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Stochastic Processes in Evolution and Genetics

The main theme of this course is the rigorous mathematical analysis of probabilistic and combinatorial structures arising from biology, mostly in the study of evolution and genetics. No biology background is required. The course should be of interest to probabilists, combinatorialists, applied mathematicians, theoretical computer scientists, computational biologists, and biostatisticians.
Various stochastic processes on combinatorial structures will be considered, including random trees, Markov models on trees, multitype branching processes, finite Markov chains, random walks, exchangeable partitions, and Kingman's coalescent. Here is a tentative list of topics:

  • Mathematical Phylogenetics (a.k.a. the mathematics behind the Tree of Life): Trees and splits; Characters and compatibility; Tree-based metrics; Markov models on trees; Ancestral reconstruction
  • Mathematical Population Genetics: Wright-Fisher model and Kingman's coalescent; Infinite-alleles and infinite-sites models; Ancestral recombination graph; Diffusion theory
Department: 
Math/Stat
Course#: 
833
Course: 
Stochastic Processes in Evolution and Genetics
Credits: 
3
Instructor(s): 
Roch, Sebastien
Website: 
http://www.math.wisc.edu/~roch/teaching_files/833.f12/
Semester: 
Fall 2012