Testing Ecological Theory Using the Information-theoretic Approach: Examples and Cautionary Results

Ecologists are increasingly applying model selection to their data analyses, primarily to compare regression models. Model selection can also be used to compare mechanistic models derived from ecological theory, thereby providing a formal framework for testing the theory. The Akaike Information Criterion (AIC) is the most commonly adopted criterion used to compare models; however, its performance in general is not very well known. The best model according to AIC has the smallest expected Kullback-Leibler (K-L) distance, which is an information-theoretic measure of the difference between a model and the truth. I review the theory behind AIC and demonstrate how it can be used to test ecological theory by considering two example studies of foraging, motivated by simple foraging theory. I present plausible truths for the two studies, and models that can be fit to the foraging data. K-L distances are calculated for simulated studies, which provide an appropriate test of AIC. Results support the use of a commonly adopted rule of thumb for selecting models based on AIC differences. However, AICc, a corrected version of AIC commonly used to reduce model selection bias, showed no clear improvement, and model averaging, a technique to reduce model prediction bias, gave mixed results.