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Fast likelihood calculations for comparative analyses
Article first published online: 11 JUL 2012
© 2012 The Author. Methods in Ecology and Evolution © 2012 British Ecological Society
Methods in Ecology and Evolution
Volume 3, Issue 5, pages 940–947, October 2012
How to Cite
Freckleton, R. P. (2012), Fast likelihood calculations for comparative analyses. Methods in Ecology and Evolution, 3: 940–947. doi: 10.1111/j.2041-210X.2012.00220.x
- Issue published online: 5 OCT 2012
- Article first published online: 11 JUL 2012
- Received 15 December 2011 Accepted 2 April 2012 Handling Editor: Emmanuel Paradis
- Brownian motion;
- evolutionary model;
- generalised least squares;
- phylogenetic contrasts
1. Modern comparative approaches use model-based methods to describe evolutionary processes. Generalised least squares calculations lie at the heart of many methods; however, they can be computationally intensive. This is because it is necessary to form a variance–covariance matrix, then to calculate the inverse and determinant of this.
2. Based on an algorithm provided by Felsenstein (American Journal of Human Genetics, 1973, 25, 471), I show how to perform comparative calculations that avoid these computational steps.
3. I apply the method to several problems in comparative analysis, including calculating likelihoods, estimating Pagel’s λ for one or several traits and fitting linear models.
4. R code is provided, which implements the algorithm described. Examples are included to demonstrate the computational gains possible for several commonly used comparative methods.