Ecological Studies

I Epidemics, Their Mathematical Analysis and Modeling: An Introduction.- 1. Concepts and Scope of Epidemiology.- 2. Mathematics in Epidemiology.- 3. Models and Their Role in Epidemiology.- 4. Mathematical Analysis of Epidemics.- 5. Models as Synoptics Tools.- 6. Outlook.- 7. References.- II Mathematics and Statistics for Analysis in Epidemiology.- 1. Introduction.- 2. Experimentation in Epidemiology.- 2.1 Kind of Experiments.- 2.1.1 Field Experiments.- 2.1.2 Growth Chamber Experiments.- 2.1.3 Combination of Field and Growth Chamber Experiments.- 2.2 Measurements in Epidemiology.- 2.2.1 Measurement of the Pathogen.- 2.2.2 Measurement of the Host.- 2.2.3 Measurement of the Disease.- 2.2.4 Measurement of the Environment.- 3. Common Mathematical Analyses.- 3.1 Analysis of Variance.- 3.2 Linear Regression Analysis.- 3.3 PathAnalysis.- 3.4 Nonlinear Regression Analysis.- 4. Multivariate Analyses.- 4.1 Classification.- 4.1.1 Discriminant Analysis.- 4.1.2 Cluster Analysis.- 4.2 Ordination.- 4.2.1 Principal Component Analysis.- 4.2.2 Factor Analysis.- 4.2.3 Canonical Correlation Analysis.- 5. Other Mathematical Methods.- 5.1 Analysis of the Diversity of Populations.- 5.2 Analysis of the Fitness of Competing Subpopulations.- 5.3 Models for the Buildup of Fungicide-Resistant Subpopulations.- 5.4 Modeling the Effects of Cultivar Mixtures and Multilines.- 6. Concluding Remarks.- References.- III Mathematical Analysis and Modeling of Spatial Aspects of Plant Disease Epidemics.- 1. Introduction.- 2. Populations Changing in Space.- 2.1 Host Plant Populations.- 2.2 Pathogen Populations.- 2.3 Spatial Patterns of Disease.- 2.4 Comparing Spatial Patterns of Inoculum and Disease.- 2.5 Environmental and Genetic Spatial Variability.- 3. Population Models of Spatial Change.- 3.1 Airborne Dispersal of Fungal Spores.- 3.1.1 Long-Distance Transport.- 3.1.2 Within-Canopy Transport.- 3.1.3 Splash and Other Short-Range Dispersal.- 3.2 Soilborne Dispersal of Fungal Propagules.- 3.2.1 Models of Root Growth.- 3.2.2 Models of Pathogen Growth.- 3.3 Vector Dispersal.- 3.4 Dispersal Gradients.- 3.5 Disease Gradients.- 4. Spatial and Temporal Spread of Disease.- 4.1 Statistical Models.- 4.2 Population Dynamic Models.- 4.3 A Generalization of Disease Gradients.- 4.4 Theoretical Models of Focus Expansion.- 4.5 Prospect.- References.- IV Mathematical Modeling and Analysis of Soilborne Pathogens.- 1. Introduction.- 2. Conceptual Models for Subterranean Epidemics.- 2.1 Importance of Inoculum and Related Concepts.- 2.2 Models for Disease Progress.- 2.2.1 Generalized Models.- 2.2.2 Introduction on Inoculum into Models.- 2.2.3 Shapes of Inoculum Decay Curves.- 2.2.4 Introduction of Host Growth into Models.- 2.2.5 Non-Monotonic Models.- 2.2.6 Introduction of Growth of Infections and Lesions into Models.- 2.2.7 Discrete Recurrence Models.- 2.3 Parameters from Conceptual Models.- 3. Analysis of Subterranean Epidemics.- 3.1 Problems in Analysis of Field Epidemics.- 3.2 Selection of Random Variables for Inoculum, Infection, Disease and Host Growth.- 3.3 Sampling Method and Spatial Pattern.- 3.3.1 Random Versus Systematic Sampling.- 3.3.2 Control of Precision.- 3.4 Temporal Analysis.- 3.4.1 Use of Conceptual Models.- 3.4.2 Use of Empirical Statistical Models.- References.- V Multiple Regression Analysis in the Epidemiology of Plant Diseases.- 1. Introduction.- 2. The Nature of Multiple Regression Analysis in Epidemiology.- 3. The Execution of Multiple Regression Analysis.- 3.1 Some Problems with the Data.- 3.2 Assembling a Multiple Regression Equation.- 4. The Interpretation of Relationships Exposed by Multiple Regression Analysis.- 5. The Applications of Multiple Regression Analysis in Epidemiology.- 5.1 Progress of the Epidemic.- 5.2 The Rate of Disease Increase.- 5.3 Disease Severity.- 5.4 Events in the Disease Cycle.- 5.5 Crop Loss.- 6. Conclusions: The Place of Multiple Regression in CurrentApproaches to Epidemic Analysis.- References.- VI Nonlinear Disease Progress Curves.- 1. Introduction.- 2. Linear and Nonlinear Models.- 2.1 Basic Concepts.- 2.2 Statistical Models and Regression Analysis.- 2.3 Model Evaluation.- 2.4 Temporal Autocorrelation.- 3. Models of Disease Progression.- 3.1 Models with Three or Fewer Parameters.- 3.1.1 Exponential.- 3.1.2 Monomolecular.- 3.1.3 Logistic.- 3.1.4 Gompertz.- 3.1.5 Log-logistic.- 3.2 Models with Shape Parameters.- 3.2.1 Von Bertalanffy-Richards.- 3.2.2 Turner's Generic Model.- 3.3 Probability Density Functions and Cumulative Distributions.- 3.3.1 Normal.- 3.3.2 Weibull.- 3.4 Polynomials.- 4. Model Selection and Parameter Estimation.- 4.1 Graphical Techniques.- 4.2 Parameter Estimation.- 4.2.1 Nonlinear Regression Analysis.- 4.2.2 Linear Regression Analysis.- 4.3 Discussion.- 5. Model Extensions.- 5.1 Variable Host.- 5.2 Changing r.- 5.3 Multiple Diseases.- 5.4 Spatial Aspects.- 5.5 Disease Components.- 6. Discussion.- References.- VII Assembling and Using Models of Epidemics.- 1. Introduction.- 2. The Classes of Models.- 2.1 Form.- 2.2 Form and Function Mixed.- 2.3 Function.- 3. Accuracy of Models.- 3.1 Introduction.- 3.2 How Inaccurate Can a Profitable Forecast Be?.- 3.2.1 How Decisions Are Made.- 3.2.2 An Example.- 4. Summaries by Regression Equations.- 4.1 Multiple Linear Regression.- 4.2 Law of the Minimum.- 4.3 Various Purposes.- 5. Analytic Equations.- 5.1 Their Form and Use in Fitting Courses of x.- 5.2 Analysis by Differential Equations.- 6. Simulators of Disease.- 6.1 Distinctive Characteristics.- 6.2 A Difference Between Models of Crops and Pests.- 6.3 Models of Development.- 6.4 Entire Simulators.- 7. Dispersal.- 7.1 Analytic Equations and Dispersal.- 7.2 Gradients.- 7.3 Simulators.- 8. Models of Crops and Pests.- 8.1 Coupling Models with Caution.- 8.2 Regressions of Yield on Disease.- 8.3 Differential Equations.- 8.4 Simulator.- 8.5 Summary Model.- References.