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Book Categories |
Preface | ||
Note on MATLAB | ||
1 | Dynamic Modeling with Difference Equations | 1 |
1.1 | The Mathlusian 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 |
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 |
B: For Further Reading | 362 | |
References | 365 | |
Index | 367 |
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