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Parametric bootstrap. When some predicted values (pi) are close to zero or when the number of individuals in some orchards (ni) is very low, the assumptions for the asymptotic results are not met. This situation can arise quite frequently in epidemiological surveys. In such circumstances, parametric bootstrap procedures could be used more frequently when satisfactory resampling models are available. Here, we expressed the parameters of the betabinomial distribution as a function of φ and pi (the overdispersion parameter and estimated proportions, respectively). To our knowledge, it is a new result that allows computing parametric bootstrap confidence intervals for overdispersed logistic models. In practice, bootstrap and asymptotic methods gave consistent results in the identification of outliers, and similar confidence intervals for the species effect (Table 2) as well as for half of the parameters of the final model (Table 3). For the other parameters, the bootstrap intervals were wider, hence more conservative. Concluding Remarks Performing a large-scale disease assessment, for a control program for example (11,12,20), can provide reliable information for epidemiological studies. In such situations, a close collaboration with plant protection services from the initial steps is a prerequisite to ensure an optimal exploitation of the collected data. Otherwise, some data which are inexpensively and easily obtained and which are important for epidemiological exploitation could be omitted because of lack of interest in the control strategy. The analysis of such a survey with a logistic regression model enabled the identification and ranking of general risk factors for ESFY incidence. In summary, in addition to the obvious cumulative effect of the age, the main determinant was the choice of the scion (the species being of major importance, followed by the cultivar). This result highlights the need for a rigorous experimental or field evaluation of the sensitivity of different cultivars to ESFY, as a basis for future genetic improvement. The planting density and the rootstock appeared to play a secondary role, and at least one unidentified human factor had a significant impact. More detailed investigations of the grower-specific agricultural practices would possibly identify other risk factors, and the analysis of the spatiotemporal point pattern formed by the diseased trees would probably provide insight into the transmission behavior of C. pruni. APPENDIX Here we show how the parameters of a beta-binomial model can be derived from an overdispersed binomial model fitted by the Williams procedure (48) providing estimates of both pi and the overdispersion parameter φ. Let Yi be a binomial random variable: Yi ~ B(ni,pi). The variance of Yi is: Var(Yi) = ni pi (1-pi). As explained in pp.192-195 of Collett (8), the variance of an overdispersed binomial variable Yi can be written: Var(Yi) = ni pi (1-pi) (1+(ni-1)φ). This is in particular the variance of a beta-binomial random variable Yi in which Yi|Pi ~ B(ni,pi), Pi having a Beta distribution with E(Pi) = pi and Var(Pi) = φ pi (1-pi). As the mean and variance of a random variable Pi with a Beta distribution (with shape parameters αi and βi) are E(Pi) = αi/(αi+βi) = pi, and Var(Pi) = pi (1-pi)/(αi+βi+1), we obtain by identification and resolution of the subsequent twoparameter equation: ⎛ 1 ⎞ ⎛ 1 ⎞ αi = pi⎜ −1⎟ and βi = (1-pi) ⎜ −1⎟ . ⎝φ ⎠ ⎝φ ⎠ Thus, the parameters pi and φ estimated by Williams’ algorithm define the parameters αi and βi of the beta-binomial distribution. These parameters can then be used in a parametric bootstrap procedure to derive confidence intervals for the predicted incidence in the orchards (pi) and for the parameters (ak) of the logistic regression model. - 36 -
ACKNOWLEDGEMENTS We are much indebted to the growers of Crau, to I. Ricavy and Y. Fradin (experimental station La Pugère), and to the Chambre d’Agriculture des Bouches-du-Rhône for data collection, and for creating and actualizing the database. We wish to thank E. Klein and C. Bruchou for helpful discussions, J.-N. Bacro and S. Dallot for critically reviewing the manuscript and M. Hilf for improving the English. This study was partly funded by the Conseil Régional de PACA. LITERATURE CITED 1. Aegerter, B. J., Nuñez, J. J., and Davis, R. M. 2003. Environmental factors affecting rose downy mildew and development of a forecasting model for a nursery production system. Plant. Dis. 87:732-738. 2. Burt, C. 1950. The factorial analysis of qualitative data. Br. J. Stat. Psychol. 3:166-185. 3. Carraro, L., Ferrini, F., Ermacora, P., and Loi, N. 2002. Role of wild Prunus species in the epidemiology of European stone fruit yellows. Plant Pathol. 51:513-517. 4. Carraro, L., Ferrini, F., Ermacora, P., and Loi, N. 2004. Transmission of European stone fruit yellows phytoplasma to Prunus species by using vector and graft transmission. Acta Hortic. 657:449-453. 5. 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. 6. Carraro, L., Osler, R., Refatti, E., and Favali, M. A. 1992. Natural diffusion and experimental transmission of plum leptonecrosis. Acta Hortic. 309:285-290. 7. Chabrolin, C. 1924. Quelques maladies des arbres fruitiers de la vallée du Rhône. Annales des Epiphyties 10:263-338. 8. Collett, D. 1991. Modelling Binary Data. 1st ed. Chapman and Hall, London. 9. Cook, R. D., and Weisberg, S. 1982. Residuals and Influence in Regression. Chapman and Hall, London. 10. Crowder, M. J. 1978. Beta-binomial anova for proportions. Appl. Stat. 27:34-37. 11. Dallot, S., Gottwald, T., Labonne, G., and Quiot, J.-B. 2003. Spatial pattern analysis of Sharka disease (Plum pox virus strain M) in peach orchards of southern France. Phytopathology 93: 1543-1552. 12. Dallot, S., Gottwald, T., Labonne, G., and Quiot, J.-B. 2004. Factors affecting the spread of Plum pox virus strain M in peach orchards subjected to roguing in France. Phytopathology 94:1390-1398. 13. De Wolf, E. D., Madden, L. V., and Lipps, P. E. 2003. Risk assessment models for wheat Fusarium head blight epidemics based on within-season weather data. Phytopathology 93:428-435. 14. Diggle, P. J. 1983. Statistical Analysis of Spatial Point Patterns. Mathematics in Biology. Academic Press, London. 15. Duval, H. 1999. Prunes japonaises : un défi à relever. L'Arboriculture Fruitière 524:35-41. 16. Duval, H., Jullian, J.-P., and Lemaire, J.-M. 1999. Enroulement chlorotique de l'abricotier : évaluation de la sensibilité des principales variétés de prunier japonais... et du nouveau sur le vecteur. Phytoma 516:38-40. 17. Efron, B., and Tibshirani, R. J. 1993. An Introduction to the Bootstrap. Chapman and Hall, New York. 18. Garrett, K. A., Madden, L. V., Hughes, G., and Pfender, W. F. 2004. New applications of statistical tools in plant pathology. Phytopathology 94:999-1003. 19. Goidanich, G. 1933. Un deperimento dei susini. Boll. Reg. Staz. Patol. Veg. Roma 13:160-173. 20. Gottwald, T. R., Sun, X., Riley, T., Graham, J. H., Ferrandino, F., and Taylor, E. L. 2002. Geo-referenced spatiotemporal analysis of the urban citrus canker epidemic in Florida. - 37 -
