Mathematics of evolution and phylogeny (Oxford University Press, 2005)
Includes index
List of Contributors -- 1 The minimum evolution distance-based approach of phylogenetic inference -- 1.1 Introduction -- 1.2 Tree metrics -- 1.2.1 Notation and basics -- 1.2.2 Three-point and four-point conditions -- 1.2.3 Linear decomposition into split metrics -- 1.2.4 Topological matrices -- 1.2.5 Unweighted and balanced averages -- 1.2.6 Alternate balanced basis for tree metrics -- 1.2.7 Tree metric inference in phylogenetics -- 1.3 Edge and tree length estimation -- 1.3.1 The LS approach -- 1.3.2 Edge length formulae -- 1.3.3 Tree length formulae -- 1.3.4 The positivity constraint -- 1.3.5 The balanced scheme of Pauplin -- 1.3.6 Semple and Steel combinatorial interpretation -- 1.3.7 BME: a WLS interpretation -- 1.4 The agglomerative approach -- 1.4.1 UPGMA and WPGMA -- 1.4.2 NJ as a balanced minimum evolution algorithm -- 1.4.3 Other agglomerative algorithms -- 1.5 Iterative topology searching and tree building --
- 1.5.1 Topology transformations.; 1.5.2 A fast algorithm for NNIs with OLS -- 1.5.3 A fast algorithm for NNIs with BME -- 1.5.4 Iterative tree building with OLS -- 1.5.5 From OLS to BME -- 1.6 Statistical consistency -- 1.6.1 Positive results -- 1.6.2 Negative results -- 1.6.3 Atteson's safety radius analysis -- 1.7 Discussion -- Acknowledgements -- 2 Likelihood calculation in molecular phylogenetics -- 2.1 Introduction -- 2.2 Markov models of sequence evolution -- 2.2.1 Independence of sites -- 2.2.2 Setting up the basic model -- 2.2.3 Stationary distribution -- 2.2.4 Time reversibility -- 2.2.5 Rate of mutation -- 2.2.6 Probability of sequence evolution on a tree -- 2.3 Likelihood calculation: the basic algorithm -- 2.4 Likelihood calculation: improved models -- 2.4.1 Choosing the rate matrix -- 2.4.2 Among site rate variation -- 2.4.3 Site-specific rate variation -- 2.4.4 Correlated evolution between sites -- 2.5 Optimizing parameters -- 2.5.1 Optimizing continuous parameters --
- 2.5.2 Searching for the optimal tree.; 2.5.3 Alternative search strategies -- 2.6 Consistency of the likelihood approach -- 2.6.1 Statistical consistency -- 2.6.2 Identifiability of the phylogenetic models -- 2.6.3 Coping with errors in the model -- 2.7 Likelihood ratio tests -- 2.7.1 When to use the asymptotic x2 distribution -- 2.7.2 Testing a subset of real parameters -- 2.7.3 Testing parameters with boundary conditions -- 2.7.4 Testing trees -- 2.8 Concluding remarks -- Acknowledgements -- 3 Bayesian inference in molecular phylogenetics -- 3.1 The likelihood function and maximum likelihood estimates -- 3.2 The Bayesian paradigm -- 3.3 Prior -- 3.4 Markov chain Monte Carlo -- 3.4.1 Metropolis-Hastings algorithm -- 3.4.2 Single-component Metropolis-Hastings algorithm -- 3.4.3 Gibbs sampler -- 3.4.4 Metropolis-coupled MCMC -- 3.5 Simple moves and their proposal ratios -- 3.5.1 Sliding window using uniform proposal --
- 3.5.2 Sliding window using normally distributed proposal.; 3.5.3 Sliding window using normal proposal in multidimensions -- 3.5.4 Proportional shrinking and expanding -- 3.6 Monitoring Markov chains and processing output -- 3.6.1 Diagnosing and validating MCMC algorithms -- 3.6.2 Gelman and Rubin's potential scale reduction statistic -- 3.6.3 Processing output -- 3.7 Applications to molecular phylogenetics -- 3.7.1 Estimation of phylogenies -- 3.7.2 Estimation of species divergence times -- 3.8 Conclusions and perspectives -- Acknowledgements -- 4 Statistical approach to tests involving phylogenies -- 4.1 The statistical approach to phylogenetic inference -- 4.2 Hypotheses testing -- 4.2.1 Null and alternative hypotheses -- 4.2.2 Test statistics -- 4.2.3 Significance and power -- 4.2.4 Bayesian hypothesis testing -- 4.2.5 Questions posed as function of the tree parameter -- 4.2.6 Topology of treespace -- 4.2.7 The data -- 4.2.8 Statistical paradigms --