BIOL4250
Population Genetics
Tu, Th 1:30 -- 2:45 pm, online, synchronous.


Instructor | Course description | Text | Grading policy | Academic Integrity Policy | Syllabus | Homework | Class Notes

Instructor

Course description

In molecular evolution, random events such as pointwise DNA mutations and chromosomal rearrangement events (inversion, reciprocal translocation) create genetic variation in a diploid population that undergoes selection of the fittest to survive. This course describes mathematical models, both deterministic and stochastic, that provide a theoretical foundation for understanding modern genetics. The types of questions we'll address include the following. In a large population, how do haplogype frequencies change both in the presence and absence of selection and restricted migration? What is linkage disequilibrium and how is it measured? In situations of a population bottleneck, caused for instance by limited environmental resources, what is the probability that a particular allele will become fixed in the population, and what is the expected time until fixation? What is the coalescent? In addition, some original research papers will be presented. Prerequisites: working knowledge of probability and statistics or approval by the instructor.


Additional description and disclaimer: In addition to the topics listed below in the tentative syllabus below, you will learn how to use Mathematica and Python programs for some of the computations and graphs discussed in population genetics. Although we will recall/review certain notions from Probability/Statistics, please understand that any course in Population Genetics assumes that you have a descent understanding of probability/statistics -- probabably more elementary probability theory (binomial, Poisson, geometric, normal distributions, variance, covariance) than statistics (in the course, we'll apply χ2 test, correlation). Population genetics is a course in the general area of mathematical biology, and so appeals to students who like rigor, sharp analysis, and clean mathematical arguments -- I find it exciting, like in theoretical physics, to learn how to create a mathematical model for something as truly complex as the interaction of genes in a finite population of evolving individuals. To understand the mathematical model involves getting one's hands "dirty" in the actual mathematics, as opposed to memorizing formulas.


Textbook

After taking this course, you may be interested in additional books that treat population genetics. Here is a list of books that I like, many of which you can find in the library or through inter-library loan.

  1. Molecular Population Genetics, by Matthew W. Hahn, Oxford University Press, 2018.
    Comment: This was the only textbook that I could find which treated population genetics from a modern perspective -- i.e. in the genomic era, with the availability of a large amount of sequencing data including that from the HapMap (haplotype mapping) project, 1000 Genomes Project, etc. However, in my opinion, the book at times provids scanty poor explanations, lists formulas with no mathematical derivations, and simply lists references for extensions of various approaches. In my opinion, the value of this text would be in a second course in population genetics, after the basic concepts have been learned.
  2. Understanding Population Genetics , by Torbjörn Säll and Bengt O. Bengtsson, John Wiley and Sons, Inc.
    Comment: In my opinion, this book is mathematically somewhat too advanced and specific for an undergraduate course in population genetics. ISBN 9781119124030 (paperback), ISBN 9781119124054 (epub), ISBN 9781119124078 (pdf).

Grading Policy

Homework and quizzes 25%
Final presentation 5%
Midterm examination 35%
Final Exam 35%

Class policy is that unexcused absences from midterm examinations receive a 0. Absences due to illness, medical or family emergencies and comparable serious situations are excused provided that a letter from the dean is presented.

No late homework will be accepted.

The grading policy is subject to change. If so, then this will be clearly announced with ample time.

Academic Integrity Policy

Any work handed in with your name on it is presumed to be your own work. This applies to all coursework, including homework assignments, final projects, and tests. If you use library or Internet resources to solve homework problems, then please be sure to give detailed references including any URLs used -- this practice is standard in any profession, and not providing references constitutes plagiarism.

You may work with one or two other students on the homework. In fact, I encourage such collaborations, since (provided that each person prepares), it is possible to learn the material more efficiently. Moreover, work in in a research lab is invariably collaborative, so this is good preparation. If you do work with others, then please state the names of your collaborators at the top of the first page. However, each person is responsible for writing up and submitting their own homework.

