Agriculture Reference
In-Depth Information
Interpretation of analytical models should be tempered by at least two important
considerations. First, all of the assumptions (implicit as well as explicit) used for
model construction need to considered when interpreting model results. This is
sometimes very difficult because implicit assumptions may be difficult to identify
exactly because of their extreme familiarity. For example, use of the logistic model
for many purposes assumes a constant environment and constant host susceptibility,
assumptions that are probably usually violated when considering real epidemics.
The influence of a non-constant environment would have caused incorrect
inferences if the logistic model had been used in all cases to compare the effects of
fungicide and cultivar resistance (Fry, 1978). Some authors have identified these
non-constant influences and have attempted to modify models to reflect changing
influences on disease progress (Berger and Jones, 1985; Waggoner, 1986). Second,
it is also important to use caution when inferring biological meaning from certain
mathematical parameters.
To improve the performance of analytical models, more detailed modelling of
the system can be achieved by linked differential equations. This approach can give
better representations of some sub-processes of epidemics (Van Oijen, 1992). As
an example, a S-I-R (Susceptible-Infectious-Removed) model, with intrinsically
linked differential equations, was used to study the importance of different fitness
components on breeding programmes. Van Oijen (1989) predicted that infection
efficiency and lesion growth rate are important components to look at when
breeding for resistance. This hypothesis was tested using field data and indeed lesion
growth rate was found to be one of the most important components in breeding for
late blight resistance (Colon
et al
., 1995). These investigations not only illustrate the
potential contribution of models from human epidemiology in plant disease but also
and more importantly, a clever usage of mathematical models to generate a testable
hypothesis.
Complex simulation models allow for more detailed and specific temporal-spatial
investigations. Several such models have been constructed (Waggoner and Horsfall,
1969; Bruhn and Fry, 1981; Van Oijen, 1995; Apel
et al
., 2003). Simulation
employs numerical solution to evaluate different treatments and analysis of a
considerable range of situations under known conditions. With simulation, a better
understanding of sub-processes can be accomplished. Inferences and decision-
making based on the analysis of simulation modelling may be more readily
acceptable because the relationships between cause and effect can be identified.
Such approaches have contributed to devising efficient late blight management
strategies: timing initial sprays and subsequent applications; evaluation of the
importance of individual sprays in controlling the disease and determining the
contribution of host resistance in an integrated disease management programme
(Shtienberg
et al
., 1994; Van Oijen, 1995; Apel
et al
., 2003). Thus it appears that
simulators are useful if properly verified and validated but verification and
validation require considerable time and effort. Finally, it must be constantly
remembered that simulators are constructed from a given set of conditions and
use of the models is only known to be appropriate for that set of conditions.
Extrapolation to different conditions should be done with caution.
