STP 421 –
Probability Theory
Fall 2016
Instructor: Dr. Jay Taylor, office: Wexler/PSA 447;
phone: 9652641; email: jetaylo6@asu.edu
Time:
Tuesdays and Thursdays 12:001:15
Location: Wexler/PSA
306
Office Hours: Tuesdays 1:303:00 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, integrationbyparts), 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 takehome 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 1.11.2 
23 Aug 
Probability spaces and the laws of probability 
Taylor 1.31.4 
25 Aug 
Conditional probabilities and independence 
Taylor 2.12.2 
30 Aug 
The law of total probability and Bayes' formula 
Taylor 2.32.4 
1 Sept 
Discrete random variables 
Taylor 3.1.1; 4.14.2 
3 Sept 
Continuous random variables 
Taylor 3.1.2; 4.34.4 
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 2.12.2 
20 Sept 
Evolution and mutation 
Nowak 2.3 
22 Sept 
Mendelian genetics and HardyWeinberg 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 3.13.3 
4 Oct 
Error threshholds 
Nowak 3.43.6 
6 Oct 
Fall Break 

11 Oct 
Fall Break 

13 Oct 
Evolutionary games 
Nowak 4.1 
18 Oct 
Nash equilbria and evolutionarily stable strategies 
Nowak 4.24.4 
20 Oct 
Replicator dynamics 
Nowak 4.54.9 
25 Oct 
Prisoner’s dilemma 
Nowak 5.15.5 
27 Oct 
Prisoner’s dilemma 
Nowak 5.15.5 
1 Nov 
Prisoner’s dilemma 
Nowak 5.15.5 
3 Nov 
Genetic drift 
Nowak 6.16.2 
8 Nov 
Selection in finite populations 
Nowak 6.36.4 
10 Nov 
Coalescents and genealogies 

15 Nov 
Coalescents and genealogies 

17 Nov 
Games on graphs 
Nowak 8.48.7 
22 Nov 
Games on graphs 
Nowak 8.48.7 
24 Nov 
Thanksgiving 

29 Nov 
Cancer dynamics 
Nowak 12.112.3 
1 Dec 
Cancer dynamics 
Nowak 12.4 