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Description

These lecture notes cover basic stochastic processes and combinatorial structures arising in evolutionary genetics with an eye towards the rigorous analysis of statistical methods. The material is divided into two parts that are more or less independent: phylogenetics and population genetics. The notes were developed for a one-semester graduate course on this topic at UW-Madison (Fall 2012) and UCLA (Spring 2010). Some of this material is covered in greater depth in the following references:

• [SS] Phylogenetics by Semple and Steel
• [D] Probability Models for DNA Sequence Evolution by Durrett

Lectures Notes

Phylogenetics

• Notes 1: X-trees
• Notes 2: Splits-Equivalence Theorem
• Notes 3: Maximum Parsimony
• Notes 4: Approximating Maximum Parsimony
• Notes 5: Quartet Theorem
• Notes 6: Tree metrics
• Notes 7: Tree-metric theorem
• Notes 8: Markov models on trees
• Notes 9: Consistency
• Notes 10: Asymptotic sample complexity
• Notes 11: Ancestral reconstruction
• Notes 12: Kesten-Stigum bound
• Notes 13: Eigenvector-based estimation
• Notes 14: Steel's conjecture

Population genetics

• Notes 15: Wright-Fisher model
• Notes 16: Kingman's coalescent
• Notes 17: Ewens' Sampling Formula
• Notes 18: Chinese restaurant process
• Notes 19: Infinite-sites model
• Notes 20: Testing neutrality
• Notes 21: Recombination
• Notes 22: Estimating the recombination rate
• Notes 23: Wright-Fisher diffusion
• Notes 24: Fixation in the diffusion limit

Other useful references

• Inferring phylogenies by Felsenstein
• Fundamentals of molecular evolution by Graur and Li
• Combinatorial Stochastic Processes (St-Flour Lectures) by Pitman
• Ancestral Inference in Population Genetics (St-Flour Lectures) by Tavare
• Recent progress in coalescent theory by Berestycki
• Logarithmic Combinatorial Structures by Arratia et al.
• Mathematical Population Genetics by Ewens
• Algebraic statistics for computational biology edited by Pachter and Sturmfels