New methodologies for the use of cladistic-type matrices to measure

morphological disparity and evolutionary rate

@GraemeTLloyd

Acknowledgements

Matt Friedman

Liam Revell

MarkBell

PeterSmits

SteveBrusatte

Roger Benson

SteveWang

RichFitzjohn

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

- Missing data common

Acladistic analyses

Disparity Rates

Acladistic analyses

Common Rare

Disparity Rates

Acladistic analyses

Common

No models

Rare

Simple models

Disparity Rates

Acladistic analyses

Common

No models

Single approach (GED)

Rare

N approaches ≈ N studies

Simple models

Disparity Rates

Acladistic analyses

Common

No models

Single approach (GED)

Rare

N approaches ≈ N studies

Simple models

Disparity Rates

Time series an issue

Claddis

github.com/graemetlloyd/Claddis

Disparity

Toljagicand

Butler2013

Disparity studies

Brusatte et al2008

Thorneet al2011

Butler et al. 2011

Cladistic disparity

Cladisticmatrix

Distancematrix

Ordination ‘Morphospace’

Cladistic disparity

Cladisticmatrix

Distancematrix

Ordination ‘Morphospace’

Distancemetric

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 fidelity2. be normally distributed

Desiderata

An ideal distance metric should:

1. have high fidelity2. be normally distributed3. be Euclidean

Desiderata

An ideal distance metric should:

1. have high fidelity2. be normally distributed3. be Euclidean4. be calculable

Desiderata

An ideal distance metric should:

1. have high fidelity2. be normally distributed3. be Euclidean4. be calculable5. be easily visualised

Generalised Euclidean Distance

Wills 2001

Generalised Euclidean Distance

Wills 2001

But: Sijk is incalculable if k values for i or j (or both) are missing

Wills 2001

Generalised Euclidean Distance

Wills 2001

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

Gower

Raw GED

Alternate distances

Gower

Raw GED

MOD

Simulations

20 taxa

50 binary characters

0-80% missing data

Input

Simulations

20 taxa

50 binary characters

0-80% missing data

Mantel test

N taxa retained

Variance of first two PCA axes

Shapiro-Wilk test

Input Output

Calculable

Gower

Raw GED

MOD

Incompleteness

% t

axa

reta

ined

0% 80%0%

100%

Visualisation

Gower

Raw GED

MOD

Incompleteness

% v

aria

nce

axe

s 1

& 2

0% 80%

15%

45%

Normalcy

Gower

Raw GED

MOD

Incompleteness

Shap

iro

-Wilk

test

0% 80%

0.75

1.00

Fidelity

Gower

Raw GED

MOD

Incompleteness

Co

rrel

atio

n

0% 80%-30%

+30%

Fidelity

Gower

Raw

GED

MOD

Incompleteness

% h

igh

est

fid

elit

y

0% 80%

0%

100%

% missing data

Incompleteness

N d

ata

sets

0% 80%

0

30

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

Devonianhigh rates

Lloyd et al 2012

Lungfish

post-Devonianlow rates

Lloyd et al 2012

Parsimony problem

?

?

?

Changeearly

Changelate

DELTRAN ACCTRAN

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

Brusatte et al 2014

high rateslow rates

Rates revisited

Brusatte et al 2014

high rateslow rates

Time series problems

Toljagicand

Butler2013

Disparity time series

Brusatte et al2008

Thorneet al2011

Butler et al. 2011

Toljagicand

Butler2013

Brusatte et al2008

Thorneet al2011

Butler et al. 2011

Disparity time series

4 time bins 4 time bins

2 time bins14 time bins

Rate time series

Lloyd et al 2012

No completenessBranch-binning

Ruta et al2006

Rate time series

N changes | Δt | Completeness

Conclusions

Gower

Raw GED

MOD

Conclusions

Gower

Raw GED

MOD

PC

O 1

PCO 2

?

Conclusions

Gower

Raw GED

MOD

PC

O 1

PCO 2

?

Conclusions

Gower

Raw GED

MOD

Rat

e

t

?P

CO

1

PCO 2

?