Validating mathematical models of plant-disease progress in space and time

Mathematical Medicine and Biology

Volumn 14, Issue 2, 1997, Pages 85-112

  Hughes, Gareth ^a   McRoberts, Neil ^b   Madden, Laurence V ^c   Nelson, Scot C ^d  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b SCOTTISH AGRICULTURAL COLLEGE   (United Kingdom)

^c OHIO STATE UNIVERSITY   (United States)

^d UNIVERSITY OF HAWAII   (United States)

Author keywords

botanical epidemiology; data analysis; experimentation; statistical methods; strategic models; validation

Indexed keywords

STATISTICAL METHODS;

BOTANICAL EPIDEMIOLOGY; EXPERIMENTATION; MODEL OUTPUTS; MODEL VALIDATION; PLANT DISEASE; PLANT PATHOGEN; SPACE AND TIME; SPATIAL ASPECT; STRATEGIC MODELING; VALIDATION;

EPIDEMIOLOGY;

EID: 0002460910     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/14.2.85     Document Type: Article

References (93)

1. BALD, J. G., 1937. Investigations on 'Spotted Wilt' of Tomatoes III: Infection in Field Plots. Melbourne: Council for Scientific and Industrial Research.
2. BERTSCMNGER, L., KELLER, E. R., & GESSLER, C, 1995. Development of EPrVTT, a simulation model for contact-and aphid-transmitted potato viruses. Phytopathology 85, 801-14.
3. BLISS, C. I., 1958. The analysis of insect counts as negative binomial distributions. Proceedings of the 10th International Congress of Entomology, Vol. 2, pp. 1015-32.
4. BLODGETT, F. M., 1941. A method for the determination of losses due to diseased or missing plants. Am. Potato J. 18, 132-5.
5. BURROUGH, P. A., 1987. Spatial aspects of ecological data. In: Data Analysis in Community and Landscape Ecology (R. H. G. Jongman, C. J. F. ter Braak, & O. F. R. van Tongerman, eds.), pp. 213-51. Wageningen: PUDOC.
6. CAMPBELL, C. L., & MADDEN, L. V., 1990. Introduction to Plant Disease Epidemiology. New York: Wiley.
7. CAMPBELL, C. L., & NOE, J. P., 1985. The spatial analysis of soilbome pathogens and root diseases. Ann. Rev. Phytopathol. 23, 129-48.
8. CAMPBELL, C. L., & VAN DER GAAG, D. J., 1993. Temporal and spatial dynamics of microsclerotia of Macrophomina phaseolina in three fields in North Carolina over four to five years. Phytopathology 83, 1424-40.
9. CHELLEMI, D. O., ROHRBACK, K. G., YOST, R. S., & SONODA, R. M., 1988. Analysis of the spatial pattern of plant pathogens and diseased plants using geostatisucs. Phytopathology 78, 221-6.
10. CHELLEMI, D. O., OLSON, S. M., VANDERLERCKHOVE, G. A., & FUNDERBURK, J. E., 1994. Impact of insecticide applications on the temporal and spatial dynamics of flower inhabiting thrips and epidemics of tomato spotted wilt virus (Abstract). Phytopathology 84, 1073.
11. CLIFF, A. D., &ORD, J. K., 1981. Spatial Processes: Models and Applications. London: Pion.
12. COCHRAN, W. G., 1936. The statistical analysis of field counts of diseased plants. J. R. Statist. Soc. (Suppl.) 3, 49-67.
13. COE, R. D., 1989. The stochastic spreadsheet: A new statistical computing tool. The Statistician 38, 117-20.
14. DlGGLE, P. J., 1983. Statistical Analysis of Spatial Point Patterns. London: Academic Press.
15. DONCASTER, J. P., & GREGORY, P. H., 1948. The spread of virus diseases in the potato crop. ARC Report Series No. 7. London: HMSO.
16. FAGERSTRdM, T, 1987. On theory, data and mathematics in ecology. Oikos 50, 258-61.
17. FERRANDINO, F. J., 1996. Two-dimensional distance class analysis of disease incidence data: Problems and possibilities. Phytopathology 86, 685-91.
18. FERRISS, R. S. & BERGER, P. H., 1993. A stochastic simulation model of epidemics of arthropod-vectored plant viruses. Phytopathology 83, 1269-78.
19. FISHER, R. A., 1925. Statistical Methodsfor Research Workers. Edinburgh: Oliver and Boyd.
20. GIBSON, G. J., & AUSTIN, E. J., 1996a. Fitting and testing spatio-temporal stochastic models with application in plant epidemiology. Plant Pathology 45, 172-84.
