{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fcharset0 Arial;}} {\*\generator Msftedit 5.41.15.1507;}\viewkind4\uc1\pard\f0\fs20\par \pard\qc\b\fs24 Lateblight\par Model Description\par \b0\fs20\par Simulation by\par W. E. Fry, M. G. Milgroom, M. A. Doster,\par J. A. Bruhn, and R. I. Bruck\par \par Java adaptation by\par Joshua M. Goldfarb and Phil A. Arneson\par \par \'a9 2002 Cornell University\par All rights reserved\par \pard\par \par \par This version of Lateblight was adapted from the simulation originally written by J. A. Bruhn et al. (1980) and modified in various ways over the years by different people working in the research program of W. E. Fry, Department of Plant Pathology, Cornell University. We have attempted to retain as much as possible the original structure of the model, but some small modifications have been necessary to enhance its pedagogical value. While the simulation is sufficiently realistic for teaching purposes, this version should not be trusted as a research tool or a management decision making aid.\par \par In order to make "Lateblight" respond as realistically as possible to environmental and management variables, the development of the pathogen is simulated mechanistically, closely following the Phytophthora infestans life cycle. The model's state variables represent the major morphological stages in the pathogen's development:\par \par Sporangia (landed on susceptible sites)\par Zoospores (following indirect germination)\par Germinated sporangia\par Germinated zoospores\par Latent lesions\par Sporulating, expanding lesions\par Sporulating, inactive lesions (not expanding)\par Inactive lesions (nonsporulating, necrotic tissue)\par Sporangia available for dispersal\par Dispersed sporangia \par \par The model's transfer functions describe different developmental processes:\par \par Indirect germination\par Direct germination\par Infection\par Lesion expansion\par Sporulation\par Lesion inactivation (cessation of expansion)\par Necrosis (cessation of sporulation)\par Dispersal of sporangia\par Catch of sporangia \par \par The model operates on a daily time step.\par \par \b Temperature Effects\b0\par \par The effect of temperature on disease development is simulated independently for each of six different developmental processes using polynomial equations (Table 1).\par \par Table 1. Rates of Pathogen Development as a Function of Temperature (C)\par Temperature\par Effect \tab Equation \tab Min \tab Max\par Direct Germination \tab TempEffDirect = 2.1 - 0.48 TempLeafWet + 0.031 TempLeafWet2 - 0.00045 TempLeafWet3 - 4.5 10-6 TempLeafWet4 \tab 14 \tab 29\par Indirect Germination \tab TempEffIndir = 0.0134 + 0.0698 TempLeafWet + 0.0185 TempLeafWet2 - 0.00223 TempLeafWet3 + 7.48 10-5 TempLeafWet4 - 7.68 10-7 TempLeafWet5 \tab 0 \tab 24\par Zoospore Germination \tab TempEffZoosp = 0.00494 + 0.364 TempLeafWet - 0.05813 TempLeafWet2 + 0.00452 TempLeafWet3 - 1.617 10-4 TempLeafWet4 + 2.068 10-6 TempLeafWet5 \tab 0 \tab 28\par Infection \tab TempEffInfec = 0.4846 + 0.3735 TempHumid90 - 0.03556 TempHumid902 + 0.001509 TempHumid903 - 2.405 10-5 TempHumid904 \tab 1.5 \tab 30\par Lesion Expansion \tab TempEffLesEx = sqrt (8.4 10-4 + 0.1261 DailyMeanTemp - 0.03079 DailyMeanTemp2 + 0.00308 DailyMeanTemp3 - 1.152 10-4 DailyMeanTemp4 + 1.414 10-6 DailyMeanTemp5) \tab 0 \tab 33\par Sporulation \tab TempEffSporu = - 0.3882 + 0.2482 TempHumid90 - 0.03817 TempHumid902 + 0.00252 TempHumid903 - 5.32 10-5 TempHumid904 \tab 0 \tab 26\par Parameters of the polynomial equations were estimated by multiple regression using the data of Crosier (1934).\par \par \b Sporangial Germination\b0\par \par Sporangia germinate by two pathways, direct and indirect, depending on the ambient temperature during the period of leaf wetness: (See Table 1.)