Ecole Nationale Supérieure Agronomique de Montpellier ... - CIAM

MATERIALS AND METHODS
Characteristics of the Group of Orchards
The 4 contiguous plots, planted in 1982, are located in the Rhone Valley near the city of
Valréas (Vaucluse, France). They are quite isolated from other orchards (the closest one is
about 3 km away). Their size ranges from 68 to 596 trees, and the planting distance is 5 m
within and across rows. Each orchard was planted with a different combination
rootstock/cultivar. Three apricot cultivars (‘Polonais’, ‘Rouge de Fournès’ and ‘Modesto’),
and four rootstocks were used: myrobalan (P. cerasifera), GF 8-1 (P. marianna), GF 31
(P. cerasifera × P. salicina) and P. armeniaca ‘Manicot’ (for more details, see Fig. 1A).
Symptomatic trees were not removed. Most of them died within about 2 years. Before 1993,
dead trees were replaced; after this year, they were just cut.
Disease Assessment
From March 1984 to March 2000, this group of orchards was inspected twice a year (in
March and October). The trees with typical ESFY symptoms (early bud break, paper-like
rolled leaves, off-season growth) were located on a map. The trees with new symptoms in
March were pooled with those recorded in October the year before, because the vectors live
on Prunus from March to July (Labonne and Lichou, 2003). Replanted trees were not taken
into account in the analyses in order to avoid additional uncontrolled variability because of
age or cultivar differences.
Statistical Methods
1. Temporal Analysis. We depicted both annual disease incidence and cumulative
disease incidence. Incidence is defined as the ratio of the number of new symptomatic trees to
the number of susceptible trees (living trees that never showed symptoms).
2. Spatio-temporal Analysis. The data set was cut into 4 distinct periods (1983-85; 1986-
89; 1990-95; 1996-99) based on the temporal evolution of disease incidence. We first tested
the evenness of disease introduction between the 4 orchards during the years 1983-85 and
1986-89, so we calculated the likelihood to see no symptomatic tree inside 2 plots out of 4,
under the assumption of a random introduction of the disease.
In a second test, we inspected the spatial randomness of diseased trees for each period and
also for the whole duration of the epidemic. We used a method based on distances between all
possible pairs of points and related to 2DCLASS (Gray et al., 1986; Nelson et al., 1992). For
each possible pair of symptomatic trees, the distance between the two points was computed
and assigned to a distance class (noted d). Then we performed 1000 simulations under the
spatial randomness hypothesis by reallocating (randomly) an equal number of diseased trees
within each orchard (thus conserving the structure of the group of orchards). For each
simulation (noted s), the number of pairs of symptomatic trees in the distance class d, noted
Nsim(s,d), was counted. Then for each of the 21 distance classes, we calculated R(d) which is
the ratio between the number of observed pairs Nobs(d), and the mean number of simulated
pairs Nsim (d) . Each R(d), mathematically defined below, was then plotted with its 95%
confidence interval.
1000
N
∑
s=
sim(s,
d)
Nobs(d)
1
R(d) = , with Nsim (d) =
Nsim(d)
1000
For the first test, the likelihood was straightforward to obtain, whereas for distance class
tests the statistic R(d) was compared to an empirical 95% confidence interval (Diggle,1983)
estimated after 1000 simulations of the null hypothesis (the 25 th and 975 th smallest values of
the simulated statistic were used). The points lying outside the confidence interval indicate
distance classes that depart from the null hypothesis.
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