Resolution of Probabilistic Weather Forecasts with Application in Disease Management.

Predictive systems in disease management often incorporate weather data among the disease risk factors, and sometimes this comes in the form of forecast weather data rather than observed weather data. In such cases, it is useful to have an evaluation of the operational weather forecast, in addition to the evaluation of the disease forecasts provided by the predictive system. Typically, weather forecasts and disease forecasts are evaluated using different methodologies. However, the information theoretic quantity expected mutual information provides a basis for evaluating both kinds of forecast. Expected mutual information is an appropriate metric for the average performance of a predictive system over a set of forecasts. Both relative entropy (a divergence, measuring information gain) and specific information (an entropy difference, measuring change in uncertainty) provide a basis for the assessment of individual forecasts.

Development and use of microsatellite markers to study diversity, reproduction and population genetic structure of the cereal pathogen Ramularia collo-cygni.

Ramularia collo-cygni (Rcc) is a major pathogen of barley that causes economically serious yield losses. Disease epidemics during the growing season are mainly propagated by asexual air-borne spores of Rcc, but it is thought that Rcc undergoes sexual reproduction during its life cycle and may also disperse by means of sexual ascospores. To obtain population genetic information from which to infer the extent of sexual reproduction and local genotype dispersal in Rcc, and by implication the pathogen's ability to adapt to fungicides and resistant cultivars, we developed ten polymorphic microsatellite markers, for which primers are presented. We used these markers to analyse the population genetic structure of this cereal pathogen in two geographically distant populations from the Czech Republic (n=30) and the United Kingdom (n=60) that had been sampled in a spatially explicit manner. Genetic diversity at the microsatellite loci was substantial, Ht=0.392 and Ht=0.411 in the Czech and UK populations respectively, and the populations were moderately differentiated at these loci (Θ=0.111, P<0.01). In both populations the multilocus genotypic diversity was very high (one clonal pair per population, resulting in >96% unique genotypes in each of the populations) and there was a lack of linkage disequilibrium among loci, strongly suggesting that sexual reproduction is an important component of the life cycle of Rcc. In an analysis of spatial genetic structure, kinship coefficients in all distance classes were very low (-0.0533 to 0.0142 in the Czech and -0.0268 to 0.0042 in the Scottish population) and non-significant (P>0.05) indicating lack of subpopulation structuring at the field scale and implying extensive dissemination of spores. These results suggest that Rcc possesses a high evolutionary potential for developing resistance to fungicides and overcoming host resistance genes, and argue for the development of an integrated disease management system that does not rely solely on fungicide applications.

Information graphs for binary predictors.

Binary predictors are used in a wide range of crop protection decision-making applications. Such predictors provide a simple analytical apparatus for the formulation of evidence related to risk factors, for use in the process of Bayesian updating of probabilities of crop disease. For diagrammatic interpretation of diagnostic probabilities, the receiver operating characteristic is available. Here, we view binary predictors from the perspective of diagnostic information. After a brief introduction to the basic information theoretic concepts of entropy and expected mutual information, we use an example data set to provide diagrammatic interpretations of expected mutual information, relative entropy, information inaccuracy, information updating, and specific information. Our information graphs also illustrate correspondences between diagnostic information and diagnostic probabilities.

Information graphs for binary predictors.

Binary predictors are used in a wide range of crop protection decision making applications. Such predictors provide a simple analytical apparatus for the formulation of evidence related to risk factors, for use in the process of Bayesian updating of probabilities of crop disease. For diagrammatic interpretation of diagnostic probabilities, the receiver operating characteristic is available. Here, we view binary predictors from the perspective of diagnostic information. After a brief introduction to the basic information theoretic concepts of entropy and expected mutual information, we use an example data set to provide diagrammatic interpretations of expected mutual information, relative entropy, information inaccuracy, information updating and specific information. Our information graphs also illustrate correspondences between diagnostic information and diagnostic probabilities.

Disease risk curves.

Disease risk curves are simple graphical relationships between the probability of need for treatment and evidence related to risk factors. In the context of the present article, our focus is on factors related to the occurrence of disease in crops. Risk is the probability of adverse consequences; specifically in the present context it denotes the chance that disease will reach a threshold level at which crop protection measures can be justified. This article describes disease risk curves that arise when risk is modeled as a function of more than one risk factor, and when risk is modeled as a function of a single factor (specifically the level of disease at an early disease assessment). In both cases, disease risk curves serve as calibration curves that allow the accumulated evidence related to risk to be expressed on a probability scale. When risk is modeled as a function of the level of disease at an early disease assessment, the resulting disease risk curve provides a crop loss assessment model in which the downside is denominated in terms of risk rather than in terms of yield loss.