Weather

Applescab is driven by the daily mean temperature, rainfall, and hours of leaf wetness coded into five weather data sets derived from several years of central Michigan weather data:

• Cool and wet
• Hot and dry
• Moderate and dry
• Moderate and moderate
• Moderate and wet

Tree Growth Submodel

The hypothetical orchard in Applescab consists of 100 semi-dwarf trees per acre with a potential maximum yield 1000 apples per tree. The trees and the apples are uniform in size such that there are 100 apples per bushel at harvest. A grossly simplified tree growth model simulates the growth stage of the tree, the total leaf area, the leaf area susceptible to apple scab, the total surface area of the fruit, and a fungicide dilution factor due to tree growth. >From April 1 until petal fall, the tree growth model is driven by degree-days accumulated from February 1 with a base temperature of 43ºF. (Anstey, 1965; Sisler and Overholser, 1943) The growth stages and their associated degree-days are: green tip, 700; half-inch green, 750; tight cluster, 800; pink, 900; full bloom, 1000; and petal fall, 1100. After petal fall, tree growth is a function of days from petal fall (Fischer, 1962). Fruit set, terminal bud set, and harvest occur 7, 56, and 126 days after petal fall, respectively.

Leaf and fruit areas are tracked separately to obtain the distribution of infections between leaves and fruit. The leaf area per spur at each growth stage from green tip to petal fall was estimated from photographs of the growth stages (Chapman and Catlin, 1976). To obtain a value per acre, the area per spur was multiplied by the number of apples per acre, assuming an average of one apple per spur. A value of one vegetative shoot for every three spurs was used. The total leaf area at harvest was estimated using the value of 1600 cm² of leaf surface per mature apple (Magness, 1928). For lack of any better data, total leaf area was assumed to increase linearly from petal fall to terminal bud set. The daily dilution factor due to the increasing surface area (supplied to the fungicide model) is simply the inverse of the daily increase in total surface area.

Since no quantitative information was available at the time the simulation was written, the area of susceptible leaf tissue was based on an educated guess. It was assumed the leaves are susceptible to ascospore infections only during their period of expansion; that is, only the daily increment in leaf area is susceptible to infection. The fruit area was kept at a constant level of 10⁶ cm² per acre from green tip to petal fall and then increased linearly to 1.36 x 10⁷ cm² per acre at harvest.

Disease Development Submodel

Applescab is an attempt to design a disease simulator whose structure is based on the biology and epidemiology of the pathogen and which is as accurate a simulation as can be constructed from the available literature. The approach used is a time-varying distributed delay with attrition. Kranz, et al. (1973) used a similar approach to model the secondary infection cycle of apple scab. Each stage in the development of the pathogen is represented by a state variable, and the rates of movement from one stage to another are represented by transfer coefficients having values between zero and one. The transfer coefficients are products of several independent factors, such as temperature, leaf wetness, fungicide activity, host resistance, etc. Each state variable also has a mortality factor between zero and one.

Perithecia. The state variable for perithecia is bypassed when the simulation is initiated with "Begin New." Initially the user enters the level of primary inoculum as ascospores per acre (in the "Inoculum" menu). The default is 10¹⁰, which was obtained by multiplying the values provided by Brook (1976), which ranged from 5,000 to 125,000 ascospores per leaf, by 7.5 x 10⁶ leaves per acre (Magness, 1928). If the user opts to continue from one season to the next (selecting "Continue" in the "Simulation" menu), the total lesion area at the end of the season is divided by the average area per lesion (0.25 cm²) to get the number of dormant, overwintering lesions. This value is multiplied by the average number of perithecia per lesion (85.5) and by the average number of ascospores per perithecium (320) (Adams, 1925) to obtain the the total number of ascospores per acre potentially available.

Developing ascospores. The ascospores are matured according to the model developed by Massie and Skolnik (1975):

CPROB = 5.7507 + 3.345 LOG₁₀(DD) + 0.00132CP

PROBIT(X) = 1/(1 + 19466e^{-1.97529 X})

Ready ascospores. The ready ascospores are those that have fully matured and are ready for discharge with the next rain. Discharge does not occur until there has been two hours of wetting. While the ascospores are waiting to be discharged, we assume that there is a small amount of mortality. For lack of a better estimate, we used that of Kranz et al. (1973), 1 - 0.9996⁸.

Released ascospores. The ascospore released in the simulated orchard are augmented by the ascospores blown in from outside the orchard at this stage. The level of blown in inoculum can be set with the "Inoculum" menu. They are matured and released in the same proportions as the ascospores within the orchard. Since the ascospores are airborne, we assume an even distribution of ascospores over the entire orchard. Therefore, the proportion of ascospores landing on susceptible sites is the area of susceptible tissue divided by the total surface area of the orchard. By selecting "Ascospore Report" in the "Management" menu, the user can see the percent of ascospores that are in the various stages of development.

