Applescab
Model Description

Simulation by
Phil A. Arneson, Timothy R. Oren,
Rosemary Loria, Jeffrey R. Jenkins,
Eric D. Goodman, and William E. Cooper

Java adaptation by
Joshua M. Goldfarb and Phil A. Arneson

© 2002 Cornell University
All rights reserved

This version of Applescab was adapted from the simulation originally written in Fortran by Phil A. Arneson et al. (1977). While the simulation is sufficiently realistic for teaching purposes, this model should not be trusted as a research tool or a management decision making aid.

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 

Three-day forecasts of mean temperature and the probability of rain are available by clicking on "Weather Report" in the "Management" menu. In an attempt to make the forecasts realistic, an error factor is used that simulates an actual forecast from the U.S. Weather Bureau. For temperature, a normal distribution is generated for the known mean for the given day, and the forecast mean is randomly selected from that distribution. The standard deviations of the distribution are 3º for tomorrow's forecast, 6º for the two-day forecast, and 8º for the three-day forecast. To forecast rainfall, a number is randomly selected from a uniform distribution between zero and one. The number is then squared and multiplied by a factor according to the day of the forecast (0.6 for tomorrow, 0.9 for the 2-day forecast, and 1.0 for the three-day forecast). This value predicts a forecast probability of rain when there is no rain; this value is subtracted from one to get the forecast probability of rain when there is rain. To weight the probability of predicting rain when there is a heavy rain, the amount of rain is multiplied by 10 and added to the forecast probability of rain.

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 

where CPROB is the probit of ascospore maturation, DD is the degree-days with base 0ºC, and CP is the precipitation in hundreths of an inch accumulated from December 1 of the previous season. The probit function was approximated with a logistic function, which fits the probit curve exactly at 1%, 50%, and 99%:

    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 

where X = (TempC - 0.5)/31.5. This value is multiplied by the wetting period, and the product is tested against a threshold obtained from the Mills table (Mills, 1944). The fungicide effects are obtained from the dosage response curves.

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) 

where RAIN is the rainfall in inches.

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)) 

For lack of more appropriate data, the temperature effect on the conidia, T2, was assumed to be the same as that on the ascospores, T1. However, since the the infection period for conidia is shorter than that for ascospores (Mills and LaPlante, 1951), a lower threshold was used for the wetting period. The inhibition of conidial germination by fungicides was assumed to be the same as the effect on ascospores.

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 

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.

REFERENCES

Adams, J. F. 1925. The spore discharge of the apple scab fungus in Delaware. Univ. Delaware Agr. Exp. Sta. Bull. No. 140, 16 pp.

Aderhold, R. 1896. Die Fusicladien userer Obstbäume. Landwr Jahrb. 25:875-914.

Albert, J. J. and J. W. Heuberger. 1961. Apple scab I. Effect of one application of fungicides on leaf lesions on previously unsprayed trees. Plant Disease Reporter 45(10):759-763.

Albert, J. J. and K. D. Hickey. 1972. In: Amer. Phytopath. Soc. Fungicide and Nematicide Tests, Results of 1972. p. 5.

Albert, J. J. and F. H. Lewis. 1962. Effect of repeated applications of dodine and of captan on apple scab foliage lesions. Plant Disease Reporter 46(3):163-167.

Alexander, S. A. and F. H. Lewis. 1975. Reduction of apple scab fungus inoculum with fungicides. Plant Disease Reporter 59(11):890-894.

Analytis, S., J. Kranz, and A. Stumpf. 1971. Eine Method Zur Berechnung der Blattfläche. Angew. Botanik 45:111-114.

Analytis, S. 1973. Zur Methodik Analyse van Epidemien, dargestellt am Apfelschorf (Venturia inaequalis [Cooke] Aderh.). Acta Phytomedica 1:1-76.

Analytis, S. 1974. Die Einsatz van Wachstumsfunktioner zur Analyse der Befallskurven van Pflanzenkrankheiten. Phytopathol. Z. 81(2):133-144.

Anstey, T. H. 1965. Prediction of full bloom date, apple, pear, cherry peach and apricot from air temperature data. Proc. Am. Soc. Hort. Sci. 88:57-66.

Arneson, P. A. 1971. Unpublished data.

Baude, F. J., J. A. Gardiner, and J. C. Y. Han. 1973. Characterization of residues on plants following foliar spray applications of benomyl. J. Agr. Food Chem. 21(6):1084-1090.

Bratley, C. O. 1937. Incidence and development of apple scab on fruit during the late summer and while in storage. USDA Technical Bull. No. 563, 45 pp.

Brook, P. J. 1966. The ascospore production season of Venturia inaequalis (Cke) Wint., the apple black spot fungus. N. Z. Jour. Agr. Res. 9: 1064-1069.

