Examining the pattern of nucleotide substitution for the control region of mitochondrial DNA ( mtDNA ) in humans and chimpanzees, we developed a new mathematical method for estimating the number of transitional and transversional substitutions per site, as well as the total number of nucleotide substitutions. In this method, excess transitions, unequal nucleotide frequencies, and variation of substitution rate among different sites are all taken into account. Application of this method to human and chimpanzee data suggested that the transition / transversion ratio for the entire control region was - 15 and nearly the same for the two species. The 95% confidence interval of the age of the common ancestral mtDNA was estimated to be 80,000-480,000 years in humans and 0.57-2.72 Myr in common chimpanzees.

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Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees.

The main purpose of this article is to present several new statistical tests of neutrality of mutations against a class of alternative models, under which DNA polymorphisms tend to exhibit excesses of rare alleles or young mutations. Another purpose is to study the powers of existing and newly developed tests and to examine the detailed pattern of polymorphisms under population growth, genetic hitchhiking and background selection. It is found that the polymorphic patterns in a DNA sample under logistic population growth and genetic hitchhiking are very similar and that one of the newly developed tests, Fs, is considerably more powerful than existing tests for rejecting the hypothesis of neutrality of mutations. Background selection gives rise to quite different polymorphic patterns than does logistic population growth or genetic hitchhiking, although all of them show excesses of rare alleles or young mutations. We show that Fu and Li's tests are among the most powerful tests against background selection. Implications of these results are discussed.

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Statistical tests of neutrality of mutations against population growth, hitchhiking and background selection.

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of “relaxed phylogenetics.” Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.

/pdf/relaxed-phylogenetics-and-dating-with-confidence-5ez5tgzy1b.pdf

Relaxed Phylogenetics and Dating with Confidence

This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems.

Probability: Theory and Examples

* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical Limit Theorems * Conditioning and Disintegration * Martingales and Optional Times * Markov Processes and Discrete-Time Chains * Random Walks and Renewal Theory * Stationary Processes and Ergodic Theory * Special Notions of Symmetry and Invariance * Poisson and Pure Jump-Type Markov Processes * Gaussian Processes and Brownian Motion * Skorohod Embedding and Invariance Principles * Independent Increments and Infinite Divisibility * Convergence of Random Processes, Measures, and Sets * Stochastic Integrals and Quadratic Variation * Continuous Martingales and Brownian Motion * Feller Processes and Semigroups * Ergodic Properties of Markov Processes * Stochastic Differential Equations and Martingale Problems * Local Time, Excursions, and Additive Functionals * One-Dimensional SDEs and Diffusions * Connections with PDEs and Potential Theory * Predictability, Compensation, and Excessive Functions * Semimartingales and General Stochastic Integration * Large Deviations * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices

http://cyber.sibsutis.ru:82/Monarev/docs/nauka/PROBABILITY/Kallenberg%20O.%20Foundations%20of%20Modern%20Probability%20(Springer,1997)(ISBN%200387949577)(535s).pdf

Foundations of modern probability

On random sequences with spherical symmetry

The stochastic theory of regenerative events

Infinitely Divisible Point Processes

1. The asymptotic speed and shape of a particle system D. Aldous and J. Pitman 2. On doubly stochastic population processes M. S. Bartlett 3. On limit theorems for occupation times N. H. Bingham and J. Hawkes 4. The Martin boundary of two dimensional Ornstein-Uhlenbeck processes M. Cranston, S. Orey and U. Rosler 5. Green's and Dirichlet spaces for a symmetric Markov transition function E. B. Dynkin 6. On a theorem of Kabanov, Liptser and Sirjaev G. K. Eagleson and R. F. Gundy 7. Oxford Commemoration Ball J. M. Hammersley 8. Invariant measures and the q-matrix F. P. Kelly 9. The appearance of a multivariate exponential distribution in sojourn times for birth-death and diffusion processes J. T. Kent 10. Three unsolved problems in discrete Markov theory J. F. C. Kingman 11. The electrostatic capacity of an ellipsoid P. A. P. Moran 12. Stationary one-dimensional Markov random fields with a continuous state space F. Papangelou 13. A uniform central limit theorem for partial-sum processes indexed by sets R. Pyke 14. Multidimensional randomness B. D. Ripley 15. Some properties of a test for multimodality based on kernel density estimates B. W. Silverman 16. Criteria for rates of convergence of Markov chains, with application to queueing and storage theory R. L. Tweedie 17. Competition and bottle-necks P. Whittle.

Probability, statistics, and analysis

Certain stochastic models used in population genetics have the form of Markov processes in which a group of N points moves randomly on a line, and in which an equilibrium distribution exists for the relative configura­tion of the group The properties of this equilibrium are studied, with particular reference to a certain limiting situation as N becomes large In this limit the group of points is distributed like a large sample from a distribution which is itself subject to random variation

J. F. C. Kingman

Papers

On random sequences with spherical symmetry

The stochastic theory of regenerative events

Infinitely Divisible Point Processes

Probability, statistics, and analysis

Coherent random walks arising in some genetical models