STP 421 – Probability Theory
Spring 2017
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jetaylo6@asu.edu
Time: Tuesdays and
Thursdays 3:004:15
Location: WXLR/PSA 203
Office
Hours: Wednesdays 11:001:00 in PSA 447.
Text:
Evolutionary
Dynamics by
M. Nowak (Belknap, 2006); Mathematical
Models
of Social Evolution
by
R. McElreath and R. Boyd (Chicago, 2007).
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.
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 (30%) and three exams (70%).
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 
10 Jan 
Overview: probability and uncertainty 
Taylor 1.11.2 
12 Jan 
Probability spaces and the laws of probability 
Taylor 1.31.4 
17 Jan 
Conditional probabilities and independence 
Taylor 2.12.2 
19 Jan 
The law of total probability and Bayes' formula 
Taylor 2.32.4 
24 Jan 
Discrete random variables 
Taylor 3.1.1; 4.14.2 
26 Jan 
Continuous random variables 
Taylor 3.1.2; 4.34.4 
31 Jan 
Expectations and moments 
Taylor 3.2 
2 Feb 
Normality and the central limit theorem 
Taylor 4.5 
7 Feb 
Exam 1 

9 Feb 
Mendelian genetics and HardyWeinberg equilibrium 

14 Feb 
Evolution and selection 
MB 1.11.4 
16 Feb 
Animal conflict and the hawkdove game 
MB 2.1 
21 Feb 
Retaliation 
MB 2.22.3 
23 Feb 
Asymmetrical and sequential games 
MB 2.42.6 
28 Feb 
Altruism and the prisoner's dilemma 
MB 3.13.2 
2 March 
Inclusive Fitness 
MB 3.3 
7 March 
Spring Break 

9 March 
Spring Break 

14 March 
Hamilton's Rule 
MB 3.43.5 
16 March 
Hamilton's Rule 
MB 3.6 
21 March 
Exam 2 

23 March 
Reciprocity and the iterated prisoner's dilemma 
MB 4.1 
28 March 
Errors and cooperation 
MB 4.2 
30 March 
Partner choice 
MB 4.3 
4 April 
Indirect reciprocity 
MB 4.4 
6 April 
Collective action 
MB 4.5 
11 April 
The Price equation 
MB 6.16.2 
13 April 
Group selection 
MB 6.3 
18 April 
Dispersal 
MB 6.4 
20 April 
Genetic drift 

25 April 
Selection in finite populations 

27 April 
Exam 3 
