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New methodologies for the use of 
cladistic-type matrices to measure 
morphological disparity and 
evolutionary rate 
@Gra...
Acknowledgements 
Matt 
Friedman 
Liam 
Revell 
Mark 
Bell 
Peter 
Smits 
Steve 
Brusatte 
Roger 
Benson 
Steve 
Wang 
Ric...
Cladistic-type data 
- Discrete morphological data
Cladistic-type data 
- Discrete morphological data 
- Limited to 32 states (often 
less)
Cladistic-type data 
- Discrete morphological data 
- Limited to 32 states (often 
less) 
- Frequently non-Euclidean
Cladistic-type data 
- Discrete morphological data 
- Limited to 32 states (often 
less) 
- Frequently non-Euclidean 
- Mi...
Acladistic analyses 
Disparity Rates
Acladistic analyses 
Disparity Rates 
Common Rare
Acladistic analyses 
Disparity Rates 
Common 
No models 
Rare 
Simple models
Acladistic analyses 
Disparity Rates 
Common 
No models 
Single approach (GED) 
Rare 
Simple models 
N approaches ≈ N stud...
Acladistic analyses 
Disparity Rates 
Common 
No models 
Single approach (GED) 
Rare 
Simple models 
N approaches ≈ N stud...
Claddis 
github.com/graemetlloyd/Claddis
Disparity
Toljagic 
and 
Butler 
2013 
Disparity studies 
Brusatte et al 
2008 
Thorne 
et al 
2011 
Butler et al. 2011
Cladistic disparity 
Cladistic 
matrix 
Distance 
matrix 
Ordination ‘Morphospace’
Cladistic disparity 
Cladistic 
matrix 
Distance 
matrix 
Ordination ‘Morphospace’ 
Distance 
metric
Desiderata 
An ideal distance metric should:
Desiderata 
An ideal distance metric should: 
1. have high fidelity
Desiderata 
An ideal distance metric should: 
1. have high fidelity 
2. be normally distributed
Desiderata 
An ideal distance metric should: 
1. have high fidelity 
2. be normally distributed 
3. be Euclidean
Desiderata 
An ideal distance metric should: 
1. have high fidelity 
2. be normally distributed 
3. be Euclidean 
4. be ca...
Desiderata 
An ideal distance metric should: 
1. have high fidelity 
2. be normally distributed 
3. be Euclidean 
4. be ca...
Generalised Euclidean Distance 
Wills 2001
Generalised Euclidean Distance 
But: Sijk is incalculable if k values for i or j (or both) are missing 
Wills 2001
Generalised Euclidean Distance 
But: Sijk is incalculable if k values for i or j (or both) are missing 
Wills 2001
Alternate distances 
GED
Alternate distances 
Raw GED
Alternate distances 
Raw GED 
Gower
Alternate distances 
Raw GED 
Gower 
MOD
Simulations 
Input 
20 taxa 
50 binary characters 
0-80% missing data
Simulations 
Input Output 
20 taxa 
50 binary characters 
0-80% missing data 
N taxa retained 
Variance of first two PCA a...
Calculable 
Raw GED 
Gower 
MOD 
Incompleteness 
100% 
% taxa retained 
0% 80% 
0%
Visualisation 
Raw GED 
Gower 
MOD 
Incompleteness 
45% 
% variance axes 1 & 2 
0% 80% 
15%
Normalcy 
Raw GED 
Gower 
MOD 
Incompleteness 
1.00 
Shapiro-Wilk test 
0% 80% 
0.75
Fidelity 
Raw GED 
Gower 
MOD 
Incompleteness 
+30% 
Correlation 
0% 80% 
-30%
Fidelity 
Gower 
Raw 
GED 
MOD 
Incompleteness 
100% 
% highest fidelity 
0% 80% 
0%
% missing data 
Incompleteness 
30 
N data sets 
0% 80% 
0
Rates
Rate studies 
Derstler 1982 Forey 1988 
Ruta et al 2006 Brusatte et al 2008
Rate calculation 
Rate = N changes / 
Δt × Completeness
Null hypothesis 
H0 = equal rates
Alternate hypothesis 
Halt = +
Lungfish 
Westoll 1949
Lungfish 
Devonian 
high rates 
Lloyd et al 2012
Lungfish 
post-Devonian 
low rates 
Lloyd et al 2012
Parsimony problem 
DELTRAN ACCTRAN 
? 
