VIEW ARTICLE

Ecology and Epidemiology

Modeling of Tobacco Virus Epidemics As Spatio-Temporal Autoregressive Integrated Moving-Average Processes. L. V. Madden, Associate professor, Department of Plant Pathology, The Ohio State University (OSU), Ohio Agricultural Research and Development Center (OARDC), Wooster 44691; K. M. Reynolds(2), T. P. Pirone(3), and B. Raccah(4). (2)Former post-doctoral research associate, Department of Plant Pathology, The Ohio State University (OSU), Ohio Agricultural Research and Development Center (OARDC), Wooster 44691, Current address: Forest Sciences Lab, 201 E. 9th Ave., Suite 105, Anchorage, AK 99501; (3)Professor, Department of Plant Pathology, University of Kentucky, Lexington 40546; (4)Senior research scientist, Virus Laboratory, Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel. Phytopathology 78:1361-1366. Accepted for publication 24 May 1988. Copyright 1988 The American Phytopathological Society. DOI: 10.1094/Phyto-78-1361.

Epidemics caused by tobacco etch virus (TEV) and tobacco vein mottling virus (TVMV) were monitored in six experimental fields of tobacco in Kentucky from 1983 to 1985. Fields were divided into contiguous quadrats of 40 or 60 plants each, and disease intensity was represented as the logit of disease incidence in quadrat i at time t (y_{i, t}). A spatio-temporal autocorrelation analysis of 16 virus epidemics was performed by calculating autocorrelations and partial autocorrelations for up to three lags in time and space. As expected, y in each quadrat was highly correlated (P < 0.01) with y in the same quadrat at the previous time (6 or 7 days earlier, the approximate disease latent period), and also with y in the neighboring quadrats at the previous time. Autocorrelograms indicated that the epidemics were not stationary over time or space, i.e., expected disease level depended on location and assessment period. Therefore, simultaneous spatio-temporal differences (∇ _STy_{i, t}) were calculated; autocorrelations and partial autocorrelations were determined for the differenced data. Differencing eliminated all significant autocorrelations and partial-autocorrelations in nine of 16 analyzed epidemics, suggesting that the expected ∇ _STy_{i, t} equaled a constant. This means that y_{i, t} was determined by y at the previous time in the same quadrat and the increase in y in the proximal quadrats. Six epidemics had significant and nondeclining partial autocorrelations over time at zero spatial lags, indicating that, in addition to the relation found for the first nine epidemics, y_{i, t} could be represented by an autoregressive model with terms consisting of differenced y’s for three temporal lags but no spatial lags. Finally, one epidemic was identified as being described by a mixed autoregressive moving-average model. Here, y_{i, t} could be modeled as a function of the differenced y’s and differenced error (disturbance) terms at one temporal and spatial lag. Interpretations of the identified models are presented.