1Institute of Ecology and Resource Management, University of Edinburgh, Edinburgh EH9 3JG, Scotland, UK; 2Biomathematics and Statistics Scotland, Mayfield Road, Edinburgh EH9 3JZ, Scotland, UK; 3USDA Agricultural Research Service, Orlando, FL 32803, USA

Background and objectives
Citrus tristeza virus (CTV) disease is the most economically important viral disease of citrus in the world. As a result, substantial resources have been devoted to gathering data on the spread of CTV disease in time and space. While these data were intended primarily as a basis for devising and monitoring CTV disease management programmes, they are also sufficiently extensive for use in the identification of empirical generalizations about observed patterns of disease (dispersion) [1], and in the development of stochastic models of disease spread (dispersal) [2].

Materials and methods
Data sets from four large surveys of CTV disease incedence formed the basis of the present study. In Spain [3] and California (T.R.G., unpublished data), the predominant vector species was the melon aphid (Aphis gossypii), whereas in Costa Rica [4] and the Dominican Republic [4], the predominant vector species was the brown citrus aphid (Toxoptera cittricida). In each case, CTV disease incidence was determined by ELISA of leaf material sampled from individual trees. Small-scale patterns of disease were summarized using the methodology suggested in [1]. For each CTV disease assessment, the resulting map showing the location and disease status of each individual tree was divided into quadrats containing four trees in a two-by-two arrangement. The frequency distribution of diseased trees per quadrat was compiled for each assessment. For each frequency distribution, the observed mean and variance of disease incidence were calculated, as was the theoretical variance for the binomial (random) distribution with the same mean as that of the observed data. For each location, a graph of observed variance against binomial variance (with logarithmic scales on both axes) was plotted.

Mechanisms of spatio-temporal disease spread were investigated using stochastic models as outlined in [2], using small subsets of the data from Spain [3], Costa Rica [4], and the Dominican Republic [4]. This involved the estimation of two parameters, one characterizing the rate at which susceptible trees in a grove acquire CTV via background transmission from a primary source outside the grove, the other characterizing the rate at which local (within-grove) transmission of CTV from an infected tree to a susceptible tree declines with increasing distance between them.

Results and conclusions
For each location, the relationship between the observed variance and the binomial variance (on logarithmic axes) was linear. For the data sets from Spain and California, the results suggested that the pattern of CTV disease incidence at the within-quadrat scale was indistinguishable from random. For the data sets from Costa Rica and the Dominican Republic, the majority of data points lay above the 'binomial line', indicating aggregation at the within-quadrat scale. Analysis of two subsets of the data from Spain using stochastic models [2] did not support the idea that the patterns observed were the result only of local interactions within groves, or of random processes involving background transmission from an external source. The most likely dispersal model incorporated a combination of short-range local transmission and background infection. Similar analysis of subsets of the data from Costa Rica and the Dominican Republic provided evidence that observed patterns of CTV disease incidence were primarily the result of within-grove transmission. Differences in the parameter estimates for the dispersal model and in the statistical summary of observed patterns of disease reflect aspects of the behavioural ecology of two main vector species, since citrus is the preferred host for T. ;citricida, but not for A. ;gossypit.

1. Hughes G, Madden LV, 1992. Plant Pathology 41, 657-660.
2. Gibson GJ, 1997. Phytopathology 87, 139-146.
3. Gottwald TR, Cambra M, Mopreno P, Cumarasa E, Piquer J, 1996. Phytopathology 86, 45-55.
4.Gottwald TR, Garnsey SM, Borbon J, 1998. Phytopathology 88, in press.