STP 421 – Probability Theory
Fall 2016


Instructor: Dr. Jay Taylor, office: Wexler/PSA 447; phone: 965-2641; e-mail: jetaylo6@asu.edu
Time:
Tuesdays and Thursdays 12:00-1:15
Location:
Wexler/PSA 306
Office Hours:
Tuesdays 1:30-3:00 in Wexler/PSA 447.
Text:
Evolutionary Dynamics use by Martin A. Nowak (Belknap, 2006).

Course Description: This course will begin with an introduction to probability theory and the mathematics of uncertainty. Topics covered will include Bayesian and frequentist interpretations of probability, probability spaces, conditional distributions, random variables, expectations and the Central Limit Theorem. We will then see how these mathematical ideas can be applied to genetics and evolutionary biology, two subjects that have particularly close connections with probability. Particular attention will be given to the interplay between selection and demographic stochasticity to better understand how evolutionary dynamics can be influenced by population size and structure. We will conclude with an overview of some mathematical models of cancer evolution.

Prerequisites: Formally, three semesters of calculus, up through multivariate calculus. In practice, you should be familiar with differentiation (product, quotient and chain rules), integration (definite and indefinite integrals, substitution, integration-by-parts), Taylor series expansions and Jacobians. If your calculus is rusty, please review it at the beginning of the semester. No prior knowledge of biology will be assumed.

Grades: Course grades will be based on exercises (20%), two take-home midterms (20% each) and a final exam (40%).

Exercises: These will be posted on the course web page at the following link, along with their solutions. You are welcome to work in groups, but you should write up your solutions individually and you should always give credit if your solution came from another source, such as a textbook or an online resource, or from one of your classmates. Please note that late assignments will only be accepted at the instructor's discretion and no assignments will be accepted once the solutions have been posted.

Quizzes: There will be occasional unannounced quizzes which will count as extra credit towards your exercise score. Missed quizzes cannot be made up, but will not count against you.

ASU Policy on Academic Integrity: `Academic honesty is expected of all students in all examinations, papers, laboratory work, academic transactions and records. The possible sanctions include, but are not limited to, appropriate grade penalties, course failure (indicated on the transcript as a grade of E), course failure due to academic dishonesty (indicated on the transcript as a grade of XE), loss of registration privileges, disqualification and dismissal. For more information, see http://provost.asu.edu/academicintegrity.'

Course notes: These are posted here. In addition, I have prepared a short document summarizing the most important concepts in probability theory. This is the material that you would be expected to have mastered should you take a more advanced probability or statistics course in the future.



Date

Topic

Reading

18 Aug

Overview: probability and uncertainty

Taylor 1.1-1.2

23 Aug

Probability spaces and the laws of probability

Taylor 1.3-1.4

25 Aug

Conditional probabilities and independence

Taylor 2.1-2.2

30 Aug

The law of total probability and Bayes' formula

Taylor 2.3-2.4

1 Sept

Discrete random variables

Taylor 3.1.1; 4.1-4.2

3 Sept

Continuous random variables

Taylor 3.1.2; 4.3-4.4

8 Sept

Expectations and moments; covariance

Taylor 3.2

13 Sept

Normality and the central limit theorem

Taylor 4.5

15 Sept

Evolution and selection

Nowak 2.1-2.2

20 Sept

Evolution and mutation

Nowak 2.3

22 Sept

Mendelian genetics and Hardy-Weinberg equilibrium

Nowak 2.4

27 Sept

Price’s equation and the fundamental theorem of natural selection

Taylor notes

29 Sept

Fitness landscapes and quasispecies

Nowak 3.1-3.3

4 Oct

Error threshholds

Nowak 3.4-3.6

6 Oct

Fall Break

 

11 Oct

Fall Break

 

13 Oct

Evolutionary games

Nowak 4.1

18 Oct

Nash equilbria and evolutionarily stable strategies

Nowak 4.2-4.4

20 Oct

Replicator dynamics

Nowak 4.5-4.9

25 Oct

Prisoner’s dilemma

Nowak 5.1-5.5

27 Oct

Prisoner’s dilemma

Nowak 5.1-5.5

1 Nov

Prisoner’s dilemma

Nowak 5.1-5.5

3 Nov

Genetic drift

Nowak 6.1-6.2

8 Nov

Selection in finite populations

Nowak 6.3-6.4

10 Nov

Coalescents and genealogies

slides

15 Nov

Coalescents and genealogies

slides

17 Nov

Games on graphs

Nowak 8.4-8.7

22 Nov

Games on graphs

Nowak 8.4-8.7

24 Nov

Thanksgiving

 

29 Nov

Cancer dynamics

Nowak 12.1-12.3

1 Dec

Cancer dynamics

Nowak 12.4