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measurements of severity. Three types of analysis have been used to describe the I-S
relationship: these are correlation and regression, multiple infection models and the
measurement of aggregation (Seem, 1984). Drawing on Seem's approach, Hughes
et al. (1997) formulated relationships between measurements of disease incidence
made at two levels in a spatial hierarchy. Disease incidence at the higher scale was
shown to be an asymptotic function of incidence at the lower scale, the degree of
aggregation at that scale, and the size of the sampling unit. Turechek and Madden
(2003) extended this work to a three-scaled hierarchial system. Daamen (1986b)
studied the I-S relationship in powdery mildew of winter wheat. The model
explained the effects of leaf, pustule and cluster size on the I-S relationship and
could also be applicable to systemic foliar diseases when a minimum lesion size is
defined. Hughes et al . (2004) revisited Daamen's I-S relationship with the aim of
widening the application of the model. Fitt et al . (1998) working with light leaf spot
(caused by Pyrenopeziza brassicae ) on winter oilseed rape studied the I-S
relationship by assessing the disease as % plants, % leaves or % leaf area (severity);
regression analyses showed good relationships between % leaves (incidence at the
leaf scale and severity at the plant scale) and % plants (incidence) until % plants
approached 100%. Silva-Acuna et al. (1999) working with coffee rust found
incidence could be used to estimate two measures of severity. Groth and Ozmon
(1999) tested the repeatability and relationship of incidence and severity assessments
in Fusarium ear blight of wheat over a three-year period and found them to be
highly correlated. Xu et al. (2004) also investigated the I-S relationship in Fusarium
ear blight of wheat in order to predict disease severity (number of infected spikelets)
using infected ear incidence. This relationship was considered important for
predicting the risk of mycotoxin contamination in the grain. The authors found a
robust I-S relationship assuming a fixed variance-mean relationship and a negative
binomial distribution for the number of infected spikelets and based on the
complementary log-log or logit transformation of ear and spikelet infection
incidence. However, incidence can be overestimated in an entire field and a more
reliable method might be to visually estimate the incidence of Fusarium ear blight in
several sub-samples and then to calculate an average for the field or plot (Shaner,
2003). Xu and Madden (2002) explored the relationships between disease incidence
and colony density at the same scale and across scales (leaf and shoot) in apple
powdery mildew with the aim of finding a robust relationship for predicting density
using leaf or shoot incidence. The authors pointed out that with binomially
distributed random data, incidence at the lower scale could be predicted from that at
the higher scale, but with aggregated data, the beta-binomial distribution could not
easily predict incidence of the lower scale from that at the higher scale.
Other direct methods of quantifying disease may involve estimations of disease
intensity or prevalence. Intensity is often used to denote measures of the number of
fungal colonies on leaves; it is also measured as both incidence and severity. Jeger
(1981) found consistent relationships between incidence and intensity for apple scab
caused by Venturia inaequalis. Daamen (1986a) working with wheat powdery
mildew concluded that at low disease intensities (<5 pustules per leaf) and small
sample sizes (<12 leaves) it was more efficient to sample the upper surface only than
both surfaces. Prevalence is an ambiguous term and usually refers to disease
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