Good quantitative information on the effects of various fungicides on apple scab at specific stages of development is very
difficult to find in the literature. In general, the kind of data reported for fungicide tests are not useful in
constructing a model of this kind. However, since we were dealing with hypothetical fungicides, we were not restricted to using
real data, and where hard figures were not available for a fungicide, we either used figures from closely related
compounds or made an educated guess. Protectan was patterned after glyodin, but where necessary we also used data from ferbam
and sulfur; Eradican was based on benomyl, but some triarimol and EL 222 data were also used. Combocide represents dodine,
using captan data where necessary.
The dosage response curves are linear functions of probit germination versus log dose. The dosage response for Combocide
is that published for dodine (Gilpatrick and Blowers, 1974). The other dosage response curves were fabricated from a number
of different sources where the the efficacy of various fungicides at different rates was compared (Hamilton, 1937; Kendrick
and Middleton, 1954; McCallan et al., 1959; Miller, 1949; Miller, 1960; Mitchell and Moore, 1962; Powell, 1958, 1960;
Szkolnik, 1977; Weaver, 1958; Wicks, 1974; Wilcoxson and McCallan, 1939).
For lack of any better data, the dosage response for a specific fungicide was used for all effects of that fungicide.
All of the fungicides inhibit germination of ascospores and conidia. All of them except Protectan have the limited
after-infection activity that inhibits development between spore germination and the incubating lesion stages. Eradican
also affects other stages of fungus development, including inhibition of conidia development, mortalities of germinated
spores, mortalities of incubating lesions, and mortalities of developing conidia.
The Fungicide Attenuation Submodel
This submodel attenuates the fungicide residues on the fruit and leaf surfaces on a daily basis throughout the growing
season. The following factors are known to influence the disappearance of pesticide deposits:
- The nature of the treated plant and its surfaces
- Dilution of pesticides by plant growth
- Loss due to weathering by rain, wind, and mechanical action
- Effects of pesticide formulation on its tenacity
- Susceptibility of the pesticide to chemical, photochemical and microbial degredation, and volatilization
Due to the complexity of the interaction of these factors in the environment, delineation of their individual effects on
pesticide degradation and weathering has been difficult, and very little information is available. Therefore,
in Applescab, all factors except weathering by rainfall and dilution due to growth have been combined into a single
attenuating factor. Information about tree growth (leaf and fruit areas) is supplied by the tree growth submodel and is
used to dilute fungicide residues.
Attenuation factors. It has been claimed that the disappearance of foliar-applied pesticides generally follows
first-order kinetics (Courshee, 1967). However, according to Gunther and Blinn (1955, 1956), Gunther (1969), Hill (1971),
and Van Dyk (1974, 1976), this first-order loss curve is only an approximation of a bilinear or trilinear loss curve. The
first part of the bilinear curve shows rapid loss due to weathering, and the second part indicates a loss that is primarily
a function of pesticide degradation and volatilization.
The fungicide attenuation submodel uses a first-order approximation of the bilinear curve to estimate loss from the plant
surface:
- dC/dt = KC
Where t is time, C is pesticide concentration, and K is the rate constant. If the rate constant and the initial pesticide
concentration, C0, are known, the pesticide residue at any point in time,
Ct, can be calculated:
Ct = C0e-Kt
Rate constants for the hypothetical fungicides used in Applescab were estimated from the literature describing rates
of loss of fungicides of the type that they represent. The K value for Combocide was set at 0.10, estimated from data on
dodine residues on apple foliage under various application regimes (Mitchell and Moore, 1962). The loss rate of Eradican
was inferred from data on benomyl which was applied to cucumber leaves (Baude, et al., 1973). No data could be found
for the loss of glyodin from plant surfaces, but it known to be more persistent than dodine (Szkolnik, 1977), so it was given
a K value slightly lower.
Rainfall effects. If rainfall has occurred, the fungicide residue is attenuated based on the precipitation for that
day. A bilinear loss curve has been shown to approximate the effect of the quantity of rainfall on the loss of fungicide
residues (Burchfield and Goenaga, 1957). Since fungicides are known to vary in their susceptibility to wash-off by
rainfall, a tenacity function ,
EXP(-ALPHA*SQRT(BETA))
was used, where ALPHA is the tenacity factor and BETA is the rainfall in inches. Data on the removal of cuprous oxide
from banana leaves (Burchfiled and Goenaga, 1957) and parathion from lemons and grapefruit (Van Dyk, 1976) were used to
estimate the order of magnitude of the exponent in the above function and its relationship to the amount of rainfall. The
tenacity factors were set at .5, .33, .25, and .67 for Satafol, Eradican, Protectan, and Combocide, respectively.
Concentration effects. Another function, GAMMA, is used to modify the fungicide loss so that as fungicide is removed
by rainfall or other attenuating processes, it becomes increasingly difficult to remove the residue that remains:
GAMMA = EXP((Ct/C0 -1)*A)
where Ct is the amount of fungicide remaining at time t, C0 is
the amount of fungicide at the time of application, and A is a constant which was set equal to 3. If
Ct+1 is the output of the first-order loss equation, then to account for rainfall loss
Ct+1 = Ct*EXP(-ALPHA*GAMMA*SQRT(BETA))
Absorption of the systemic fungicide. Benomyl, the fungicide after which Eradican was patterned, is absorbed
by the leaves and fruit. Once this occurs, it is no longer susceptible to wash-off by rain. Approximately 50% of the
fungicide is absorbed in the first 24 hours after application, and about half the remaining residue is absorbed each
day thereafter (Solel and Edgington, 1973). Therefore, in our model the residues of Eradican were divided into external
residues and internal residues, with half the external residues becoming internal residues each day. Only the external
residues are subject to the weathering by rainfall.
Spraying in the rain. Another rainfall effect that needs to be considered is application of fungicides in the rain.
The start of a rainfall often signals the beginning of an infection period. If the fungicide residues are low and the rain
continues for more than 48 hours, the pest manager must decide whether to spray in the rain or not. If he or she does
decide to spray, the effectiveness of the application will be greatly reduced, since those deposits reaching the plant
surface will be diluted by the rainfall and are easily removed by the rain while they are still in suspension on the
plant surface. There seems to be no data in the literature on the reduced effectiveness of fungicides applied in the rain.
Since the decision to spray in the rain is made too frequently for it to be ignored, a function describing this process was
included despite the lack of data. A logistic function based on the amount of rainfall occurring on the day of the
application determines the amount of the initial deposit that remains. Half of the initial deposit is removed by one-tenth
inch of rain.
DEPOSIT REMAINING = (INITIAL DEPOSIT)*(.25/(.25 + RAIN*2.54))
Redistribution. No attempt was made to model fungicide redistribution in Applescab, although it is understood
that rainfall can redistribute fungicides, especially at low amounts and intensities of rainfall. The model assumes uniform
coverage of host tissues by the fungicide, and all effects of rainfall result in loss of residue from the plant surface.
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