Contents

Preface page vii
NoteonMATLAB xi
1. Dynamic Modeling with Difference Equations 1
1.1. The Malthusian Model 2
1.2. Nonlinear Models 11
1.3. Analyzing Nonlinear Models 20
1 .4. Variations on the Logistic Model 33
1.5. Comments on Discrete and Continuous Models 39
2. Linear Models of Structured Populations 41
2.1 . Linear Models and Matrix Algebra 41
2.2. Projection Matrices for Structured Models 53
2.3. Eigenvectors and Eigenvalues 65
2.4. Computing Eigenvectors and Eigenvalues 78
3. Nonlinear Models of Interactions 85
3.1. A Simple Predator-Prey Model 86
3.2. Equilibria of Multipopulation Models 94
3.3. Linearization and Stability 99
3.4. Positive and Negative Interactions 105
4. Modeling Molecular Evolution 113
4.1. Background on DNA ' 114
4.2. An Introduction to Probability 116
4.3. Conditional Probabilities 130
4.4. Matrix Models of Base Substitution 138
4.5. Phylogenetic Distances 155
5. Constructing Phylogenetic Trees 171
5.1. Phylogenetic Trees 172
5.2. Tree Construction: Distance Methods - Basics 180
5.3. Tree Construction: Distance Methods - Neighbor
Joining 191
VI
Contents
5.4. Tree Construction: Maximum Parsimony 198
5.5. Other Methods > 206
5.6. Applications and Further Reading 208
6. Genetics 215
6.1. Mendelian Genetics 215
6.2. Probability Distributions in Genetics 228
6.3. Linkage 244
6.4. Gene Frequency in Populations 261
7. Infectious Disease Modeling 279
7.1. Elementary Epidemic Models 280
7.2. Threshold Values and Critical Parameters 286
7.3. Variations on a Theme 296
7.4. Multiple Populations and Differentiated Infectivity 307
8. Curve Fitting and Biological Modeling 315
8.1. Fitting Curves to Data 316
8.2. The Method of Least Squares 325
8.3. Polynomial Curve Fitting 335
A. Basic Analysis of Numerical Data 345
A. 1. The Meaning of a Measurement 345
A.2. Understanding Variable Data - Histograms and
Distributions < 348
A.3. Mean, Median, and Mode 352
A.4. The Spread of Data 355
A.5. Populations and Samples 359
A.6. Practice 360
B. For Further Reading 362
References 365
Index 367