Testing for heterogeneity in rates of morphological evolution: discretecharacter change in the evolution of  lungfish (Sar...
Rates of evolution• Has several meanings and can be taxic- or  character-based• Can inform us about the mode of evolution•...
Discrete character rates: a brief history
Discrete character rates: a brief historyDerstler 1982                               Forey 1988                Ruta et al....
Problems with previous methodsPhyletic or phylogenetic:Zero duration branch problem:
Problems with previous methods• Still to be addressed:  – Uncertainty over dating  – Phylogenetic uncertainty  – Uncertain...
Some solutions•   Dating approach (Ruta et al./Brusatte et al.)•   Randomising dates (accuracy vs. precision)•   Multiple ...
Data set• Chose lungfish for initial study as thought to  have a marked difference in rates between  early Devonian and po...
Method 1 - Changes over time• Problem of branches is they have a time span,  where do we bin them if this crosses two time...
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...
Method 2 - Randomisation branch test
Method 3 - likelihood branch test• Model no. of changes along branch i as a  Poisson process with rate parameter λi• Test ...
Method 3 - likelihood branch test
Method 4 - likelihood clade test• Finally we were interested in applying a similar  likelihood approach to ask the questio...
Method 4 - likelihood clade test
Conclusions• We introduce four methods for examining the  evolutionary tempo of discrete characters on a  phylogeny• These...
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Testing for heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi)

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  • Earliest attempts are Olsen (1944) and Westoll (1949) Both constructed pre-cladistic character taxon matrices, but Westoll made the key leap by plotting the resulting scores against time [Westoll plot image]
  • First cladistic use wasn’t until much later (Derstler 1982) Despite proliferation of cladistic matrices little has happened since (Forey 1988, Cloutier 1991, Ruta et al. 2006) The reason is perhaps an issue of methodology
  • Westoll assumed single phyletic lineage (not branching phylogeny) Derstler, Forey and Cloutier encountered zero duration branch problem (Norris?) Ruta et al. best effort so far, and probably best solution to zero duration branch problem, but only look at rate over time, not across tree
  • (Steve B will talk about archosaurs later)
  • Result [IMAGE] Plus Westoll (1949) for comparison (DELTRAN similar0 Essentially the same result despite the addition of knowledge in the 60 years in between Late Permian rise a new phenomenon
  • Where are rates 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 Null hypothesis based on a single rate for the whole tree that is given as: total number of character changes / total duration of branches. The result is the average change occurring along a branch per million years. This then used to randomly permute changes across the tree. Repeating 1,000 times gives a distribution of change per branch that we can then compare to our recorded changes per branch to test for significant excursions Because this probability is low the distribution often includes zero, so we opted for a one tail test - i.e. to look for significantly high rates only.
  • Point out pie charts show unceratinty in dating and optimisation Obvious that most branches are significantly high Rates are heterogeneous However, greater proportion of high rates:non-significant rates are found in Devonian taxa Anything else to say about rate distribution
  • You can say in the talk (although it's not on the slide itself) that the lambda_i_ is a measure of the rate of morphological change. You could also mention here that we account for incompleteness of specimens in the model.
  • Result [IMAGE] Can now see high and low rates Low rates clearly concentrated in post-Devonian Following backbone to crown shows that only one branch leading directly to the extant taxa This is Mesozoic in age indicating the major slowdown leading to the extant taxa was much later than the Devonian-Carboniferous transition suggested by the Westoll plot
  • Result [IMAGE] Now a very clear pattern of slow-down along almost the entire backbone of the tree is evident Post-Devonian clades are also comparatively slower Devonian clades on the other hand mostly show significantly higher rates
  • Testing for heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi)

    1. 1. Testing for heterogeneity in rates of morphological evolution: discretecharacter change in the evolution of lungfish (Sarcopterygii; Dipnoi)Steve C. Graeme T. Stephen L. Wang Lloyd Brusatte
    2. 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. 3. Discrete character rates: a brief history
    4. 4. Discrete character rates: a brief historyDerstler 1982 Forey 1988 Ruta et al. 2006 Brusatte et al. 2008
    5. 5. Problems with previous methodsPhyletic or phylogenetic:Zero duration branch problem:
    6. 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. 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. 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. 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. 10. Method 1 - Changes over time
    11. 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. 12. Method 2 - Randomisation branch test
    13. 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. 14. Method 3 - likelihood branch test
    15. 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. 16. Method 4 - likelihood clade test
    17. 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

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