Statistical Methods in Ecology—Fall 2012

ECOL/BIOL 563

Course Details

Instructor: Jack Weiss
Curriculum for the Environment and Ecology
317 Whitehead Hall
962-5930
jack_weiss@unc.edu

Text: There is no official text. Readings from various online e-books and articles will be assigned from time to time. A few texts that come close to covering the topics in this course are the following.

1. Stauffer, Howard B. 2008. Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists. Wiley, New York.
2. Zuur, Alain F., Elena N. Ieno, Neil J. Walker, Anatoly A. Savelieve, and Graham M. Smith. 2009. Mixed Effects Models and Extensions in Ecology with R. Springer, New York. [Available as a UNC e-book]
3. Qian, Song S. 2010. Environmental and Ecological Statistics with R. Chapman & Hall/CRC Press, Boca Raton, FL.
4. Bolker, Benjamin M. 2008. Ecological Models and Data in R. Princeton University Press.
5. Kery, Marc. 2010. Introduction to WinBUGS for Ecologists: Bayesian Approach to Regression, ANOVA, Mixed Models and Related Analyses. Elsevier, Inc.
6. Ntzoufras, Ioannis. 2009. Bayesian Modeling Using WinBUGS. Wiley, New York.

Software: We will use two different software packages in this course: R and WinBUGS (or JAGS).

1. R is a freeware implementation of the S language. The R home page is http://www.r-project.org. The software can be downloaded from http://cran.r-project.org. There are versions of R for all platforms.
2. WinBUGS is a freeware program for Bayesian statistical inference, downloadable from http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml Note: WinBUGS only runs on Windows.
3. An alternative to WinBUGS for Macintosh users is JAGS. JAGS is available for both Windows and Macintosh operating systems. http://www-ice.iarc.fr/~martyn/software/jags/

Course Website: https://sakai.unc.edu/portal/site/ecol563

Public Site: https://sakai.unc.edu/access/content/group/3d1eb92e-7848-4f55-90c3-7c72a54e7e43/public/index.html

Office Hours: I'm available after class on MW but you are welcome to stop by at any time. My office is 317 Whitehead Hall. This is the former dormitory at the corner of South Rd. and Columbia St. Because I'm frequently consulting with students and faculty in the Curriculum you might want to send me an email first to check my availability.

Evaluation: Weekly data analysis homework using R and/or WinBUGS/JAGS plus a takehome final exam.

Registration Details: Seats are reserved separately for ECOL 563 (10 seats) and BIOL 563 (10 seats). If the course is closed for one of these listings, try registering for the other one.

Overview of the Course

This is a course in statistical modeling for ecologists. We focus on elementary statistical methods, primarily regression, and describe how they can be extended to make them more appropriate for analyzing ecological data. These extensions include using more realistic probability models (beyond the normal distribution) and accounting for situations in which observations are not statistically independent. For each model we consider we will see how to estimate it using both frequentist (when possible) and Bayesian methods. Our emphasis here is on depth rather than breadth. (The other graduate course that I teach, ECOL 562, is a survey course that covers a wide range of statistical methods useful in environmental science. This course focuses on 40% of the material from that course but covers it in greater depth.)

Familiarity with the standard parametric approaches of statistical analysis such as hypothesis testing is assumed. The course is intended to serve as a transition between what is typically taught in an undergraduate statistics course and what is actually needed to successfully analyze data in ecology and environmental sciences. The ideal enrollee is an upper level undergraduate or beginning graduate student who has already taken an introductory statistics course and wishes to see the modern application of statistics to environmental science and ecology.

Prerequisites

The prerequisites are modest, a one semester undergraduate or high school course in statistics (the equivalent of STOR 155 at UNC) and some exposure to the concepts of calculus. If you have never studied statistics, this is probably not the course for you. I expect you to be familiar with (as in heard of and can quickly relearn) the following concepts:

1. elementary probability theory including the notion of conditional probability and continuous and discrete random variables,
2. the standard parametric approaches to hypothesis testing, e.g., one and two-sample t-tests, etc., and
3. elementary linear regression in which there is a single response and a single predictor.

Just about any elementary statistics text covers this material. The book Introduction to the Practice of Statistics by David S. Moore and George P. McCabe, the text that has been used in undergraduate statistics courses at UNC, is an adequate choice as is any other text written at this level. Classic texts for biologists that cover this material, plus a lot more, are Biostatistical Analysis by Jerrold Zar and Biometry by Robert R. Sokal and F. James Rohlf.

Statistical Software

No familiarity with statistical software is assumed. We will be using R, an implementation of the S language, available for free download at http://cran.r-project.org. The current version is R 2.11. R runs on all major operating systems, including Windows, Unix, and Mac OS X. R is a state-of-the-art modern statistical package actively supported by the worldwide scientific community. It is not easy to use but it has become the de facto standard for scientific research.

For Bayesian estimation we will use WinBUGS, downloadable for free from http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml. WinBUGS is the most popular implementation of Markov chain Monte Carlo methods for Bayesian estimation and has a large online support group. WinBUGS only runs on Windows but I have achieved good performance running WinBUGS on a Mac using VMWare Fusion to run Windows. An alternative to WinBUGS, especially for Macintosh users, is JAGS: http://www-ice.iarc.fr/~martyn/software/jags/. The modeling language of JAGS is nearly identical to that of WinBUGS. Both JAGS and WinBUGS can be called directly from R through the use of add-on packages, and this is how we will use them.

You will need to install R and either WinBUGS or JAGS on your own laptop. It is recommended that you bring your laptop to class on Mondays. Typically our Monday (and occasional Wednesday) sessions will be devoted to carrying out analyses on real data using R and/or WinBUGS/JAGS. These analyses will then form the basis for that week's homework assignment.

NB: Before coming to each class you should check the course web site to see what data sets you should download and what R packages, if any, you should install!

Course Content

This is a course in regression and includes an extensive introduction into one specific approach to the analysis of structured data, mixed effects models, from both a frequentist and Bayesian perspective. Our topics include the following.

1. Basic concepts in regression: continuous predictors, categorical predictors, and interactions
2. Analyzing standard statistical designs with a continuous response: analysis of variance, analysis of covariance, and split plot designs
3. Bayesian approach to statistics
4. Mixed effects models for analyzing structured data
   1. Random intercepts and slopes models
   2. Multilevel models with 2 and 3 levels
   3. Hierarchical Bayesian modeling
   4. Nonlinear mixed effects models
   5. Models with nested and crossed random effects
5. Likelihood theory and its application to regression
6. Analysis of binomial data
7. Analysis of count data: Poisson and negative binomial regression (both NB1 and NB2); ZIP models

Course Home Page