\par \par GermSporangia = LandedSporangia * (DIRMAX * TempEffDirect)\par \par Zoospores = LandedSporangia * (INDMAX * ZSPR * TempEffIndir) \par \par where DIRMAX = 0.29 sporangia/day, INDMAX = 0.81 sporangia/day, and ZSPR = 6.567 zoopores/sporangium (Marks, 1965; Ullrich and Schober, 1972; Warren and Calhoun, 1975). The temperature effect is determined by the appropriate polynomial function in Table 1.\par \par The zoospores germinate only while the leaves are wet and in response to the mean temperature during the period of leaf wetness:\par \par GermZoospores = Zoospores * ZOOMAX * TempEffZoosp \par \par where ZOOMAX = 0.96 zoospores/day.\par \par \b Infection\b0\par \par Infection efficiency is a function of leaf wetness, mean temperature during the period of leaf wetness, the susceptibility of the potato cultivar, the type of fungicide and its residue level, and the amount of uninfected tissue remaining.\par \par LatentInfections = (INFMAX_SP * GermSporangia) + (INFMAX_ZSP * GermZoospores) + (TempEffInfec * LeafWetEff * Susceptibility * FungicideEffect * (1.0 - BlightProportion)) \par \par where INFMAX_SP = 0.1 infections/germinated sporangium/day and INFMAX_ZSP = 0.01 infections/germinated zoospore/day (Lapwood and McKee, 1966). The temperature effect is determined by the appropriate polynomial function in Table 1. Maximum infection efficiency occurs at 21 C with 24 hours of leaf wetness, but the effects of temperature on infection efficiency are small between 10 and 22 C. No infections occur below 1.5 C or above 30 C (Crosier, 1934). Infection occurs only if the leaves are wet. The susceptibility factors for the susceptible, moderately resistant, and resistant cultivars are 1.0, 0.9, and 0.8, respectively. The protectant and systemic fungicides have different dose responses, the systemic requiring a lower residue to achieve the same effect. (See "Fungicide effects" below.)\par \par \b Lesion development\b0\par \par Lesions are divided into four types:\par \par Latent lesions\par Sporulating, expanding lesions\par Sporulating, inactive lesions (not expanding)\par Inactive lesions (nonsporulating, necrotic tissue) \par \par All successful infections produce latent lesions. The latent periods for the susceptible, moderately resistant, and resistant cultivars are 6, 6, and 7 days, respectively. At the end of the latent period, the lesion diameter is set at 2 mm, following which the sporulating lesions expand for four days:\par \par LesionDiam[age] = LesionDiam[age-1] + (MAXLES * TempEffLesEx * LesionExp * IncrFact * FungicideFact * (1.0 - BlightProportion)) \par \par where MAXLES = 4.35 mm/day (Guzman-N, 1964; Lapwood, 1961). the temperature effect is determined by the appropriate polynomial function in Table 1, and LesionExp is 1.5, 1.4, and 1.4 for the susceptible, moderately resistant, and resistant cultivars, respectively. IncrFact is a factor that decreases linearly from 1.0 to 0.0 over the five days following the latent period. FungicideFact is a factor between zero and one calculated from the dose response of the fungicide. (See "Fungicide effects" below.)\par \par The total lesion area assumes circular lesions:\par \par LesionArea[age] = LesionNumber[age] * LesionDiam[age] * LesionDiam[age] * PIBY4 \par \par where PIBY4 = 0.7854.\par \par In the original model, the numbers of lesions of each age were passed daily into the next age class:\par \par LesionNumber[age] = LesionNumber[age-1] \par \par In the current version of the model, this has been modified to pass a proportion of the lesions in each class on to the next age class each day:\par \par LesionNumber[age] = LesionNumber[age] + LesionNumber[age-1] * TRANSFER\par LesionNumber[age-1] = LesionNumber[age-1] - LesionNumber[age-1] * TRANSFER \par \par where TRANSFER = 0.38 (essentially a "tuning parameter", adjusted so that the model's output gave a good fit to disease progress observed in the field trials in 1977 and 1978 near Freeville, NY.)