By J. Kranz (auth.), Professor Dr. Jürgen Kranz (eds.)
In this quantity specialists current the most recent prestige of mathematical and statistical equipment in use for the research and modeling of plant affliction epidemics. subject matters handled are - tools in multivariate analyses, ordination and category, - modeling of temporal and spatial features of air- and soilborne illnesses, - the right way to examine and describe pageant between subpopulations, e.g. pathogen races and - their interplay with resistance genes of host crops - assemblage and use of types - mathematical simulation of epidemics. New chapters at the modeling of the spreading of illnesses in air and in soil are integrated during this moment edition.
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Factors 2 to 4 had a high loading for the duration of the epidemic and differed in the duration of the degressive phase, of the progressive phase and of the entire epidemic respectively. The fifth factor showed an antithetic relationship between the time of the year when the epidemics started and the effect of the attack. In factor 6 the apparent infection rate had the highest loading. In a comparable study, Campbell et ai. (1980a) examined 100 bean root rot epidemics, each of which were described by eight curve elements, by means of principal FA followed by varimax rotation.
In this case the estimation of parameters by the least squares method leads to a system of equations with at least one nonlinear equation. Therefore, the system cannot be solved in a straightforward manner and must be solved iteratively. To start iteration, a first approximation ofthe parameter values is needed, which is then improved during the procedure. These starting values should be as near as possible to the unknown true values in order to accelerate iteration. For those nonlinear models which are intrinsically linear, the back transformed parameter values obtained by linear B.
Madden and Campbell (Chapter 6) also refer to this statistical method which is used to fit experimental data with linear models. The simplest linear model is a straight line which can be expressed in mathematical terms as (1) where Y is the dependent variable, X the independent variable, e is an error term and Po and PI are the parameters of the model to be estimated from the data. The usual method of estimating the parameters of this equation is the least squares method which minimizes the sum of squares of the deviation between Mathematics and Statistics for Analyses in Epidemiology 19 observed and calculated values.