? 
? 
Change 
early 
Change 
late
Parsimony problem 
Lloyd et al 2012
Parsimony problem 
Lloyd et al 2012
Parsimony problem 
? 
? 
? 
? 
? 
?
Parsimony problem 
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
? No changes
Internal vs. terminal 
Rate 
>
Internal vs. terminal 
Changes 
≈
Internal vs. terminal 
Duration 
<
Internal vs. terminal 
Solution
Rates revisited 
high rates 
low rates 
Brusatte et al 2014
Rates revisited 
high rates 
low rates 
Brusatte et al 2014
Time series problems
Toljagic 
and 
Butler 
2013 
Disparity time series 
Brusatte et al 
2008 
Thorne 
et al 
2011 
Butler et al. 2011
Toljagic 
and 
Butler 
2013 
Disparity time series 
4 time bins 4 time bins 
Brusatte et al 
2008 
Thorne 
et al 
2011 
14...
Rate time series 
Lloyd et al 2012 
Ruta et al 
2006 
Branch-binning No completeness
Rate time series 
N changes | Δt | Completeness
Conclusions 
Raw GED 
Gower 
MOD
Conclusions 
Raw GED 
Gower 
MOD 
PCO 1 
? 
PCO 2
Conclusions 
Raw GED 
Gower 
MOD 
PCO 1 
? 
PCO 2
Conclusions 
Raw GED 
Gower 
MOD 
Rate 
? 
? 
t 
PCO 1 
PCO 2
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New methodologies for the use of cladistic-type matrices to measure morphological disparity and evolutionary rate

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Slides from my talk at the Radiation-Extinction meeting (Linn. Soc., November 2014)

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New methodologies for the use of cladistic-type matrices to measure morphological disparity and evolutionary rate

  1. 1. New methodologies for the use of cladistic-type matrices to measure morphological disparity and evolutionary rate @GraemeTLloyd
  2. 2. Acknowledgements Matt Friedman Liam Revell Mark Bell Peter Smits Steve Brusatte Roger Benson Steve Wang Rich Fitzjohn
  3. 3. Cladistic-type data - Discrete morphological data
  4. 4. Cladistic-type data - Discrete morphological data - Limited to 32 states (often less)
  5. 5. Cladistic-type data - Discrete morphological data - Limited to 32 states (often less) - Frequently non-Euclidean
  6. 6. Cladistic-type data - Discrete morphological data - Limited to 32 states (often less) - Frequently non-Euclidean - Missing data common
  7. 7. Acladistic analyses Disparity Rates
  8. 8. Acladistic analyses Disparity Rates Common Rare
  9. 9. Acladistic analyses Disparity Rates Common No models Rare Simple models
  10. 10. Acladistic analyses Disparity Rates Common No models Single approach (GED) Rare Simple models N approaches ≈ N studies
  11. 11. Acladistic analyses Disparity Rates Common No models Single approach (GED) Rare Simple models N approaches ≈ N studies Time series an issue
  12. 12. Claddis github.com/graemetlloyd/Claddis
  13. 13. Disparity
  14. 14. Toljagic and Butler 2013 Disparity studies Brusatte et al 2008 Thorne et al 2011 Butler et al. 2011
  15. 15. Cladistic disparity Cladistic matrix Distance matrix Ordination ‘Morphospace’
  16. 16. Cladistic disparity Cladistic matrix Distance matrix Ordination ‘Morphospace’ Distance metric
  17. 17. Desiderata An ideal distance metric should:
  18. 18. Desiderata An ideal distance metric should: 1. have high fidelity
  19. 19. Desiderata An ideal distance metric should: 1. have high fidelity 2. be normally distributed
