These lecture notes are from a graduate-level statistics course I taught at the University of California, Berkeley in 2008, 2011, and 2015. The first six chapters are in decent shape, but the later chapters are somewhat unpolished and have incomplete sections. I have taken a long hiatus from writing and it is unclear when I will be able to get back to it. Hence, I have decided to release this draft version in the hope that some students may find it useful.
There already exist several excellent books (e.g., Durrett, 2008; Ewens, 2004; Hein et al, 2004; Tavaré, 2004; Wakeley, 2008) on mathematical population genetics, and I myself have learned from studying them. The reader is strongly encouraged to look into these other resources to get a more complete view of the topic. You will notice that many important topics and references (apologies for not citing your work) are left out from this monograph, as it is NOT meant to be a comprehensive exposition of population genetics. Rather, the primary goal of these notes is to introduce mathematically-inclined students to the basic concepts underpinning the subject, so that they can get started on population genetics research.
The word "computational" is in the title of this work because efficient algorithms are indispensable in empirical population genetics and I try to highlight this aspect when I can. The special topics covered in these notes are mainly from my own research, simply because they reflect my own interest and expertise. Apologies for the personal bias.
Special thanks goes to Paul Jenkins for writing parts of Chapters 8 and 12 while he was a postdoc in my lab. I am also grateful to many students who scribed notes for my lectures and to my lab members for their contributions to research.
Yun S. Song
Berkeley, CA
Jan 11, 2021: Added a new section (Chapter 5.4: A warning on conditioning on the number of segregating sites). Minor edits in Chapter 2.3.
Apr 22, 2021: Added a new section (Chapter 9.5: Estimation of pairwise coalescence times), inspired by a private communication with Regev Schweiger and Richard Durbin.