Mathematical models in agriculture : quantitative methods for the plant, animal and ecological sciences

Title:

Personal Author:

Thornley, J. H. M.

Edition:

2nd ed.

Publication Information:

London, UK : CABI, 2007

Physical Description:

xvii, 906 p. : ill. ; 25 cm.

ISBN:

9780851990101

Subject Term:

Agriculture -- Mathematical models

Added Author:

France, J.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010185195	S494.5.M3 T49 2007	Open Access Book	Book	Searching... Unknown

Bringing together the disciplines of agriculture, animal science, plant science and ecology, this book explores how mathematics can be used to understand and explain agricultural processes. It starts by providing a review of the mathematical models currently available to agriculturalists, and the philosophy behind, and objectives of, modeling. The book then applies these techniques to real-life problems faced by people managing crops and animals, including the influence of digestion on animal growth rates and levels of photosynthesis on crop yield.

Contents

Preface

I Techniques

1 Role of mathematical models

Summary

1.1 Agriculture and science

1.2 What is a mathematical model?

1.3 Hierarchy in biology

1.4 Types of models

1.5 Evaluation and validation of models

1.6 Possible modelling objectives

1.7 Models for research and models for application

1.8 Models: documentation, presentation and reviewing

1.9 Units

Exercises

2 Dynamic deterministic models

Summary

2.1 Variables

2.1.1 State Variables

2.1.2 Rate Variables

2.1.3 Driving Variables

2.1.4 Other Variables

2.2 Parameters and constants

2.3 Differential equations

2.3.1 Explicit Time Dependence

2.3.2 Memory And Delay

2.4 Numerical integration

2.4.1 Euler's Method - A First-Order Method

2.4.2 Trapezoidal Method - A Second-Order Method

2.4.3 Runge-Kutta Method - A Fourth-Order Fixed Step Method

2.4.4 Oscillations Caused By Too Large An Integration Step

2.4.5 Stiff Equations

2.5 Models and data: to fit or not to fit

2.5.1 Predictions And Measurements

2.5.2 Residual Lack Of Fit

2.5.3 Confidence Limits For Fitted Parameters

2.5.4 Sensitivity Analysis

2.6 Multiple steady states

2.6.1 Switches

2.6.2 Catastrophe

2.6.3 Oscillations

2.6.4 Chaos

Exercises

3 Mathematical programming

Summary

3.1 Introduction

3.2 Mathematical formulation

3.2.1 Example

3.3 Graphical solution

3.4 Computer solution

3.5 Worked example

3.5.1 Formulation

3.5.2 Solution

3.6 Special topics

3.6.1 Parametric Programming

3.6.2 Separable Programming

3.6.3 Integer Programming

3.6.4 Goal Programming

3.6.5 Dynamic Programming

Exercises

4 Basic biological processes

Summary

4.1 Chemical kinetics

4.1.1 First-Order Reactions

4.1.2 Second-Order Reactions

4.1.3 Stochastic Approach To Chemical Kinetics

4.2 Catalysis

4.2.1 Arrhenius Equation

4.2.2 Phenomenological Temperature Function

4.3 Biochemical kinetics

4.3.1 Michaelis-Menten Kinetics

4.3.2 Sigmoidal Kinetics

4.3.3 Transport Plus Michaelis-Menten Kinetics

4.3.4 Bisubstrate Michaelis-Menten Equation

4.3.5 Inhibition

4.3.6 Activation

4.3.7 Futile Cycles

4.4 Transport

4.4.1 Diffusion - Fick's Law

4.4.2 Convection

4.4.3 General Equation For Transport And Chemical Reaction

4.4.4 Examples

4.4.5 Lumped Representation Of Transport

4.4.6 Difference Equation Representation

4.5 Local and non-local variables

Exercises

5 Growth functions

Summary

5.1 Introduction

5.2 Exponential growth

5.3 Monomolecular equation

5.4 Logistic equation

5.5 Gompertz equation

5.6 Chanter equation

5.7 Exponential quadratic equation

5.8 Von Bertalanffy equation

5.9 Richards equation

5.10 Schumacher equation

5.11 Morgan equation

5.12 Other growth equations

Exercises

6 Interesting simple models

Summary

6.1 Introduction

6.2 Autocatalytic growth with sigmoidal substrate limitation

6.3 Delayed growth

6.4 C

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