Brook, P. J. 1969. Effects of light, temperature, and moisture on release of ascospores by Venturia inaequalis (Cke.) Wint. N. Z. Jour. Agr. Res. 12:214-227.

Brook, P. J. 1976. Seasonal pattern of maturation of Venturia inaequalis ascospores in New Zealand. N. Z. Jour. Agr. Res. 19:103-109.

Bruhn, J. A. 1977. Personal communication.

Burchfield, H. P. and A. Goenaga. 1957. Some factors governing the deposition and tenacity of copper fungicide sprays. Contrib. Boyce Thompson Inst. 19:141-156.

Burchfield, H. P. and A. Goenaga. 1957. Equipment for producing simulated rain for measuring the tenacity of spray deposits to foliage. Contrib. Boyce Thompson Inst. 19:133-140.

Burchill , R. T. 1972. Comparison of fungicides for suppressing ascospore production by Venturia inaequalis (Cke.) Wint. Plant Pathology 21(1): 19-22.

Burchill , R. T., K. E. Hutton, J. E. Cross and C. M. E. Garrett. 1965. Inhibition of the perfect stage of Venturia inaequalis (Cooke) Wint. by urea. Nature 205(4970):520-521.

Chapman, P. J. and G. A. Catlin. 1976. Growth stages in fruit trees from dormant to fruit set. New York Food and Life Sciences Bull. No. 58, NYS Agr. Exp. Sta., Geneva.

Chapman, R. A., J. G. Horsfall , and H. L. Keil. 1950. Predicting protective value of fungicide from slope of wash-off curve. (Abstr.) Phytopathology 40(1):4-5.

Chiba, M. and J. Northover. 1977. Distribution and dissipation of captafol applied to apple trees. J. Agr. Food Chem. 25(1):39-42.

Connor, S. R. and J. W. Heuberger. 1968. Apple scab. V. Effect of late-season applications of fungicides on prevention of perithecial development by Venturia inaequalis. P1ant Disease Reporter 52(8):654-658.

Courshee, R. J. 1967. Application and use of foliar fungicides. In: D. C. Torgeson (ed.) Fungicides: An Advanced Treatise, Vol. 1. Academic Press. pp. 239-286.

Curtís, K. M. 1924. Black Spot of apple and pear: Experiments in possible methods of reducing infection. N. Z. Jour. Agr. 27(1):21-28.

Dale, W. T., B. C. Knight, and H. E. Croxall. 1970. Effect of starting date and number of sprays on apple scab control. Plant Pathol. 19(2): 51-59.

Davis, R. H., L. T. Alexander, and S. L. Yelon. 1974. Learning System Design, An Approach to the Improvement of lnstruction. McGraw-Hill. 342 pp.

Decker, G. C. 1957. Pesticide residue on plants. Agri. Chemicals 12(2): 39-40.

Ebeling, W. 1963. Analysis of the basic processes involved in the deposition, degradation, persistence and effectiveness of pesticides. Residue Reviews 3:35-163.

Fisher, D. V. 1962. Heat units and number of days required to mature some pome and stone fruit in various areas of N. America. Proc. Am. Soc. Hort. Sci. 80:114-124.

Gilpatrick, J. D. 1977. Personal communication.

Gilpatrick, J. D., M. Szkolnik, and S. D. Gibbs. 1971. A single, high rate application of difolatan for the control of apple scab. (Abstr.) Phytopathology 61 :893.

Gilpatrick, J. D. and D. R. Blowers. 1974. Ascospore tolerance to dodine in relation to orchard control of apple scab. Phytopathology 64(5): 649-652.

Gunther, F. A. 1969. lnsecticide residues in California citrus fruits and products. Residue Reviews 28:1-119.

Gunther, F. A. and R. C. Blinn. 1956. Persisting residues in plant materials. Ann. Rev. Entomol. 1:167-180.

Gunther, F. A. and R. C. Blinn. 1955. Analysis of insecticides and acaricides. lnterscience, New York and London.

Hamilton, J. M. 1931. Studies of the fungicial action of certain dusts and sprays in the control of apple scab. Phytopathology 21(5):445-523.

Heuberger, J. W. and R. K. Jones. 1962. Apple Scab II. Effect of serial applications of fungicides on leaf lesions on previously unsprayed trees. Plant Disease Reporter 46(3):159-162.

Heuberger, J. W., J. D. Bates and R. K. Jones. 1963. Apple Scab IV. Effect of temperature and relative humidity on the viability of conidia of Venturia inaequalis. Plant Disease Reporter 47(9):826-830.

Hill, K. R. 1971. JUPAC Commission on Terminal Residues, Report of the "half-life" working party. Jour. Assoc. Offic. Anal. Chemists 54:1316-1317.