\par \par \b Sporulation\b0\par \par Sporulation occurs on lesions from the end of the latent period until they are 14 days old:\par \par AttachedSporangia = SPRMAX * SporulationFct * TempEffSporu * HumidityFct * SysFungicideFct * TotalLesionArea * (1.0 - BlightProportion) \par \par where SPRMAX = 763.2 (Lapwood, 1961) and the SporulationFct is 0.55, 0.45, and 0.45 for the susceptible, moderately resistant, and resistant cultivars, respectively. The temperature effect is determined by the appropriate polynomial function in Table 1. Sporulation occurs only if the relative humidity is above 90% (DeWeille, 1963). The effect of the systemic fungicide on sporulation is determined by the dose response discussed below.\par \par \b Lesion inactivation\b0\par \par On the fifteenth day following its initiation, a lesion ceases sporulation and its area is added to the inactive lesion area, which is added to the total blighted area when calculating the blight proportion. All lesions become inactive if the daily mean temperature exceeds 41 C for three consecutive days (Wallin and Hoyman, 1958).\par \par \b Dispersal of sporangia\b0\par \par No attempt has been made in "Lateblight" to simulate the biophysical mechanisms of dispersal of sporangia. All of the spores that are produced are dispersed, but the proportion of sporangia surviving are first adjusted for temperature dependent mortality:\par \par if (DailyMeanTemp > 21.0)\par SporeSurvival = exp (6.0 * (-0.0256 * DailyMeanTemp + 0.537)) ;\par else\par SporeSurvival = 1.0 \par \par The numbers of sporangia landing on susceptible sites (and thus available for infection) depend on the hours of leaf wetness (Crosier, 1934; Glendinning, et al., 1963; Melhus, 1915), the amounts washed off by heavy rains (Waggoner and Horsfall, 1969), and by the amount of foliage present:\par \par LandedSporangia = AttachedSporangia * SporeSurvival * LeafWetCatch * RainWashFact * (LeafAreaIndex / MaxLeafAreaIndex) \par \par where LeafWetCatch = 0.28.0/LeafWetHrs and RainWashFact = 0.3Rainfall*10.0.\par \par \b Host growth\b0\par \par The increase in leaf area index is simply linear up to the day determined by the characteristics of the cultivar (early-, mid-, or late-season) and reaches a maximum, also characteristic of the cultivar:\par \par \pard\fi2790 Early \tab Mid \tab Late\par \pard Day foliage growth stops \tab 44 \tab 52 \tab 59\par Maximum leaf area index \tab 2.5 \tab 3.5 \tab 4.5\par \par Tuber production is a function of temperature, cultivar, time. Tuber initiation can occur above 0 and below 30 C. A temperature factor for tuber initiation is generated by the quadratic:\par \par TuberInitFact = - 0.00911 + 0.1038 Temp - 0.00296 Temp2 \par \par Physiological time is then accumulated at a rate that depends on the cultivar:\par \par TuberInitTime = TuberInitTime + CvTuberFact * TuberInitFact \par \par where CvTuberFact is 1.600, 1.404, and 1.333 for the early-, mid-, and late-season cultivars, respectively. Tuber production is initiated when 45 physiological time units have accumulated. The rate of tuber production is also a quadratic function of temperature:\par \par TuberProdFact = - 0.3837 + 0.1261 Temp - 0.00298 Temp2 \par \par Again physiological time is accumulated for the production of tubers:\par \par TuberProdTime = TuberProdTime + CvTuberFact * TuberProdFact \par \par The production of tubers in tons/hectare is then simply:\par \par Tubers = 0.56 * TuberProdTime \par \par \b Fungicide effects\b0\par \par The details of the simulation of the attenuation of the protectant fungicide residues are described by Bruhn and Fry (1982). Basically the canopy is divided into four layers, and the fungicide residues are redistributed among the layers in response to rain. The residues of the systemic fungicide are a linear function of time after spraying only (Milgroom et al., 1988).