculated in terms of either constituent, and expected similar Joint
effect can be read off the dosage-mortality curve for the constituent
chosen. Thla predicted effect can be compared with the actual. It
li desirable also to have a dosage-mortality curve for different con-
centrations of a mixture of given proportions. This is not essential,
however, for preliminary determination, if one concentration that
will cause mortality between 50 and 90 percent is available. Results
with this me concentration of a mixture, if adequately replicated,
aW be compared with calculated Joint effect derived from veil-
determined dosage -mortality curves of individual materials. The com-
parison involves the determination of -stignificance, the second step
mentioned. Significance is basically determined from consistency.
Finney(Q) discusses methods of determination of significance; the
author, in the next section, suggests a simple method.
To determine the equivalence, similar lopes in both dosage-
mortality curves ust be assumed. This is a fairly safe assumption for
poisons of similar Joint effect. In limited bxperimhntC slopes are
not likely to differ significantly, and a cou.on s W uay be derived
and used. If slopes realLU differ. equivrlance will wj at different
points. This condition may occur and add to complexity in some cases
where action is independent; it seems unlik ly that synergism will be
found under such conditions.
7izmq (1) gives a good exposition of methods of calculation,
using data from an article by Martin (4) in the same Journal. Finney
illustrates the calculation of equivalence from log-probit dosage-
mortality curves for a mixture for each ingredient, with common slope,
and the statemnt of concentration of a mixture in terms of one of
the substanes involved. A dosage-mortality equation can then be
written for the mixture, using the equation for that ingredient in
terms of which the mixture is stated. The dosage giving 50 percent
mortality (LD. 50), or any other mortality level desired for com-
parison, can be readily calculated, Finney (.) outlines a chi-square
test to compare the actual effect of a mixture iOilth that expected from
either independent or similar Joint effect. He also cites a rather
complex fazulla for standard error of difference of L. D. 50 of a
mixture from predicted L. D. 50 on a joint-action basis. Calculations
are based on statistical methods developed for probit analysis.
Much time m be saved in getting a preliminary determialnation of
equivalence by short-out methods, using log-probability paper and
pgraphic determinations. For example, we my take the date of Martin
used by Finney On the effects of rotenone and deguelin on an aphid,
Macroslphoniella sanborni (Gill). Sam results obtained over a range
of toxicity aited to the problems are tabulated as follows:
The data given above are plotted on log-probability paper (fig. 1),
and ey-fitted lines are drawn. A reading taken from these lines at
50 percent ehovs that 13.2 units of cZ.-lin are required to equal 4.8
of rotenone, or that deguelin is about 0.36 as toxic as rotennce. At
the 90 percent level 9.7 units of rotenone appear to equal 28.0 of
deguelin, giving deguelin an equivalence of 0.35. The average is 0.355
(Finney's ooquted value is 0.37-).
According to Martin, the mixture of rotenone ari deguelin gave the
results shown In table 1.
Table l.--The actual and the interpolated mortality obtained vith
a mixture of rotenone and deguelin of given concentrations
g./liter M./lter Percent Percent
1.0 4.1 2.5 47.8 11.2 --
2.0 8.1 4.9 58.7 = 5.0 51
3.0 12.2 7.3 79.2 10.2 78
4.0 16.3 9.8 93.5 2.9 90
Y Rotenone + 0.355 deguelin.
/ See fig. 1.
- 5 -
By using the "rotenonb equivalentO as concentration, the expected
Joint effect can be read off from, the eye-fitted rotenone line. For
instance, with equivalent of 7.3 the expected kill is read as 78 per-
cent. It will be shown at each point that the actual is somewhat
greater than the estimated effect, but the estimated effect conme within
1 or 2 standard errors of the actual. More exact calculation will
give a little better results. The estimated, as vell as the actual,
values have calculable standard errors, which decreases the tendency
to significant differences; on the other hand, the fact that all dif-
ferences are in the samen direction will increase this tendency. The
conclusions of Finney are the same as have been reached by the shorter
method in a few minutes work. mixture tends to produce an effect
exceeding Joint action, but this tendency does not reach significance.
The other cases treated by Martin and Finney have been studied in
the same vay. Working as above, the author calculated a rotenone
equivalent of 0.215 for elliptone, as compared with Finney 0.20. For
toxicarol the equivalent calculated is 0.175, as compared with Finney's
0.16. The conclusions as to synergism, arrived at by the rapid method
were the sam as those reached by Finney by the more complex =athe-
Dosage-mortality curves from replicated experiments would afford
opportunity for several independent determinationsm of equivalence, and
of expected mortality from a mixture. The latter could be used in
calculating a standard error. With error estimates for both calculated
and actual effects, the error and significance of the difference could
easily be calculated.
The author defines the types of Joint action of insecticides com-
bined in a mixture. He then ose that, in order to prove the exis.a-
tence of synergism, the effect of the mixture must be shown to be
significantly greater than the maximmnn effect predictable from separate
actions of the insecticides. This maxlmm is given by assumption of
similar joint effect. Dosage-mortality curves for separate ingredients
=y be used to estimate equivalence and expected similar Joint effect.
Replicated trials with a mixture my be used for comparison with the
estimated effect. A much-shortened graphic procedure will give results
of practical value. In many cases the type of action produced by a
mixture will not be exactly determinable from results, but a clear-cut
superiority over a calculated similar Joint effect will indicate
(1) Bilss, C. I.
1939. The toxicity of poisons applied Jointly. Ann. Appl. Biol.
(2) Com, A. J.
]943. Terminology of insecticides, fungicides, and other economic
poisons. Jour. Econ. Ent. 36: 813-821.
(3) nuy, B. J.
1912. The almtpli of toaioity teot- on Rixturu of ptoiMs,
Am. Appi. aol. 299l 82-9.
(4) Martin, J. T.
9Wo1 The problem of the eraatloam oaloulatlM of rotnamo-ooi-
talning plants (VI). Ann. App. Blol. 29: 69-81.
(9) Vad]A, F. M.
143. Statistical aspect. of labtratoy
Amer. Assoc. Mv. Sgo. Pab. 20:
teots of Insotoid,.
LOG.-PROBABILITY INTERVALS (FOR DOSAGE-MORTALITY ETC.)
99. --5- - - - - - .. . .. ..... .. ..... I f 1 1 - .^ -
2 9.0 _ - - - - - . ... fl n - - --.. .-.. .
__ n 13 11
U. 5 5 .0 0i
WJ 2& 0- -.. .
I1. ,====0 EEEi lEi iiiiiiii
1.5 2.0 2.5 3.0
Hill I I
15.0 200 250 300
Figure l.-The percentage of mortality obtained with several concentrations of rotenone and
deguelin, plotted on log-probability paper. Dots indicate rotenone; crosses, deguelin.
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