Testing for heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi)

Testing for heterogeneity in rates of morphological evolution: discrete

character change in the evolution of lungfish (Sarcopterygii; Dipnoi)

Steve C.Wang

Graeme T.Lloyd

Stephen L.Brusatte

• 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)

Rates of evolution

Discrete character rates: a brief history

Discrete character rates: a brief historyDerstler 1982 Forey 1988

Ruta et al. 2006 Brusatte et al. 2008

Problems with previous methodsPhyletic or phylogenetic:

Zero duration branch problem:

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

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)

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

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

Method 1 - Changes over time

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

Method 2 - Randomisation branch test

Method 3 - likelihood branch test

• Model no. of changes along branch i as a Poisson process with rate parameter i

• Test for equality of rates using likelihood ratio test:

H0: all i equal• Determine branches with significantly higher

or lower i

Method 3 - likelihood branch test

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

Method 4 - likelihood clade test

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