Agriculture Reference
In-Depth Information
where
b
1
…
b
n
are partial regression coefficients for the first and
n
th week
respectively, and
X
1
…
X
n
are the corresponding weekly disease increments for the
first and the
n
th week, respectively. In a classic study, James
et al
. (1972) developed
a multiple-point model for estimating loss in tuber yield due to late blight of potato
using disease increments during weekly intervals as the independent variable. Using
the equation, the estimated loss was within 5% of the actual loss in nine cases out
of 10. However, there is a need to examine whether a multiple-point model is
biologically meaningful, as stepwise-selected regression models often contain both
positive and negative estimated coefficients. Careful evaluation of regression results,
especially intercorrelation of the
X
s, is essential to avoid conclusions that imply an
increase in disease severity at a particular time or growth stage produces an increase
in yield, rather than a decrease.
Calpouzos
et al.
(1976) developed another form of multiple-point model for
estimating losses due to wheat stem rust. Yield loss was plotted as a response-
surface (a three-dimensional graph) and was a function of the slope of the epidemic
and the growth stage at the time of epidemic onset using the equation:
% loss (L) =
f
(
X
1
X
2
)
(2.3)
where
X
1
= slope of the epidemic (infection rate) and
X
2
= growth stage at epidemic
onset.
Van der Plank (1963) proposed a modification of the multiple-point model in
which the area under the disease progress curve (AUDPC) is used as a descriptor for
the epidemic to measure crop loss. The AUDPC, an integral model, relates loss to a
summing of disease measurements over a specific period of crop growth. AUDPC
can be estimated using the following equation of Shaner and Finney (1977):
1
∑
n
−
⎛
⎞
y
i
+
y
i
+1
t
i
)
(2.4)
AUDPC
=
(
t
i
+1
−
⎜
⎟
⎝
2
⎠
i
in which
n
is the number of assessment times,
y
is the disease measurement and
t
is
time (usually in days or degree days). AUDPC is simply
y
integrated between two
times and can be approximated using the midpoint rule or trapezoidal integration
method. As shown in Fig. 2.12 (Campbell and Madden, 1990b), the disease progress
is divided into a series of rectangles, the areas of which are summed to approximate
the total area under the curve. The narrower the intervals between assessments, the
more accurate is the determination of AUDPC, which can be standardized by
dividing its value with the total time duration (
t
n
-
t
1
) of the epidemic. This allows
for comparisons between epidemics of differing durations and allows two epidemics
to be distinguished which have different progress curves but the same disease
severity at a critical date.
AUDPC models make two assumptions: injury to the host is proportional to the
amount of tissue infected; and injury is proportional to the duration of the disease.
Most AUDPC models have been used for epidemics of relatively short duration,
