LIKELIHOOD METHODS AND MODELS IN ECOLOGY

May 29 – June 2, 2017

Colorado State University, Fort Collins, CO

INSTRUCTORS:

Dr. Charles Canham, email: canhamc@caryinstitute.org

Dr. Patrick Martin, email: patrick.martin@colostate.edu

Day 1

8:30 – 9:30 Lecture 1: An Introduction to Likelihood for Estimation and Inference

9:30 – 10:30 Case Study 1: Distribution and Abundance of Tree Species Along Climate Gradients [Canham and Thomas 2010] [Case Study 1 – R Code] [Dataset]

10:30 – 12:00 Lab 1: Calculating Likelihood, Likelihood Surfaces, and Likelihood Profiles [R Code – Section 1] [R Code – Section 2]

12:00 – 1:00 Lunch

1:00 – 2:00 Lecture 2: Parameter Estimation and Evaluation of Support

2:00 – 4:00 Lab 2: Global Optimization using Simulated Annealing and Genetic Algorithms

[R code – anneal] [R code – genoud] [R code – optim]

[BC Sapling Growth Data – Excel Version] [BC Sapling Growth Data.txt – (right click and “Save as…”)]

[Wright et al. 1998]

4:00 – 5:00 Student presentations

Recommended Reading for Day 2:

Gómez-Aparicio, L. and C. D. Canham. 2008. A neighborhood analysis of the allelopathic effects of the invasive tree Ailanthus altissima in temperate forests. Journal of Ecology 96:447-458

Day 2

8:30 – 9:30 Lecture 3: Hypothesis Testing and Statistical Inference Using Likelihood: The Central Role of Models

9:30 – 10:30 Case Study 2: Neighborhood Models Of The Allelopathic Effects Of An Invasive Tree Species

10:30 – 12:00 Lab 3: Likelihood Functions for Continuous and Count Data: A Plethora of PDFs

[McLaughin 1993 – Compendium of Common Probability Distributions]

[Normal PDF with non-homogeneous variances]

[Gamma and Lognormal PDFs] [Exponential PDF] [Beta PDF]

[Poisson, Negative Binomial, and Zero-Inflated PDFs]

12:00 – 1:00 Lunch

1:00 – 2:00 Lecture 4: Model Selection: AIC and Akaike Weights, Multi-model Inference

2:00 – 4:00 Lab 4: Model Comparison and Hypothesis Testing in a Likelihood Framework

[Lab 4 R Script]

4:00 – 5:00 Student presentations

Recommended Reading for Day 3:

Canham, C. D., M. Papaik, M. Uriarte, W. McWilliams, J. C. Jenkins, and M. Twery. 2006. Neighborhood analyses of canopy tree competition along environmental gradients in New England forests. Ecological Applications 16:540-554.

Day 3

8:30 – 9:30 Lecture 5: Model Evaluation: How good is the best model?

9:30 – 10:30 Case Study 3: Neighborhood Models of Tree Competition

10:30 – 12:00 Lab 5: Model Evaluation [Sample R Code for Model Evaluation]

12:00 – 1:00 Lunch

1:00 – 2:00 Lecture 6: Analysis of Categorical and Ordinal Data: Binomial and Logistic Regression

2:00 – 3:00 Lab 6: Developing your own binomial and logistic regression models in R

[R code – Logistic regression of windthrow data] [Damagedata.Rdata] [R code – binomial regression]

3:00 – 5:00 Student presentations

Recommended Reading for Day 4:

Canham and Uriarte 2006. Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling. Ecological Applications 16(1):62-73.

Day 4

8:30 – 9:30 Lecture 7: Avoiding and Dealing with Problems with Your Data and Models: Sampling Design, Lack of Independence, Spatial Autocorrelation, Collinearity, Parameter Tradeoffs,…

9:30 – 10:30 Case Study 4: Inverse Modeling of Seed and Seedling Dispersion

10:30 – 12:00 Lab Project: Fundamental vs Realized Niches of Tree Species Along Climate Gradients

See the Course Materials page for datasets, R scripts, and documentation for the projects

[Course Materials Page]

12:00 – 1:00 Lunch

1:00 – 5:00 Lab Project (continued):

Day 5

8:30 – 10:00 Lab Project (continued)

10:00 – 12:00 Wrap-up

COURSE HOMEPAGE