Agriculture Reference
In-Depth Information
known physiological processes or can be expanded to accommodate such processes.
Teng (1985) classified empirical loss models into six categories: (1) single-point
(critical-point) models, (2) multiple-point (multiple regression) models, (3)
response-surface models, (4) integral models, (5) generalized or non-linear models,
and (6) synoptic models. The first five models describe losses in yield due to one
disease, whereas synoptic models include variables for several diseases and non-
disease factors. Another approach to classifying such models is to consider whether
the model uses one or more independent variables or how many estimates of disease
are made over time.
In single-point or critical-point models, yield loss is related to disease
measurement at one specific time during the growing season or at a specific growth
stage. Models using time to a certain disease severity are also considered as critical-
point models. It should be remembered that a critical-point model does not imply
that a host plant responds to a disease at only one time or growth stage, but rather
that a good statistical relationship is found at one specific time. This type of model is
probably the most commonly used because of the small amount of data required and
has been heavily employed for grain crops where epidemics with a reasonably stable
infection rate occur near to grain-filling. Single-point models may be linear or non-
linear in their parameters and can be written in the form:
% loss (L) = a + bX
(2.1)
in which a and b are parameters and X is the disease measurement or a
transformation of disease measurement at a given time. Examples of critical-point
models are those developed for cereal diseases (Table 2.6) and that of Large (1952)
for late blight of potato (Fig. 2.11). The models shown for cereal foliar diseases
were developed to estimate yield loss from corresponding disease severity estimates
at particular growth stages, whereas those for cereal stem-base diseases (eyespot and
sharp eyespot) were developed for use with disease incidence values (Cook and
King, 1984). Large's critical point model for estimating yield losses from late blight
of potato uses time to a critical disease severity: the model assumes bulking up of
potato tubers ceases when 75% blight severity on the haulm is reached. A major
problem with critical-point models is that they fail to accommodate variables in
infection rates and shape of the disease progress curve.
Multiple-point models can be used for diseases with high variability in infection
rates and where the disease progress curves can be markedly different. These models
can be used for epidemics that develop over a long time period relative to the life of
the crop and where yield accumulation is a prolonged process (e.g. potatoes).
Multiple-point models relate yield loss to assessments of disease made at several
times during the growth season. Assessments can be made at specific times or at
specific host plant growth stages. Loss is then related to disease measured at each of
these points during the epidemic or to the change in disease between assessments
using a multiple regression equation, with the general form:
% loss (L) = b 1 X 1 + b 2 X 2 + b 3 X 3 b n X n
(2.2)
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