User:Carl Boettiger/Notebook/Comparative Phylogenetics/2010/10/13
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Hastings lab presentation
Presented chalk talk on the Warning Signals project (see stochastic population dynamics notebook).
Mendeley upgrade for Ubuntu up, still need to explore groups and reconsider organization of my lists...
Writing LR continues
see version history.
R list discussion continued
Good question about the applicability of lambda transforms to discrete models (though included in Geiger examples). Interpretation isn't trivial, but neither can it be dismissed as simply incorrect to do. Here's my take:
Good question. Lambda is often taken as a measure of phylogenetic signal. It's just a tree transform, so it's just a matter of trying to explain what it means to say a discrete model would fit better if you rescaled the tree like so. In the BM case, you would argue that lambda << 1 might mean something rather non-brownian is going on, making things forget their ancestry faster. In this case, it seems Lara is assuming an equal rates model, which means that an unbalanced fraction of taxa in a particular trait value can only be explained by phylogeny; not by the stationary solution of some model. A good fit with small lambda would indicate that the phylogeny was not being helpful in explaining this imbalance (imagine an 80/20 split in a binary trait arranged in the least parsimonious manner possible -- this would prefer a small lambda and a hint that ecological forces are playing a more important role than phylogenetic inertia).
If the rates can call differ, small lambda (an unimportant influence of phylogeny) may be confounding with higher transition rates, such that the system can forget its ancestry quickly and reach the stationary distribution. In such cases estimating the tree transforms such as lambda will have identifiability issues -- perhaps that plays a role in Lara's convergence error messages.
In general if the model is fitting better with the tree transform then without it, this can be taken as an indication that the model itself isn't a good description of the data. I think that's as true in the land of continuous traits and BM as it is in discrete traits, regardless of how that particular transform is defined or motivated. Perhaps others would comment on this perspective.