21. GIBSON, G. J., & AUSTIN, E. J., 1996b. Fitting and testing stochastic models for the spatio-temporal evolution of biological systems. Abstracts, 7th IMA Conference on Mathematics in Medicine and Biology. Oxford, 10-12 July, 1996.
22. GILLIGAN, C. A., 1988. Analysis of the spatial pattern of soilbome pathogens. In: Experimental Techniques in Plant Disease Epidemiology (J. Kranz & J. Rotem, eds.), pp. 85-98. Berlin: Springer-Verlag.
23. GOTTWALD, T. R., RITCHIE, S. M., & CAMPBELL, C. L., 1992. LCOR2-Spatial correlation analysis software for the personal computer. Plant Disease 76, 213-15.
24. GRAY, S. M., MOYER, J. W., & BLOOMFIELD, P., 1986. Two-dimensional distance class model for quantitative description of virus-infected plant distribution lattices. Phytopathology 76, 243-8.
25. GREIG-SMITH, P., 1952. The use of random and contiguous quadrats in the study of the structures of plant communities. Annul. Botany 16, 293-316.
26. GRIFFITHS, D. A., 1973. Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease. Biometrics 29, 637-48.
27. HEATH, O. V. S., 1970. Investigation by Experiment. London: Edward Arnold.
28. HUDELSON, B. D., CLAYTON, M. K., SMITH, K. P., & UPPER, C. D., 1993. Modelling of superimposed spatial patterns of bacterial brown spot of snap bean. Phytopathology 83, 430-8.
29. HUGHES, G., 1996. Incorporating spatial pattern of harmful organisms into crop loss models. Crop Protection 15, 407-21.
30. HUGHES, G., & MADDEN, L. V., 1992. Aggregation and incidence of disease. Plant Pathology 41, 657-60.
31. HUGHES, G., & MADDEN, L. V., 1993. Using the beta-binomial distribution to describe aggregated patterns of disease incidence. Phytopathology 83, 759-63.
32. HUGHES, G., & MADDEN, L. V., 1995. Some methods allowing for aggregated patterns of disease incidence in the analysis of data from designed experiments. Plant Pathology 44, 927-43.
33. HUGHES, G., MADDEN, L. V, & MUNKVOLD, G. P., 1996. Cluster sampling for disease incidence data. Phytopathology 86, 132-7.
34. HURLBERT, S. H., 1984. Pseudorcplication and the design of ecological field experiments. EcoL Monographs 54, 187-211.
35. JEGER, M. J., 1990. Mathematical analysis and modeling of spatial aspects of plant disease epidemics. In: Epidemics of Plant Diseases: Mathematical Analysis and Modeling, 2nd edn. (J. Kranz, ed.), pp. 53-95. Berlin: Springer-Verlag.
36. JEGER, M. J., VAN DEN BOSCH, F., MADDEN, L. V., & HOLT, J., 1996. A model for analysing plant virus transmission characteristics and epidemic development. Abstracts, 7thIMA Conference on Mathematics in Medicine andBiology. Oxford, 10-12 July 1996.
37. JOHNSON, C. S., 1991. Plant mortality distribution and crop losses in flue-cured tobacco. Plant Disease 75, 390-4.
38. KOCKS, C. G., & RUISSEN, M. A., 1994. Spatial pattern analysis of black rot epidemics in cabbage using geostatistics. In: Crop Protection Summer School-Quantitative Ecology of Pests and Diseases. The Netherlands: Wageningen Agricultural University.
39. KRANZ, J., 1988. Measuring plant disease. In: Experimental Techniques in Plant Disease Epidemiology (J. Kranz & J. Rotem, eds.), pp. 35-50. Berlin: Springer-Veriag.
40. LANNOU, C, & SAVARY, S., 1991. The spatial structure of spontaneous epidemics of different diseases in a groundnut plot. Netherlands J. Plant PathoL 97, 355-68.
41. LEPS, J., 1990. Can underlying mechanisms be deduced from observed patterns? In: Spatial Processes in Plant Communities (F. Krahulec, A. D. Q. Agnew, S. Agnew, & H. J. Willems, eds.), pp. 1-11. Prague: Academia.
42. LOOMIS, R. S., & BENNETT, C. W., 1966. Competitive relationships in virus-infested sugar beet fields. J. Am, Soc. Sugar Beet Technol. 14, 218-31.
43. MADDEN, L. V., 1986. Statistical analysis and comparison of disease progress curves. In: Plant Disease Epidemiology, Vol. 1: Population Dynamics and Management (K. J. Leonard & W. E. Fry, cds.), pp. 3-37. New York: MacMillan Publishing.
44. MADDEN, L. V., 1989. Dynamic nature of within-field disease and pathogen distributions. In: Spatial Components of Plant Disease Epidemics (M. J. Jeger, ed.), pp. 96-126. Englewood Cliffs, NJ: Prentice Hall.
