Solution Manual for Mathematical Models in Biology: An Introduction by Elizabeth S. Allman John A. Rhodes Cambridge University Press, 2003

Contents

Preface

Chapter 1. Dynamic Modeling with Difference Equations
1.1. The Malthusian Model
1.2. Nonlinear Models
1.3. Analyzing Nonlinear Models
1.4. Variations on the Logistic Model
1.5. Comments on Discrete and Continuous Models

Chapter 2. Linear Models of Structured Populations
2.1. Linear Models and Matrix Algebra
2.2. Projection Matrices for Structured Models
2.3. Eigenvectors and Eigenvalues
2.4. Computing Eigenvectors and Eigenvalues

Chapter 3. Nonlinear Models of Interactions
3.1. A Simple Predator–Prey Model
3.2. Equilibria of Multipopulation Models
3.3. Linearization and Stability
3.4. Positive and Negative Interactions

Chapter 4. Modeling Molecular Evolution
4.2. An Introduction to Probability
4.3. Conditional Probabilities
4.4. Matrix Models of Base Substitution
4.5. Phylogenetic Distances

Chapter 5. Constructing Phylogenetic Trees
5.1. Phylogenetic Trees
5.2. Tree Construction: Distance Methods – Basics
5.3. Tree Construction: Distance Methods – Neighbor Joining
5.4. Tree Construction: Maximum Parsimony
5.6. Applications and Further Reading

Chapter 6. Genetics
6.1. Mendelian Genetics
6.2. Probability Distributions in Genetics
6.3. Linkage
6.4. Gene Frequency in Populations

CONTENTS

Chapter 7. Infectious Disease Modeling
7.1. Elementary Epidemic Models
7.2. Threshold Values and Critical Parameters
7.3. Variations on a Theme
7.4. Multiple Populations and Differentiated Infectivity

Chapter 8. Curve Fitting and Biological Modeling
8.1. Fitting Curves to Data
8.2. The Method of Least Squares
8.3. Polynomial Curve Fitting

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