1. Testing for heterogeneity in rates of
morphological evolution: discrete
character change in the evolution of
lungfish (Sarcopterygii; Dipnoi)
Steve C. Graeme T. Stephen L.
Wang Lloyd Brusatte

2. Rates of evolution
• Has several meanings and can be taxic- or
character-based
• Can inform us about the mode of evolution
• Critical to understanding macroevolutioanry
dynamics (e.g. punk eek)

3. Discrete character rates: a brief history

4. Discrete character rates: a brief history
Derstler 1982 Forey 1988
Ruta et al. 2006 Brusatte et al. 2008

5. Problems with previous methods
Phyletic or phylogenetic:
Zero duration branch problem:

6. Problems with previous methods
• Still to be addressed:
– Uncertainty over dating
– Phylogenetic uncertainty
– Uncertainty over character optimisation
– Distribution of rates across tree and not
just time
– Lack of a significance test/null hypothesis

7. Some solutions
• Dating approach (Ruta et al./Brusatte et al.)
• Randomising dates (accuracy vs. precision)
• Multiple optimisations (ACCTRAN/DELTRAN)
• Examining multiple MPTs
• Patristic dissimilarity (Wagner 1997)

8. Data set
• Chose lungfish for initial study as thought to
have a marked difference in rates between
early Devonian and post-Devonian
• We use a supermatrix that contains
representatives of most known genera and
spans their entire history

9. Method 1 - Changes over time
• Problem of branches is they have a time span,
where do we bin them if this crosses two time
bins?
• Alternative approach (Chaloner & Sheerin 1979) is
to ask when changes occur
• We don’t know precisely, but we do have the
bounds of the branch duration
• We can thus select random ages for each
character change along a branch between its
beginning and end
• Repeating 1,000 times can give us a measure of
accuracy as a confidence interval

10. Method 1 - Changes over time

11. Method 2 - Randomisation branch test
• But we are also interested in where rates are distributed
across the tree
• A simple way of looking at this is to ask which branches
show a significant excursion from a null hypothesis of equal
rates
• H0 = total number of character changes / total duration of
branches = average changes occurring along a branch per
million years
• Randomly permute changes across the tree using this
value (x 1,000) gives change per branch distribution
• Real values then compared to this distribution to search for
significant excursions

12. Method 2 - Randomisation branch test

13. Method 3 - likelihood branch test
• Model no. of changes along branch i as a
Poisson process with rate parameter λi
• Test for equality of rates using likelihood
ratio test:
H0: all λi equal
• Determine branches with significantly higher
or lower λi

14. Method 3 - likelihood branch test

15. Method 4 - likelihood clade test
• Finally we were interested in applying a similar
likelihood approach to ask the question of whether
clades show a significant shift in tempo
• This approach is essentially the same as method
3, but instead of comparing one branch to the rest
of the tree we compare the sum of all branches
subtended by a node (i.e. a clade) with the rest of
the tree

16. Method 4 - likelihood clade test

17. Conclusions
• We introduce four methods for examining the
evolutionary tempo of discrete characters on a
phylogeny
• These incorporate several corrections not used by
previous workers
• Results allow simple interpretation of uncertainty in
both dating and character optimisation, enabling
greater confidence in any conclusions
• In sum, the results indicate a more nuanced
pattern of lungfish evolution than suggested by
previous workers