| Education Center | Plant Disease Management Simulations |
| Management of Potato Late Blight: Simulation with Lateblight |
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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. 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: Sporangia (landed on susceptible sites) The model's transfer functions describe different developmental processes: Indirect germination The model operates on a daily time step. Temperature Effects The effect of temperature on disease development is simulated independently for each of six different developmental processes using polynomial equations (Table 1).
Sporangial Germination Sporangia germinate by two pathways, direct and indirect, depending on the ambient temperature during the period of leaf wetness: (See Table 1.) GermSporangia = LandedSporangia * (DIRMAX * TempEffDirect)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. The zoospores germinate only while the leaves are wet and in response to the mean temperature during the period of leaf wetness: GermZoospores = Zoospores * ZOOMAX * TempEffZoospwhere ZOOMAX = 0.96 zoospores/day. Infection 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. LatentInfections = (INFMAX_SP * GermSporangia) + (INFMAX_ZSP * GermZoospores) + (TempEffInfec * LeafWetEff * Susceptibility * FungicideEffect * (1.0 - BlightProportion))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.) Lesion development Lesions are divided into four types: Latent lesionsAll 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: LesionDiam[age] = LesionDiam[age-1] + (MAXLES * TempEffLesEx * LesionExp * IncrFact * FungicideFact * (1.0 - BlightProportion))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.) The total lesion area assumes circular lesions: LesionArea[age] = LesionNumber[age] * LesionDiam[age] * LesionDiam[age] * PIBY4where PIBY4 = 0.7854. In the original model, the numbers of lesions of each age were passed daily into the next age class: LesionNumber[age] = LesionNumber[age-1]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: LesionNumber[age] = LesionNumber[age] + LesionNumber[age-1] * TRANSFERwhere 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.) Sporulation Sporulation occurs on lesions from the end of the latent period until they are 14 days old: AttachedSporangia = SPRMAX * SporulationFct * TempEffSporu * HumidityFct * SysFungicideFct * TotalLesionArea * (1.0 - BlightProportion)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. Lesion inactivation 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). Dispersal of sporangia 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: if (DailyMeanTemp > 21.0)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: LandedSporangia = AttachedSporangia * SporeSurvival * LeafWetCatch * RainWashFact * (LeafAreaIndex / MaxLeafAreaIndex)where LeafWetCatch = 0.28.0/LeafWetHrs and RainWashFact = 0.3Rainfall*10.0. Host growth 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:
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: TuberInitFact = - 0.00911 + 0.1038 Temp - 0.00296 Temp2Physiological time is then accumulated at a rate that depends on the cultivar: TuberInitTime = TuberInitTime + CvTuberFact * TuberInitFactwhere 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: TuberProdFact = - 0.3837 + 0.1261 Temp - 0.00298 Temp2Again physiological time is accumulated for the production of tubers: TuberProdTime = TuberProdTime + CvTuberFact * TuberProdFactThe production of tubers in tons/hectare is then simply: Tubers = 0.56 * TuberProdTime Fungicide effects 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). 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). Weather The following environmental variables are read from an external weather data file: Rainfall: Daily rainfall in inches In addition, two environmental variables are approximated with the following calculations: LeafWetHours = Humid90Hours + 3.0 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. Bruhn, J. A. and W. E. Fry. 1981. Analysis of potato late blight epidemiology by simulation modeling. Phytopathology 71:612-616. 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. Crosier, W. 1934. Studies in the biology of Phytophthora infestans (Mont.) DeBary. Memoir 155. Cornell University Agricultural Experiment Station. March 1934. 37 pp. DeWeille, G. A. 1963. Laboratory results regarding potato late blight and their significance in the epidemiology of blight. Eur. Potato Jour. 6:121-130. 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. Guzman-N., J. 1964. Nature of partial resistance of certain clones of three Solanum species to Phytophthora infestans. Phytopathology 54:1398-1404. Lapwood, D. H. 1961. Potato haulm resistance to Phytophthora infestans. II. Lesion production and sporulation. Ann. Appl. Biol. 49:316-330. 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. Marks, G. E. 1965. The cytology of Phytophthora infestans. Chromosoma 16:681-692. 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. Milgroom, M. G., C. E. McCulloch, and W. E. Fry. 1988 Distribution and temporal dynamics of metalaxyl in potato foliage. Phytopathology 78:555-559. Milgroom, M. G. and W. E. Fry. 1988. A model for the effects of metalaxyl on potato late blight epidemics. Phytopathology 78:559-565. Ullrich, J. and B. Schoger. 1972. Zoosporenzahl und Sporangiengrube bei Phytophthora infestans (Mont.) DeBary. Phytopath. Z. 74:268-271. 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. 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. Warren, R. C. and J. Calhoun. 1975. Viability of sporangia of Phytophthora infestans in relation to drying. Trans. Brit. Mycol. Soc. 64:73-78. |
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