Hislop, E. C. 1966. The redistribution of fungicides on plants. II. Solution of copper fungicides. Ann. Appl. Biol. 57:475-489.

Jones, R. K., J. W. Heuberger and J. O. Bates. 1963. Apple Scab III. Effect of serial applications of fungicides on leaf lesions on previously unsprayed trees: Inhibition of conidial germination, removal (suppression) of the organism, and subsequent development of late terminal infection. Plant Disease Reporter 47(5):420-424.

Keil, H. L., J. G. Horsfall and S. Rich. 1952. Relation of laboratory ED50 to field performance of fungicides. (Abstr.) Phytopathology 42(2):113.

Keitt, G. W. and L. K. Jones. 1926. Studies of the epidemiology and control of apple scab. Wis. Agr. Exp. Sta. Res. Bull. No. 73, 104 pp.

Kendrick, J. B. Jr. and J. T. Middleton. 1954. The efficacy of certain chemicals as fungicides for a variety of fruit, root and vascular pathogens. Plant Disease Reporter 38(5):350-353.

Kent, G. C. 1947. Apple Scab. (in a mimeographed laboratory text, Cornell Univ.). 24 pp.

Kovacs, A. and F. Falchieri. 1960. Laboratory tenacity trials with some fungicides. Ann. Della Sper. Agr. 14:125-133.

Kranz, J. 1974. Epidemics of Plant Diseases: Mathematical Analysis and Modeling. Springer-Verlag. 170 pp.

Kranz, J., M. Mogk and A. Stumpf. 1973. EPIVEN -- ein Simulator fur Apfelschorf. Z. Pflanzenkrankh. 80:181-187.

Lake. J. V. 1956. The effect of microclimate temperature upon the date of flowering of the apple. J. Hort. Sci. 31 :244-257.

Landsberg, J. J. 1974. Apple fruit bud development and growth; Analysis and an empirical model. Ann. Bot. 38:1013-1023.

Latorre, B. A. 1972. Late season fungicide application to control apple scab. Plant Disease Reporter 56(12):1079-1082.

Magness, J. R. 1928. Relationship of leaf area to size and quality in the apple. Proc. Amer. Soc. Hort. Sci. 25:285-288.

Massie, L. B. and M. Szkolnik. 1975. Unpublished data.

McCallan, S. E. A., H. P. Burchfield and L. P. Miller. 1959. Interpretation of dosage-response curves. (Abstr.) Phytopathology 49:544-545.

Mclntosch, O. L. 1969. A low-volume post harvest spray of benomyl prevents ascospore production in apple leaves infected by Venturia inaequalis. Plant Disease Reporter 53(10):816-817.

McMecham, A. D., C. V. G. Morgan, and G. A. Wardle. 1972. Erosion of azinphosmethyl from apple leaves by rain and overtree irrigation. J. Entomol. Soc. Brit. Columbia 69:5

Miller, H. J. 1949. Modifications of the slide-germination period of evaluating fungicides including the use of Venturia inaequalis and Phytopthora infestans. Phytopathology 39(4):245-259.

Miller, L. P. 1960. Uptake and innate toxicity of dodine (n-dodecylguanidine acetate) to fungus conidia. (Abstr.). Phytopathology 50(9):646.

Mills, W. D. 1944. Efficient use of sulfar dusts and sprays during rain to control apple scab. Cornell Univ. Ext. Bull. No. 630. 4 pp.

Mills, W. D., and A. A. LaPlante. 1951. Diseases and insects in the orchard. pp. 18-21 in NYS Agr. Exp. Sta. Ext. Bull. No. 711. 100 pp.

Mitchell, J. E. and J. D. Moore. 1962. Relation of dodine residue levels and scab development on apple fruit and leaves. Phytopathology 52:572-580.

Moore, C. S. 1969. Photography as a method of measuring apple trees. East Malling Res. Sta. Ann. Rep. 1968:111-115.

Northover, J. 1975. Captafol (single application technique -- SAT) simplifies early season control of apple scab. Plant Disease Reporter 59(4):357-360.

Pereira, J. L., H. R. Mapother, B. K. Cooke, and E. Griffiths. 1973. Redistribution of fungicides in coffee trees. Exp. Agr. 9:209-218.

Powell, D., A. Khettry, P. J. Sasaki, and G. E. Brussell. 1958. The fungicidal efficacy of Cyprex against apple scab. Plant Disease Reporter 42:493-498.

Powell, D. 1960. The inhibitory effects of certain fungicide formulations to apple scab conidia. Plant Disease Reporter 44(3):176-178.