45. MADDEN, L. V., & CAMPBELL, C. L., 1986. Descriptions of virus disease epidemics in time and space. In: Plant Virus Epidemics: Monitoring, Modelling and Predicting Outbreaks (G. D. McLean, R. G. Garrett, & W. G. Ruesink, eds.), pp. 273-93. Sydney: Academic Press.
46. MADDEN, L. V., & CAMPBELL, C. L., 1990. Nonlinear disease progress curves. In: Epidemics of Plant Diseases: Mathematical Analysis andModeling, 2nd edn. (J. Kranz, ed.), pp. 181-229. Berlin: Springer-Verlag.
47. MADDEN, L. V., & HUGHES, G., 1994. BBD-Computer software for fitting the beta-binomial distribution to disease incidence data. Plant Disease 78, 536-40.
48. MADDEN, L. V., & HUGHES, G., 1995. Plant disease incidence: Distributions, heterogeneity, and temporal analysis. Ann. Rev. PhytopathoL 33, 529-64.
49. MADDEN, L. V. & NUTTER JR, F. W., 1995. Modeling crop losses at the field scale. Canad. J. Plant Pathol. 17, 124-37.
50. MADDEN, L. V., LOUIE, R., ABT, J. J., & KNOKE, J. K., 1982. Evaluation of tests for randomness of infected plants. Phytopathology 72, 195-8.
51. MADDEN, L. V., LOUIE, R., & KNOKE, J. K., 1987a. Temporal and spatial analysis of maize dwarf mosaic epidemics. Phytopathology 71, 148-56
52. MADDEN, L. V., PIRONE.T. P., &RACCAH, B., 1987b. Temporal analysis of two viruses increasing in the same tobacco fields. Phytopathology 77, 974-80.
53. MADDEN, L. V., PIRONE.T. P., & RACCAH, B., 1987C. Analysis of spatial patterns of virus-diseased tobacco plants. Phytopathology TJ, 1409-17.
54. MADDEN, L. V., REYNOLDS, K. M., PIRONE, T. P., & RACCAH, B., 1988. Modeling of tobacco virus epidemics as spatio-temporal autoregressive integrated moving-average processes. Phytopathology 78, 1361-6.
55. MADDEN, L. V., HUGHES, G., & ELLIS, M. A., 1995a. Spatial heterogeneity of the incidence of grape downy mildew. Phytopathology 85, 269-75.
56. MADDEN, L. V., NAULT, L. R., MURRAL, D. J., & APELT, M. R., 1995b. Spatial pattern analysis of the incidence of aster yellows disease in lettuce. Res. onPopuL Ecol. 37, 279-89.
57. MADDEN, L. V., HUGHES, G., & MUNKVOLD, G. P., 1996. Plant disease incidence: Inverse sampling, sequential sampling, and confidence limits when observed mean incidence is zero. Crop Protection 15, 621-32.
58. MARCUS, R., 1991. Deterministic and stochastic logistic models for describing increase of plant diseases. Crop Protection 10, 155-9.
59. MARCUS, R., FISHMAN, S., TALPAZ, H., SALOMON, R., & BAR-JOSEPH, M., 1984. On the spatial distribution of citrus tristeza virus disease. Phytoparasitica 12, 45-52.
60. MATTHEWS, R. E. F., 1991. Plant Virology, 3rd edn. San Diego, CA: Academic Press.
61. MAY, R. M., 1974. Stability and Complexity in Model Ecosystems, 2nd edn. Princeton: Princeton University Press.
62. McROBERTS, N., HUGHES, G., & MADDEN, L. V, 1996. Incorporating spatial variability into simple disease progress models for crop pathogens. Aspects AppL Biol. 46, 75-82.
63. MiNOGUE, K. P., 1989. Diffusion and spatial probability models for disease spread. In: Spatial Components of Plant Disease Epidemics (M. J. Jeger, ed.), pp. 127-43. Englewood Cliffs, NJ: Prentice Hall.
64. MUNKVOLD, G. P., DUTHIE, J. A., & MAROIS, J. J., 1993. Spatial patterns of grapevines with Eutypa dieback in vineyards with or without perithecia. Phytopathology 83, 1440-8.
65. NELSON, M. R., FELIX-GASTELUM, R., ORUM, T. V., STOWELL, L. J., & MYERS, D. E., 1994. Geographical information systems and geostatistics in the design and validation of regional plant virus management programs. Phytopathology 84, 898-905.
66. NELSON. S. C, 1995. Spatiotemporal distance class analysis of plant disease epidemics. Phytopathology 85, 37-43.
67. NELSON, S. C, 1996. A simple analysis of disease foci. Phytopathology 86, 332-9.
68. NELSON, S. C, MARSH, P. L., & CAMPBELL, C. L., 1992.2DCLASS, a two-dimensional distance class analysis software for the personal computer. Plant Disease 76, 427-32.
