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Investigating Disease Spread between Two Assessment Dates with Permutation Tests on a Lattice

First, third, and fifth authors: Institut national de la recherche agronomique (INRA), UMR BGPI, CIRAD TA 41/K, Campus international de Baillarguet, 34398 Montpellier Cedex 5, France; first and second authors: INRA, Unité de Biométrie, Domaine Saint-Paul, Site Agroparc, 84914 Avignon Cedex 9, France; and fourth author: INRA, UMR Santé Végétale, 71 avenue Edouard Bourlaux, BP 81, 33883 Villenave-d'Ornon Cedex, France

Mapping and analyzing the disease status of individual plants within a study area at successive dates can give insight into the processes involved in the spread of a disease. We propose a permutation method to analyze such spatiotemporal maps of binary data (healthy or diseased plants) in regularly spaced plantings. It requires little prior information on the causes of disease spread and handles missing plants and censored data. A Monte Carlo test is used to assess whether the location of newly diseased plants is independent of the location of previously diseased plants. The test takes account of the significant spatial structures at each date in order to separate nonrandomness caused by the structure at one date from nonrandomness caused by the dependence between newly diseased plants and previously diseased plants. If there is a nonrandom structure at both dates, independent patterns are simulated by randomly shifting the entire pattern observed at the second date. Otherwise, independent patterns are simulated by randomly reallocating the positions of one group of diseased plants. Simulated and observed patterns of disease are then compared through distance-based statistics. The performance of the method and its robustness are evaluated by its ability to accurately identify simulated independent and dependent bivariate point patterns. Additionally, two realworld spatiotemporal maps with contrasting disease progress illustrate how the tests can provide valuable clues about the processes of disease spread. This method can supplement biological investigations and be used as an exploratory step before developing a specific mechanistic model.

Additional keyword: censoring , distance class , European stone fruit yellows , nonparametric , Plum pox virus , toroidal shift .