A Modeling Approach for Comparative Hypotheses

Marguerite Butler and Aaron King
Graduate Opportunities Available!


The comparative method is a central tool for studying adaptive evolution.

For example, suppose we hypothesize that lizard body size evolves in association with evolutionary shifts in food type.

It is important to account for:

  1. How the lizard species are related (i.e., the phylogeny)
  2. How body size changes along the phylogeny (i.e., model of trait evolution)
Many methods exist to account for phylogeny (1), but do not take explict account of natural selection on the trait (2), even though most comparative hypotheses are adaptive.
Actually, we would like to model not only natural selection, but also be able to specify multiple adaptive regimes.

Why? Because we expect herbivorous lizards to have different optimal body size than insectivores = two adaptive regimes.

We can do this by applying the Hansen model, implemented in our software package


(*Ornstein-Uhlenbeck for Comparative Hypotheses)


The Hansen model is only slightly more complicated than the more familiar Browian Motion Model, but it allows us to create more flexible and realistic evolutionary hypotheses to test our data.

The Brownian Motion model has one parameter (s):

strength of the drift parameter (movie)
Change in body size (X) is determined by
and a small amount of random change in time (t)
Click on the yellow arrow to see a movie comparing small vs. large s (100 simulations)
The Hansen Model has two additional parameters (a, b): used to model natural selection
distance of phenotype (e.g., body size) from optimal value
strength of selection (movie)
same random drift components as above
We can place different optima on the branches of the phylogeny where we suspect our species entered different adaptive regimes (for example, herbivorous diet vs. insectivorous):
A Simple Simulation
  • A simple phylogeny with a single lineage at time = 0
  • Speciation occurs at time =0.5
  • At each time interval, body size may get bigger or smaller (a random walk process) according to BM or Hansen Models
Brownian Motion Model
  • Lineages speciate at time = 0.5
  • At end of simulation, both lineages share the same distribution of body sizes, centered at starting value


(Click for larger pdf image)
Hansen Model
  • Lineages enter different adaptive optima at speciation
  • At end of simulation, each lineage has a distinct body size distribution, centered at adaptive optima!


Time Frequency
Thus, evolutionary history (including patterns of past selective regimes) is important! And we can use the evolutionary signal in our data to test alternative adaptive scenarios.

Analyze Your Comparative Data

OUCH requires:
  1. Interspecific data (currently a continous character)
  2. Phylogeny (topology + branch lengths)
  3. Biological information to guide the placement of adaptive regimes
    1. How many optima?
    2. Which branches do they go on?

download OUCH!

Read Our Paper:

Butler, M.A., King, A.A. (2004) Phylogenetic comparative analysis: a modeling approach for adaptive evolution. the American Naturalist. 164(6):683-695. Appendix

Quicktime Movies referenced in this website:

  • Increasing s, the strength of the drift parameter in a Brownian Motion process
  • Increasing a, the strength of selection in an OU (Hansen) model
  • BM vs. OU on a simple phylogeny with one branch

Graduate Opportunities Are Available for both Empirically-Oriented and Theoretically-Oriented Students.

  • Develop new empirical examples
  • Explore theoretical extensions
  • Port OUCH to Mesquite

Please send a C.V. and letter of interest to either P.I. For more information on the PI's, go to:

Marguerite Butler: mbutler <at> hawaii <dot> edu

Graduate program in Zoology at the University of Hawaii

Aaron King: kingaa <at> umich <dot> edu

Follow links for description of graduate programs in EEB, AIM, and Mathematics