Agriculture Reference
In-Depth Information
determine the appropriateness of a model do not usually consider the model's
relevance to the characteristics of the pathosystem concerned.
To compare the rate of disease increase (i.e. parameter
r
) between different
models, a weighted mean absolute rate of disease increase can be estimated as
ρ =
(Campbell and Madden, 1990), where
r
is the rate parameter of the
specific model,
K
is the estimated maximum disease and
m
is the shape parameter
(
m
= 0, 1 and 2 for the monomolecular, Gompertz and logistic models, respectively).
This absolute rate of increase is extremely valuable since it allows comparisons
between different types of models. Use of these models to describe observed
epidemics is widespread and often becomes a routine first step analysis to evaluate
treatment effects or establish relationships of disease development with crop growth
or loss (Jeger, 2004).
(
)
rK
/2
m
+
2
Figure 8.1. Examples of disease progress curves represented by monomolecular, logistic and
Gompertz models with an equivalent weighted mean absolute rate (
ρ
= 0.03),
y
0
= 0.01 and
K
= 1.0.
In the past, linearised models (Table 8.1) were usually used to fit temporal disease
data mainly because of the difficulties in performing non-linear regression analysis
using the standard statistical software packages at the time. Nowadays, advances in
computing power and widely available powerful statistical computing software have
made use of model fitting based on linearised forms far less appealing and indeed
appropriate than using non-linear regression analysis. In general, fewer assumptions
are made with non-linear analysis than with linearised regression. Furthermore, the