Any deviation from this policy, can immediately result in a course grade of "F" and be turned over to the Board of Academic Integrity for a hearing.

Please refer to BC Acdademic Integrity Policy for more details concerning the university academic integrity policy.


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Tentative Syllabus

This syllabus is subject to change.
Note; In addition to the topics listed below, you will learn how to use Mathematica and Python programs for some of the computations and graphs discussed in population genetics. As well, we will recall and review some topics from Probability/Statistics -- however, population genetics is a course in the general area of mathematical biology, and so appeals to students who like rigor and clear analysis. Population genetics assumes that you have a descent background in probability/statistics.

  1. Jan 18, 20: Chapter 1 Genetic Variation: polymorphism, fixed mutation, Hardy-Weinberg equilibrium in an infinite population

  2. Jan 25, 27: Chapter 1 Genetic Variation: continuation

  3. Feb 1, 3: Chapter 2 Genetic Drift: finite population sizes causes fixation or extinction (in contrast to Hardy-Weinberg equilibrium in an infinite population), Fisher-Wright problem, computer simulations, the Kingman coalescent, effective population, Tajima D-statistic size

  4. Feb 8, 10: Chapter 2 Genetic Drift: continuation

  5. Feb 15, 17: Chapter 2 Genetic Drift: continuation

  6. Feb 22, 24: Chapter 3 Natural Selection: Mathematical modeling of fitness and selection, heterozygosity effect, incomplete dominance, overdominance, underdominance, mutation selection balance, genetic load, Greenberg-Crow experiment, computing viability and relative viability, epistasis (multiplicative, additive, synergistic), Chapter 3 Natural Selection: continuation

  7. Mar 1, 3: Chapter 3 Natural Selection: continuation

  8. Mar 8, 10: SPRING VACATION Mar 7-12 (no class)

  9. Mar 15, 17: Chapter 4 Two-locus Dynamics: linkage disequilibrium, hypothesis testing whether linkage disequilibrium (LD) is non-zero, relation between LD and covariance, gene hitchhiking

  10. Mar 22, 24: Chapter 4 Two-locus Dynamics: continuation Midterm exam: Mar 31 on Chapters 1-4 and class notes

  11. Mar 29, 31: Chapter 5 Nonrandom mating: identity by descent, coefficient of kinship, coefficient of relatedness, effect of inbreeding on fitness, selfing in plants, when is selfing a good strategy, inbreeding due to geographic isolation, Wright's island model of migration Midterm exam: Mar 31 on Chapters 1-4 and class notes

  12. Apr 5, 7: Chapter 5 Nonrandom mating: continuation

  13. Apr 12, 14: Chapter 6 Quantitative Genetics: computing heritability from offspring/midparent scatter plots, linear regression, estimating selection differential S and response to selection R, intensity of selection i(p), Fisher's result that the genetic contribution to traits affected by many di-allelic loci (each of small effect) yields a normal distribution

  14. Apr 19, 21: Chapter 6 Quantitative Genetics: continuation No class on Apr 14 (Holy Thursday of Easter week)

  15. Apr 26, 28: Chapter 7 Evolutionary advantages/disadvantages of sexual reproduction: 2-fold cost of sexual reproduction, advantage caused by Mendelian segregation, sex reproduction versus parthenogenesis -- under which conditions is each the optimal strategy? how sex removes deleterious alleles -- Muller’s ratchet, Kondrashov’s ratchet

  16. May 3, 5: Final presentations: 2-person teams present a short talk of 8-10 minutes with PowerPoint slides on a topic that is previously authorized by the instructor. The talk should be videotaped, either with Panopto or Zoom, and uploaded to a location on the Canvas web site for our course (to be designated later). Presentations should be professionally executed, as if this were a research presentation for a job interview.
Last class on May 5. Study days begin May 6. FINAL EXAM: Monday, May 16 at 12:30 p.m.


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