\par \par The only effect of the protectant fungicide is the inhibition of infection (Bruhn and Fry, 1981), whereas the systemic fungicide not only inhibits infection but also reduces the rate of lesion expansion and inhibits sporulation (Milgroom and Fry, 1988).\par \par \b Weather\b0\par \par The following environmental variables are read from an external weather data file:\par \par Rainfall: Daily rainfall in inches\par DailyMeanTemp: Daily mean temperature (degrees Celsius)\par Humid90Hours: Hours per day of relative humidity above 90%\par TempHumid90: Mean temperature (C) during the above humid period \par \par In addition, two environmental variables are approximated with the following calculations:\par \par LeafWetHours = Humid90Hours + 3.0\par TempLeafWet = DailyMeanTemp + TempHumid90) / 2.0 \par \par \par \par \par \b REFERENCES\b0\par \par Bruhn, J. A., R. I. Bruck, W. E. Fry, P. A. Arneson, and E. V. Keokosky. 1980. Lateblight: A Disease Management Game. Computer program and manual, Department of Plant Pathology. Cornell University, Ithaca, NY.\par \par Bruhn, J. A. and W. E. Fry. 1981. Analysis of potato late blight epidemiology by simulation modeling. Phytopathology 71:612-616.\par \par Bruhn, J. A. and W. E. Fry. 1982. A mathematical model of the spatial and temporal dynamics of chlorothalonil residues on potato foliage. Phytopathology 72:1306-1312.\par \par Crosier, W. 1934. Studies in the biology of Phytophthora infestans (Mont.) DeBary. Memoir 155. Cornell University Agricultural Experiment Station. March 1934. 37 pp.\par \par DeWeille, G. A. 1963. Laboratory results regarding potato late blight and their significance in the epidemiology of blight. Eur. Potato Jour. 6:121-130.\par \par Glendinning, D. R., J. A. MacDonald and J. Grainger. 1963. Factors affecting the germination of sporangia of Phytophthora infestans. Trans. Brit. Mycol. Soc. 45:595-603.\par \par Guzman-N., J. 1964. Nature of partial resistance of certain clones of three Solanum species to Phytophthora infestans. Phytopathology 54:1398-1404.\par \par Lapwood, D. H. 1961. Potato haulm resistance to Phytophthora infestans. II. Lesion production and sporulation. Ann. Appl. Biol. 49:316-330.\par \par Lapwood, D. H. and R. K. McKee. 1966. Dose-response relationships for infection of potato leaves by zoospores of Phytophthora infestans. Trans. Brit. Mycol. Soc. 49:679-686.\par \par Marks, G. E. 1965. The cytology of Phytophthora infestans. Chromosoma 16:681-692.\par \par Melhus, I. E. 1915. Germination and infection with the fungus of the late blight of potato (Phytophthora infestans). Wisc. Agr. Exp. Sta. Res. Bull. 37:1-64.\par \par Milgroom, M. G., C. E. McCulloch, and W. E. Fry. 1988 Distribution and temporal dynamics of metalaxyl in potato foliage. Phytopathology 78:555-559.\par \par Milgroom, M. G. and W. E. Fry. 1988. A model for the effects of metalaxyl on potato late blight epidemics. Phytopathology 78:559-565.\par \par Ullrich, J. and B. Schoger. 1972. Zoosporenzahl und Sporangiengrube bei Phytophthora infestans (Mont.) DeBary. Phytopath. Z. 74:268-271.\par \par Waggoner, P. E. and J. G. Horsfall. 1969. EPIDEM: a simulator of plant disease written for a computer. Bull. Conn. Agr. Exp. Sta., New Haven, No. 698. 80 pp.\par \par Wallin, J. R. and W. G. Hoyman. 1958. Influence of post-inoculum air temperaturemaxima on survival of Phytophthora infestans on potato leaves. Amer. Potato Jour. 35:769-773.\par \par Warren, R. C. and J. Calhoun. 1975. Viability of sporangia of Phytophthora infestans in relation to drying. Trans. Brit. Mycol. Soc. 64:73-78.\par \par \par }