MW 5:00-6:45; Room to be Announced
This year the focus of the course will be equally split between stochastic dynamic programming and stochastic population theory.
Students in AMS 115 and AMS 215 will attend the same lectures. Homework will be assigned regularly and there will be a take-home final examination. In addition, graduate students will read and report on one paper from the primary literaure each week and will have to complete a term project..
The approximate topical outline is Weeks 1, 2: Review of probability models (binomial, Poisson, negative binomial distributions) and their uses. Weeks 3-6: Stochastic Dynamic Programming y. This will include i) the canonical equation for activity choice (Week 3), computer implementation of that model (Week 4), and the canonical equation for allocation processes (Weeks 5, 6) c. Weeks 7-10: Introduction to Stochastic Population Theory. This will include i) birth and death processes and the MacArthur-Wilson theory of island biogeography ii) Brownian motion and white noise, iii) Ornstein Uhlenbeck process, and iv) simple exit time problems
We will use two of my books, both of which were developed from courses at UCSC: i) CW Clark and M. Mangel (2000) DYNAMIC STATE VARIABLE MODELS IN ECOLOGY. METHODS AND APPLICATIONS Oxford University Press and ii) M. Mangel (2006) THE THEORETICAL BIOLOGIST'S TOOLXBOX, Cambridge University Press. More specifically: Weeks 1, 2: Mangel, Chapter 3; Weeks 3-6: Clark and Mangel, Chapters 1-4; Mangel, Chapter 4; Weeks 7-10: Mangel, Chapters 7, 8. I will make pdfs of the appropriate chapters available to students.
Prerequisites for this course are a working knowledge of calculus, knowledge of ordinary differential equations and probability theory comparable to a first undergraduate course in each. In addition, you will need to be able to program a computer. The language is unimportant; the problems can be done in any language from EXCEL(used by Ray Hilborn for calculations he did in The Ecological Detective) or BASIC (required by Andre Punt for his quantitative methods course at UW) through R, MATLAB, or C++. However, I will not teach programming.
Homework will be given during lecture and homework from one week will be due at the start of class on the subsequent Monday (Wednesday if Monday is a holiday). My policy about late homework is simple: it will not be accepted. I will not have office hours Monday morning (i.e. before the homework is due).
The final examination will consist of three or four common problems (which will be indicated during the lectures). The final will be given out around 20 May and due around 8 June (more details to be speficied).