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RESULTS Data Summary Fig. 1B shows that a greyscale map (of common use to summarise topography, for example) allows an intuitive overview of how the disease spreads in the orchards in space and time. For the temporal patterns, Fig. 1A enhances the contrasting evolution of annual disease incidence in the 4 adjacent orchards during the years 1983-1989. Introduction of the Disease During the years 1983-1985 (respectively 1986-1989), the probability to observe no symptomatic tree in orchards 1 and 3 (resp. 3 and 4) under the hypothesis of a random introduction of the disease over the 4 orchards (25 (resp. 41) random inoculations) is: ⎛ N1 + N 25 3 ⎞ ⎛ N 3 + N − 9 41 4 ⎞ P1 = ⎜1− ⎟ P2 = ⎜1 − ⎟ ⎝ N1 + N 2 + N 3 + N 4 ⎠ ⎝ N1 + N 2 + N 3 + N 4 − 25 ⎠ where Ni is the number of trees in the i th orchard (see Fig. 1A for the values of Ni). Both probabilities are very low (P1 = 7.5×10 -11 and P2 = 4.4×10 -4 ), which indicates a very significant uneven timing of expression of ESFY in the 4 adjacent orchards. Spatial Characteristics within Each Period of the Epidemic Whatever the period considered, there was always an excess (significant or not) of pairs of points for the first two distance classes, and often up to 35 m (data not shown). Fig. 2 is given as an example, because spatial aggregation (corresponding to an high R index) becomes obvious when we consider the whole epidemic: the points for the first distance classes are clearly outside their respective 95% confidence intervals. DISCUSSION Methodological Considerations 1. Data Summary. Although significant methodological work have been devoted to the analysis of spatio-temporal binary data in plant epidemiology, more basic aspects have been neglected, which could hamper the optimal analysis of data sets. For example, a plot of the disease progress curve may not be the most meaningful representation for this kind of epidemics, because its cumulative nature can hide temporal patterns (e.g. cyclic patterns). Thus we chose to plot both annual incidence and cumulative incidence curves (which corresponds to the classical disease progress curves). For the mapping, our visual display contrasts with typical spatio-temporal maps (for example: Jarausch et al., 2001a; Pethybridge and Madden, 2003) in that a single map allows a direct perception of disease spread in time and space. As every summary, our representation has some limits: it is only made for binary data and it is not appropriate when one wants to take account of changes in the sanitary status of infected plants (recovery or replanting of healthy material). 2. Permutation Methods. These non-parametric tests are frequently used in the literature and specific computer applications based on these methods have been dedicated to the analysis of regularly spaced binary data, as 2DCLASS (Nelson et al., 1992) and STCLASS (Nelson, 1995) which allow routine analysis of spatial patterns of plant diseases. In our study, each plot was planted with a different combination of rootstock and cultivar, which had an obvious impact on the temporal evolution of the disease in each orchard (Fig. 1A), so the permutations were made inside each orchard. If spatial randomness is to be tested in a slightly different context (e.g. irregularly spaced plants), this method can be adapted easily. Our first approach also contrasts with two-dimensional distance class analyses in that the Euclidian distance between points is the only criteria to define a distance class (i.e. no directional information was used). This choice increases the number of pairs in each distance class and - 92 -
allows summarising in one graph (i) R: the observed excess of points as a function of distance and (ii) a 95% confidence interval for each distance class. Epidemiological Interpretations There are at least three assumptions that can account for the observed independent evolution of symptom expression in the 4 orchards during the first years of the epidemic: (i) ESFY has been introduced with the planting material, (ii) the rootstock and/or the cultivar influence the incubation period, (iii) the vectors have been attracted by 2 cultivars and/or rootstocks. The pattern for the years 1986-1989 suggests the secondary hypothesis of a gradient of infectious vectors coming from outside into the upper orchards. For the second test, we can give several interpretations of the spatial dependence between the nearest neighbours within each group of years: (i) the vectors (progeny included) infect several neighbouring trees, (ii) short-distance secondary spread and symptom expression occurs within each group of years, (iii) attractiveness and/or symptom expression are conditional to an underlying factor which acts at a short range. As far as spatial randomness is concerned, each test provides a clear answer. However, the matter in epidemiology is more often to determine the cause of a given non-randomness than to simply reject randomness. Therefore, we gave for each test a set of plausible explanatory assumptions, which are non-exclusive: a pattern can be the result of two phenomena or more. In order to link the observations to their cause, it is necessary to keep in mind that the whole survey relies on the visual detection of the first typical symptoms, so we have to be aware of the potential role of the incubation period. These results suggest three major explanatory hypotheses: (i) several neighbouring trees are probably infected by each vector (or group of vectors), (ii) the combination rootstock/cultivar could influence the length of the incubation period and (iii) the planting of diseased material is suspected. These last two points remind us that the impact of the disease on production can be decreased if the planting of highly susceptible cultivars is avoided and if all the necessary steps are taken to guarantee the initial sanitary status of the material (Labonne and Lichou, 2003). Concluding remarks Our preliminary results show that a case study, although limited in time and space, is a way to gain insights into the epidemiology of a disease if one carries out a detailed analysis of both spatial and temporal patterns (a detailed analysis of annual incidence could provide more information, but this is out of the scope of this article). The flexible approach of hypothesis testing is a first step towards modelling because it summarises and emphasizes the features of disease spread. These statistical tests also foster the statement of explanatory assumptions, which can then be included in the conceptual framework of a mechanistic model. Our future work will be dedicated to design a model that explicitly takes the vectors into account. ACKNOWLEDGEMENTS We thank Dr. Sylvie Dallot for her critical analysis of the manuscript. LITERATURE CITED Carraro, L., Loi, N. and Ermacora, P. 2001. Transmission characteristics of the European stone fruit yellows phytoplasma and its vector Cacopsylla pruni. Eur. J. Plant Pathol. 107:695-700. Carraro, L., Osler, R., Loi, N., Ermacora, P. and Refatti, E. 1998. Transmission of European stone fruit yellows phytoplasma by Cacopsylla pruni. J. Plant Pathol. 80:233-239. Chabrolin, C. 1924. Quelques maladies des arbres fruitiers de la vallée du Rhône. Annales des Epiphyties. 10:263-338. - 93 -
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Ecole Nationale Supérieure Agronom
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Glossaire A leur première occurren
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C. Conclusions sur l’étude des v
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Introduction - 7 - « Deux grands m
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l’intensification permanente de l
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Ceci nous amène aux enjeux liés
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(b) Coût de la lutte contre l’ES
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Royaume- Uni Espagne Allemagne Belg
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1992) ; par contre, le cerisier dou
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6) Vection Le vecteur de l’ESFY (
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(b) Caractéristiques de la vection
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Conifères ? Rétention du phytopla
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Partie I : Identifier des facteurs
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Identifying Risk Factors from a Sur
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MATERIALS AND METHODS Data Record a
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visual inspection of their spatial
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Influence of the Risk Factors. The
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Model Application This kind of mode
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ACKNOWLEDGEMENTS We are much indebt
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42. Seemüller, E., and Schneider,
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Kamphorst E.C. , Chadøeuf J. , Jet
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RESUME Les maladies (ré-)émergent
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