Rich, S. 1954. Dynamics of deposition and tenacity of fungicides. Phytopathology 44:203-213.

Rogers, W. S. and G. A. Booth. 1964. Relationship of crop and shoot growth in apple. J. Hort. Sci. 39:61-65.

Ross, R. G. 1973. Suppression of perithecium formation in Venturia inaequalis by seasonal sprays of benomyl and thiophanate-methyl. Can. J. Plant. Sci. 53:601-602.

Ross, R. G. and R. J. Newbery. 1975. Effects of seasonal fungicides sprays on perithecium formation and ascospore production in Venturia inaequalis. Can. J. Plant Sci. 55:737-742.

Sisler, G. P. and E. L. Overholser. 1943. Influence of climatic conditions on date of full bloom of delicious apples in the Wenatchee Valley. Proc. Am. Soc. Hort. Sci. 43:29-34.

Soenen, A., G. Vanwetswinkel and E. Paternotte. 1971. Phenology of floral bud development in apple and pear trees. Rev. Agr. (Brussels) 24(2):143-148.

Solel, Z. and L. V. Edgington. 1973. Transcuticular movement of fungicides Phytopathology 63(4):505-510.

Studt, H. G. and H. C. Weltzien. 1975. Der Einfluss der Umweltfaktoren Temperatur, relative Luftfeuchtigkeit und Licht auf die Konidienbildung beim Apfelschorf, Venturia inaequalis (Cooke) Winter. Phytopath. Z. 84(2):115-130.

Sullivan, D. T. 1965. The effect of time of bloom of individual flowers on the size, shape and maturity of apple fruits. Proc. Am. Soc. Hort. Sci 87:41-46.

Sutton, T. B., A. L. Jones, and L. A. Nelson. 1976. Factors affecting dispersal of conidia of the apple scab fungus. Phytopathology 66(11): 1313-1317.

Szkolnik, M. 1969. Maturation and discharge of ascospores of Venturia inaequalis. Plant Disease Reporter 53(7):534-537.

Szkolnik, M. 1974. Problems associated with the control of deciduous tree fruit diseases. Proceedings, XIX International Horticultural Congress, Warsaw, Sept. 1974, pp. 432-446.

Szkolnik, M. 1977. Personal communication.

Szkolnik, M. and J. D. Gilpatrick. 1973. Tolerance of Venturia inaequalis to dodine in relation to the history of dodine usage in apple orchards. Plant Disease Reporter 57(10):817-821.

Szkolnik, M., J. R. Nevill, and L. M. Henecke. 1973. Fungicidal inhibition of production of new conidia from established foliar apple scab lesions. Phytopathology 63:208. (Abstr.)

Tette, J. P. 1973-76. Unpublished reports of the New York State Apple Pest Management Project.

Van Der Plank, J. E. 1967. Epidemiology of fungicidal action. In D. C. Torgenson (ed.) Fungicides: An Advanced Treatise, Volume l. Academic Press. pp. 63-92.

Van Dyk, L. P. 1974. The persistence of some pesticides on South African citrus. Pesticides, Supp. Vol. III., Lectures held at IUPAC 3rd International Congress of Pesticide Chemistry. Fredrick Coulson, Friedhelm, Korte (eds.). pp. 330-335.

Van Dyk, L. P. 1976. Parathion persistence on South African citrus. Arch. Environ. Contamin. Toxicol. 4:289-311.

Waggoner, P. E. And J. G. Horsfall. 1969. EPIDEM, a simulator of plant disease written for a computer. Bull. Connecticut Agr. Exp. Sta. No. 698. 80 pp.

Wallace, E. 1913. Scab diseases of apples. N.Y. Agr. Exp. Sta. Bull. No. 335:541-624.

Weaver, L. O. 1958. Cyprex, an eradicant for apple scab. 72nd Trans. Peninsula Hort. Soc. 48(5):49.

Westwood, M. N. and A. N. Roberts. 1970. The relationship between trunk cross-sectional area and weight of apple trees. Proc. Amer. Soc. Hort. Sci. 95(1):28-30.

Wicks, T. 1974. Tolerance of the apple scab fungus to benzimidazole fungicides. Plant ODisease Reporter 58(10):886-889.

Wilcoxson, F. and S. E. A. McCallan. 1939. Theoretical principles underlying laboratory toxicity tests of fungicides. Contrib. Boyce Thompson Inst. 10:329-338.

Williams, K. 1961. Note on the effect of rain and sprinkler irrigation on the persistence of spray residues of Guthion and Sevin on apples. Can. J. Plant Sci. 41:449-451.

Wilson, E. E. 1928. Studies of the ascigerous stage of Venturia inaequalis (Cke.) Wint. in relation to certain factors of the environment. Phytopathology 18(5):375-418.