#### Phylogenetics

There are several methods commonly used to figure out how species are related to one another: maximum parsimony, maximum likelihood, and Bayesian inference.

Parsimony is basically Occam’s Razor–the simplest answer is the most likely. This is standard in analysis of morphological data. Maximum likelihood and Bayesian inference are both model-based methods. They work great if you’re able to model the chances that one thing will evolve into another, which makes them standard for molecular data since scientists have actually determined the rates at which one base pair changes to another. But for morphological data?….not so much.

Phenotype doesn’t follow mathematical models of which molecule fits best to another or what amino acid they’ll code for. It’s completely dependent on interactions with the environment, which is complicated and changes all the time. This is far from being a perfect analogy, but using model-based methods for morphological data is almost like trying to set up a model for whether a horn will become shorter or longer, only to have it turn blue.

That’s not to say that they can’t be used for morphological data at all, but they do have a *very* strong tendency to overestimate confidence levels, which is worse than underestimating because it means the people using your phylogenetic hypotheses may very well be making incorrect *a priori *assumptions. Better to say “we aren’t sure what happened in this part of the tree”, which is what parsimony is more likely to give.

#### Morphometrics

I’ll be using several different morphometric methods. There’s traditional morphometrics, which is the use of linear measurements, angles, and ratios; then there’s geometric morphometrics, which uses landmarks, semi-landmarks, and outlines. In most studies, geometric morphometrics is preferred because it removes size (except for allometry, which can be tested for and informative in its own right), which leaves shape as the only thing being analyzed.

I’m quantifying the evolution of snout length relative to body size. Since this is a size variable more than shape, I’m using traditional morphometrics for it. I’ve already presented results of this at two meetings, and will add more data this summer and fall.

I have an undergraduate assistant using my photographs to digitize outlines of the back teeth and/or their alveoli. We’ll be doing Fourier transform to quantify these data.

I’ll also be looking at the morphological evolution of other aspects of alligatorine skeletons, and this will be through landmarks and semi-landmarks, which are point data that capture shape.

#### Biogeographic methods

There are two camps of biogeographic methods: pattern-based (e.g., TreeFitter), and process-based (e.g., dispersal-extinction cladogenesis). I’ll be using both to study alligatorines in the context of phylogeny.

#### Diversity measures

There are a lot of different ways to illustrate diversity through time. You can look at how many originations (speciation events) there are in a set period of time, how many extinctions, presence/abscence counts of lineages, etc… I’ll be doing a variety of these and comparing them to climate throughout the Cenozoic.