Ecole Nationale Supérieure Agronomique de Montpellier ... - CIAM

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 -