  20. 20. Desiderata An ideal distance metric should: 1. have high fidelity 2. be normally distributed 3. be Euclidean
  21. 21. Desiderata An ideal distance metric should: 1. have high fidelity 2. be normally distributed 3. be Euclidean 4. be calculable
  22. 22. Desiderata An ideal distance metric should: 1. have high fidelity 2. be normally distributed 3. be Euclidean 4. be calculable 5. be easily visualised
  23. 23. Generalised Euclidean Distance Wills 2001
  24. 24. Generalised Euclidean Distance But: Sijk is incalculable if k values for i or j (or both) are missing Wills 2001
  25. 25. Generalised Euclidean Distance But: Sijk is incalculable if k values for i or j (or both) are missing Wills 2001
  26. 26. Alternate distances GED
  27. 27. Alternate distances Raw GED
  28. 28. Alternate distances Raw GED Gower
  29. 29. Alternate distances Raw GED Gower MOD
  30. 30. Simulations Input 20 taxa 50 binary characters 0-80% missing data
  31. 31. Simulations Input Output 20 taxa 50 binary characters 0-80% missing data N taxa retained Variance of first two PCA axes Shapiro-Wilk test Mantel test
  32. 32. Calculable Raw GED Gower MOD Incompleteness 100% % taxa retained 0% 80% 0%
  33. 33. Visualisation Raw GED Gower MOD Incompleteness 45% % variance axes 1 & 2 0% 80% 15%
  34. 34. Normalcy Raw GED Gower MOD Incompleteness 1.00 Shapiro-Wilk test 0% 80% 0.75
  35. 35. Fidelity Raw GED Gower MOD Incompleteness +30% Correlation 0% 80% -30%
  36. 36. Fidelity Gower Raw GED MOD Incompleteness 100% % highest fidelity 0% 80% 0%
  37. 37. % missing data Incompleteness 30 N data sets 0% 80% 0
  38. 38. Rates
  39. 39. Rate studies Derstler 1982 Forey 1988 Ruta et al 2006 Brusatte et al 2008
  40. 40. Rate calculation Rate = N changes / Δt × Completeness
  41. 41. Null hypothesis H0 = equal rates
  42. 42. Alternate hypothesis Halt = +
  43. 43. Lungfish Westoll 1949
  44. 44. Lungfish Devonian high rates Lloyd et al 2012
  45. 45. Lungfish post-Devonian low rates Lloyd et al 2012
  46. 46. Parsimony problem DELTRAN ACCTRAN ? ? ? Change early Change late
  47. 47. Parsimony problem Lloyd et al 2012
  48. 48. Parsimony problem Lloyd et al 2012
  49. 49. Parsimony problem ? ? ? ? ? ?
  50. 50. Parsimony problem ? ? ? ? ? ? ? ? ? ? ? ? No changes
  51. 51. Internal vs. terminal Rate >
  52. 52. Internal vs. terminal Changes ≈
  53. 53. Internal vs. terminal Duration <
  54. 54. Internal vs. terminal Solution
  55. 55. Rates revisited high rates low rates Brusatte et al 2014
  56. 56. Rates revisited high rates low rates Brusatte et al 2014
  57. 57. Time series problems
  58. 58. Toljagic and Butler 2013 Disparity time series Brusatte et al 2008 Thorne et al 2011 Butler et al. 2011
  59. 59. Toljagic and Butler 2013 Disparity time series 4 time bins 4 time bins Brusatte et al 2008 Thorne et al 2011 14 time bins 2 time bins Butler et al. 2011
  60. 60. Rate time series Lloyd et al 2012 Ruta et al 2006 Branch-binning No completeness
  61. 61. Rate time series N changes | Δt | Completeness
  62. 62. Conclusions Raw GED Gower MOD
  63. 63. Conclusions Raw GED Gower MOD PCO 1 ? PCO 2
  64. 64. Conclusions Raw GED Gower MOD PCO 1 ? PCO 2
  65. 65. Conclusions Raw GED Gower MOD Rate ? ? t PCO 1 PCO 2

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