Agriculture Reference
In-Depth Information
In all the methods of modelling and analysing data, certain assumptions are made
in order to correctly conduct statistical analysis and interpret results. Some
assumptions are specific to each analytical method and others are needed for most
methods. The seriousness of the resulting bias in data analysis and interpretation due
to the violation of assumptions varies with individual assumptions, analytical
methods and the research question concerned. For example, one assumption is that
there is no spatial aggregation of diseases since spatial aggregation may also
influence temporal epidemic development. Analytical modelling has shown that
aggregation will slow the rate of disease development (Waggoner and Rich, 1981;
Yang and TeBeest, 1992; McRoberts
et al.
, 1996) and that assuming a constant
degree of aggregation over time, the effect of aggregation on the rate of increase is
less with low aggregation. In experimental studies with Zucchini yellow mosaic
potyvirus, an aggregated pattern of initial disease resulted in lower disease incidence
than a uniform pattern (Nelson, 1996). Unfortunately, the existence of varying
degrees of spatial aggregation of plant diseases is a rule rather than an exception.
Furthermore, often in field epidemiological investigations we do not know precisely
the density and spatial configuration of initial inoculum. Both theoretical and
experimental studies have shown that the rates of disease increase were considerably
influenced by the number of initial disease foci (Smith
et al.
, 1988; Xu and Ridout,
1998; Jeger
et al.
, 2004b). In an experiment with southern blight of processing
carrot, the rate of disease increase generally increased as the number of initial
disease foci increased (Smith
et al.
, 1988).
Therefore certain preliminary data checking is needed to identify whether
some assumptions are not met, and if so, the severity of the violations and whether
there are means to reduce the severity of the violations, such as transforming data
onto a different scale. However, often violations of some assumptions might be
inevitable and researchers need to be aware of such violations and take them into
consideration when interpreting results and make them clear in subsequent
publications.
8.3 ANALYSING INDIVIDUAL EPIDEMICS
8.3.1 Simple growth models
One of the most common methods used to describe temporal disease progress is
the use of simple growth models. Three common models used to describe
disease progress curves are the monomolecular, Gompertz and logistic models
(Table 8.1) and their application and interpretations are extensively reviewed
(Campbell and Madden, 1990) and these models can provide a range of curve
shapes (Fig. 8.1). More complicated models have also been used to describe
disease progress curves, like the generalised Richards growth functions (Hunt,
1982). These models have been used almost exclusively as statistical means to
describe the observed patterns and then use the estimated model parameters for
comparing epidemics.