69. PERRY, J. N., 1994. Sampling and applied statistics for pests and diseases. Aspects AppL Biol. 37, 1-14.
70. PIANTADOSI, S., 1987. Generalizing growth functions assuming parameter heterogeneity. Growth 51, 50-63.
71. REYNOLDS, K. M., & MADDEN, L. V, 1988. Analysis of epidemics using spatio-temporal autocorrelation. Phytopathology 78, 240-6.
72. RODRIGUEZ-DE GONZALEZ, P., CHO, J. J., ULLMAN, D., & NELSON, S. C, 1995. Effect of different initial spatial patterns of zucchini yellow mosaic virus (ZYMV) on the spatial and temporal disease spread in zucchini squash (Abstract). Phytopathology 85, 1122.
73. ROUSE, D.I., 1985. Construction of temporal models: 1. Disease progress of air-borne pathogens. In: Advances in Plant Pathology. Vol. 3: Mathematical modelling of crop disease (C. A. Gilligan, ed.), pp. 11-29. New York: Academic Press.
74. SHAW, M. W., 1994. Modelling stochastic processes in plant pathology. Ann. Rev. Phytopathology 32, 523-44.
75. SHAW, M. W., 1995. Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance. Proc. R. Soc. Land. B 259, 2434-8.
76. SHAW, M. W., 1996. Simulating dispersal of fungal spores by wind, and the resulting patterns. Aspects AppL BioL 46, 165-72.
77. SHIYOMI, M., & TAKAI, A., 1979. The spatial pattern of infected or infested plants and negative hypergeometric series. Jpn. J. AppL Entomol. Zoology 23, 224-9.
78. SKELLAM, J. G., 1948. A probability distribution derived from the binomial distribution by regarding the probability of success as a variable between sets of trials. J. R. Statist. Soc. B 10, 257-61.
79. SMITH, D. M., 1983. Maximum likelihood estimation of the parameters of the beta binomial distribution. AppL Statistics 32, 192-204.
80. SNEDECOR, G. W., & COCHRAN, W. G., 1989. Statistical Methods, 8th edn. Ames, IA: Iowa State University Press.
81. STEIN, A., KOCKS, C. G., ZADOKS, J. C, FRINKING, H. D., RUISSEN, M. A., & MYERS, D. E., 1994. A geostatistical analysis of the spatio-temporal development of downy mildew epidemics in cabbage. Phytopathology 84, 1227-39.
82. TANNE, E., MARCUS, R., DUBITZKY, E., & RACCAH, B., 1996. Analysis of progress and spatial pattern of corky bark in grapes. Plant Disease 80, 34-8.
83. TAYLOR, L. R., 1961. Aggregation, variance and the mean. Nature 189, 732-5.
84. TAYLOR, L. R., 1984. Assessing and interpreting the spatial distributions of insect populations. Ann. Rev. Entomol. 29, 321-57.
85. TENG.P. S., 1981. Validation of computer models of plant disease epidemics: Areviewof philosophy and methodology. Zeitschrift ftir Pflanzenkrankheiten and Pflanzenschutz 88, 49-63.
86. THRESH, J. M., 1974. Temporal patterns of virus spread. Ann. Rev. Phytopathol 12, 111-28.
87. UPTON, G. J. G., & FINGLETON, B., 1985. Spatial Data Analysis by Example. Vol. 1: Point Pattern and Quantitative Data. Chichester: Wiley.
88. VANDERPLANK, J. E., 1946. A method for estimating the number of random groups of adjacent diseased plants in a homogeneous field. Trans. R. Soc. S. Africa 31, 269-78.
89. VANDERPLANK, J. E., 1963. Plant Diseases: Epidemics and Control. New York: Academic Press.
90. WAGGONER, P. E., 1986. Progress curves of foliar diseases: their interpretation and use. In: Plant Disease Epidemiology. Vol. 1: Population Dynamics and Management (K. J. Leonard & W. E. Fry, eds.), pp. 3-37 New York: MacMillan Publishing.
91. WAGGONER, P. E., & RICH, S., 1981. Lesion distribution, multiple infection, and the logistic increase of plant disease. Pmc. Nat. Acad ScL, USA78, 3292-5.
92. WEISZ, R., FLEISCHER, S., & SMILOWITZ, Z., 1995. Site-specific integrated pest management for high-value crops: Sample units for map generation using the Colorado potato beetle (Coleoptera: Chrysomelidae) as a model system. J. Econ. Entomol. 88, 1069-80.
93. Xu, X.-M., & RIDOUT, M., 1996. Analysis of disease incidence data using a stochastic spatio-temporal simulation model. Aspects Appl BioL 46, 155-8.