Agriculture Reference
In-Depth Information
frequently in field epidemics. For example, incidence of diseased leaves may
decrease in time due to rapid production of new leaves and/or defoliation of diseased
leaves, commonly observed for rose downy mildew (Xu and Pettitt, 2003), or
incidence of diseased leaves may stagnate for a long period of time and then
increase rapidly, common for wet-loving pathogens in dry years. When observed
disease patterns can be fitted satisfactorily to a model, then AUDPC can be directly
obtained from the model integrated over time (Jeger and Viljanen-Rollinson, 2001).
AUDPC is usually estimated using the mid-point rule (so-called trapezoidal
integration method), although other more complicated integration methods can be
used as well:
(
)
=
n
1
y
+
y
(
)
(8.9)
AUDPC
=
i
i
+
1
×
t
t
i
i
1
2
i
1
When we compare different epidemics, it may be necessary to standardise AUDPC
values in order to take into account the fact that epidemics may differ in their
lengths of duration. A standardised AUDPC value is obtained by dividing the
AUDPC by the total duration time and sometimes by the integration interval (
t ).
AUDPC is a simple statistic and yet is found to be very useful in many
investigations in evaluating disease management practices (Jeger, 2004). For
example, AUDPC calculated from two data points provides an equivalent amount of
information as from repeated assessments in assessing wheat cultivar resistance to
stripe rust (Jeger and Viljanen-Rollinson, 2001). In addition to several other
variables describing various aspects of epidemic development, AUDPC is a useful
predictor for crop loss in chickpea due to Fusarium wilt (Navas-Cortes et al. , 2000;
see also Chapter 2).
8.3.4 Time series analysis
Successive disease assessments are usually correlated with each other. Analysis of
such a variable with temporal autocorrelation can be better approached by time
series methods (Wei, 1990). Time series analyses may reveal the nature of the
system generating the series and can be used to study the dynamic relationship
between two or more related series. As time series needs many temporal
assessments, realistically only spore trapping data are suitable for time series
analysis. There are two main methods of time series analyses: AutoRegressive
Integrated Moving Average (ARIMA) models and transfer function analysis (TF).
ARIMA models are used to study the nature of the series itself and are built from
several simpler components. In an autoregressive (AR) model, the current value is
linearly related to previous values. A random variable, a t , is added to the AR
component to account for any residual error. In an autoregressive moving average
(ARMA) model, the current value is linearly related not only to previous values, the
AR component, but also to the current and previous values of the random variable
{a t }. Terms involving the random variable are the moving average component.
Trends in a series can often be removed by differencing the series. An ARIMA
model is one in which a differenced series can be well described by the model. An
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