Landed ascospores. The ascospores that have landed on susceptible sites (the daily new leaf area) will eventually die there if the environmental conditions are not favorable for infection. The mortality factor is made up of two components, a basic attrition rate of 10% and an effective loss of 50% of the spores per day due to hardening over of susceptible tissue before the spores germinate. Ascospore germination is a function of the inherent rate of germination, temperature, leaf wetness, and fungicide inhibition. A basic germination rate of 33% percent per day was taken from Aderhold (1896). The temperature effect, T1, is a function obtained by Analytis (1973) from the data of Keitt and Jones (1926):

T1 = sin(3.14159/180*X*(197.5419*X*(-105.7569*X*110.215)))²

Germinated ascospores. Two stages are combined into one at this point, ascospores that have germinated and those that have germinated and penetrated. The mortality at this stage results from the "back-action" of the fungicides (all but "Protectan" have this effect), and the resulting aborted infections are transferred into nonfertile or "ghost" lesions. The rate at which germinated ascospores become incubating lesions is determined by the temperature, the resistance of the apple cultivar to apple scab, and the "back-action" of the fungicide. The temperature effect is the same as T1, above. The resistance factors were estimated by testing values to determine whether they gave reasonable rates of disease development.

Incubating lesion. The mortality at this stage is due to the "burn-out" effects of "Eradican," and these "burned-out" lesions also pass into the nonfertile lesion stage. There is vegetative growth of the lesion during this stage, starting from an initial size of 0.243 cm² per lesion (Bratley, 1937). The growth of the lesion and the rate of development of conidia is affected by the temperature, the cultivar resistance, and by the "burn-out" effects of "Eradican." The length of the incubation period under optimum conditions is nine days.

Developing conidia. This state variable tracks the lesions that are developing conidia. The mortality factor represents the "burn-out" effects of "Eradican." Conidia are produced at the basic rate of 25,000 per cm² per day (Albert and Lewis, 1962), which is modified by the temperature effect, T1. As the lesion grows, the central portion which has sporulated eventually dies, leaving only the outer ring to continue to grow and sporulate.

Ready conidia. This state variable represents the total pool of conidia that are ready for dispersal from both the primary and secondary lesions. The viability of these conidia is reduced by fungicides (Albert and Hickey, 1972; Alexander and Lewis, 1975) and by temperatures above 95ºF (Heuberger et al., 1963). Conidia are released by rain according to a formula adopted from EPIDEM (Waggoner and Horsfall, 1969):

RELEASE = 0.9 * RAIN/(0.04 +RAIN)

Released conidia. Once released by the rain, the conidia are also deposited by the rain:

DEPOSITION = 0.9^(100*RAIN)*(SUSCEPTIBLE AREA)/(TOTAL AREA)

Landed conidia. This stage is somewhat analogous to the landed ascospore stage. There is an attrition of 10% per day, but since secondary infections seem to occur on old leaves as well as newly expanding leaves, the effective loss of 50% per day due to leaf maturation is omitted. Conidial germination is a function of the inherent rate of germination of the conidia, temperature, leaf wetness, and fungicide inhibition. The germination rate is 22% on the leaves and 8% on the fruit (Aderhold, 1896) and is weighted by the relative areas of leaves and fruit to obtain an average germination rate:

GERMINATION RATE = (0.22*(LEAF AREA) + 0.08*(FRUIT AREA)) / ((LEAF AREA) + (FRUIT AREA))

Germinated conidia. The functions of this stage are the same as those of the germinating ascospores. The mortality rates are the same, including the "back action" of the fungicides, and the rate at which germinated conidia become incubating lesions is the same as that for germinating ascospores.

Incubating lesion. The functions of this stage are the same as those of the incubating lesions formed by ascospores.

Developing conidia. This stage corresponds to the developing conidia stage from ascospore infections and is treated in the same manner.

Nonfertile lesion. This might also be called the "ghost" lesion stage, since it represents those lesions which will continue to grow and produce a visible spot, but in which normal sporulation has been inhibited by fungicides. The growth function is the same as that for normal lesions.

Dead lesion. This stage represents those lesions or parts of lesions that have died and are no longer growing or sporulating. However, they are still counted and continue to accumulate as visible lesions and as total area affected.

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:

1. The nature of the treated plant and its surfaces
2. Dilution of pesticides by plant growth
3. Loss due to weathering by rain, wind, and mechanical action
4. Effects of pesticide formulation on its tenacity
5. Susceptibility of the pesticide to chemical, photochemical and microbial degredation, and volatilization

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

C_t = C₀e^-Kt

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))

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((C_t/C₀ -1)*A)

C_t+1 = C_t*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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