Page 1 and 2: Ecole Nationale Supérieure Agronom
Page 3 and 4: Glossaire A leur première occurren
Page 5 and 6: C. Conclusions sur l’étude des v
Page 7 and 8: Introduction - 7 - « Deux grands m
Page 9 and 10: l’intensification permanente de l
Page 11 and 12: Ceci nous amène aux enjeux liés
Page 13 and 14: (b) Coût de la lutte contre l’ES
Page 15 and 16: Royaume- Uni Espagne Allemagne Belg
Page 17 and 18: 1992) ; par contre, le cerisier dou
Page 19 and 20: 6) Vection Le vecteur de l’ESFY (
Page 21 and 22: (b) Caractéristiques de la vection
Page 23 and 24: Conifères ? Rétention du phytopla
Page 25 and 26: Partie I : Identifier des facteurs
Page 27 and 28: Identifying Risk Factors from a Sur
Page 29 and 30: MATERIALS AND METHODS Data Record a
Page 31 and 32: visual inspection of their spatial
Page 33 and 34: Influence of the Risk Factors. The
Page 35: Model Application This kind of mode
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Page 41 and 42: TABLE 5: Analysis of deviance for e
Page 43 and 44: Fig. 2. Examination of the model fi
Page 45 and 46: II. Bilan Au-delà des effets évid
Page 47 and 48: Partie II : Identifier les cycles b
Page 49 and 50: A toolbox for the specific detectio
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Page 59 and 60: ESFY G1R (X) ESFY G2 (X) AP15R (X)
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Page 63 and 64: C. pruni Reimmigrants The percentag
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Page 67 and 68: Si l’expérience est répétée d
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Page 73 and 74: inside the cage. The cages were rem
Page 75 and 76: Quantification of ‘Ca. P. prunoru
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Page 79 and 80: Table 2. Occurrence of Cacopsylla p
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émergents migrent dans des massifs
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identique à Qc(d) sauf qu’elle e
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MATERIALS AND METHODS Characteristi
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allows summarising in one graph (i)
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(A) (B) Fig. 1. Summary of the spat
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Investigating Disease Spread betwee
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when some plants may be missing for
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the graphical display by an appropr
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shows that the proportion of missin
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the approach developed by Pélissie
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APPENDIX Test 2. This section corre
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several types of points. J. R. Stat
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TABLE 4. Type I error and power of
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Fig. 2. Spatiotemporal pattern of d
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IV. Application à l’analyse de c
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Verger D1-4 Verger BH1 Verger BH2 V
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annuelle (Figure 1 de l’Article V
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consiste à disposer de vergers à
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Partie IV : Synthétiser l’inform
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Tableau 6. Propriétés biologiques
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Conclusion - 127 - « Il importe de
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fonctionnement du système épidém
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Tableau 7. Avantages et inconvénie
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malades correspondrait alors unique
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Expérimentations expérimentales S
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Références bibliographiques - 137
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30. Chabrolin C. (1924) Quelques ma
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86. Institute of Medicine (1992) Em
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138. Morvan G. (1977) Apricot chlor
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190. Torres E., Martin M. P., Paltr
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Annexes - 147 -
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if (estim!=1) W2.99) text(B2,0,past
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if ((sum(Do[1:4])!=0)&(sum(do1D)==0
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III. Annexe 3 : Programme R pour si
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IV. Annexe 4 : “Testing Boolean A
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Testing boolean assumption in the n
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ehavior, which is difficult to obse
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distributed. So, the length distrib
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ule which transforms the tangent po
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large void segments will clearly ap
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together with local measurements at
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Kamphorst E.C. , Chadøeuf J. , Jet
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c.d.f 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2
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0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4
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c.d.f. c.d.f. c.d.f. 0.0 0.2 0.4 0.
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RESUME Les maladies (ré-)émergent
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