STP 421 – Probability Theory

Spring 2017

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail: jetaylo6@asu.edu
Time: Tuesdays and Thursdays 3:00-4:15
Location: WXLR/PSA 203
Office Hours: Wednesdays 11:00-1:00 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, 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 (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 1.1-1.2

12 Jan

Probability spaces and the laws of probability

Taylor 1.3-1.4

17 Jan

Conditional probabilities and independence

Taylor 2.1-2.2

19 Jan

The law of total probability and Bayes' formula

Taylor 2.3-2.4

24 Jan

Discrete random variables

Taylor 3.1.1; 4.1-4.2

26 Jan

Continuous random variables

Taylor 3.1.2; 4.3-4.4

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 Hardy-Weinberg equilibrium


14 Feb

Evolution and selection

MB 1.1-1.4

16 Feb

Animal conflict and the hawk-dove game

MB 2.1

21 Feb

Retaliation

MB 2.2-2.3

23 Feb

Asymmetrical and sequential games

MB 2.4-2.6

28 Feb

Altruism and the prisoner's dilemma

MB 3.1-3.2

2 March

Inclusive Fitness

MB 3.3

7 March

Spring Break


9 March

Spring Break


14 March

Hamilton's Rule

MB 3.4-3.5

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 6.1-6.2

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