Congruence between Cranial and Postcranial Characters

in Vertebrate Systematics

Ross Mounce and Matthew Wills

Introduction

Total Evidence sensu Carnap (1950)

The strongest test of a phylogenetic hypothesis is

provided by the comparison of multiple lines of

independent evidence

Example Data Partitions

Molecular data

+

Morphological data

Example Data Partitions

Molecular data[nuclear genes]

[mitochondrial genes][coding and non-coding]

+

Morphological data

Morphological Data Partitions:a few examples

Cranial | Postcranial

(for Vertebrata, this study)

Genital | Non-genital

(for insects, Song & Bucheli, Cladistics, 2010)

'Hard parts' | 'Soft parts'

(in prep.)

Motivation

“It is commonly believed that there are differences in the evolutionary lability of the crania, dentition, and postcrania of mammals”

(Sanchez-Villagra & Williams, 1998)

“...postcranial characters either from the vertebral column or fins are considerably less used in phylogenetic analyses of lower actinopterygians”

(Arratia, Acta Zoologica 2009)

Generally, there are more cranial characters in real data matrices

> 60% of vertebrate characters are cranial*

* Based upon a sample of 70 vertebrate (only) data matrices published between 2001-2010, excluding matrices that were either 100% cranial or postcranial

Testing for a difference in signal

Future work: Character Compatibility tests (sensu Meacham & Estabrook, 1985)

ILD - Incongruence Length Difference (Mickevitch & Farris, 1983)

TILD - Topological ILD (W. Wheeler, 1999)

IRD - Incongruence Relationship Difference (Mounce & Wills)

PDC - Partition Distance Correlation (Mounce, Gerber, Wills)

pCI - Partition Consistency Index (steps relative to partition tree only)

HER – Homoplasy Excess Ratio (Archie, 1989)

Incongruence Length Difference

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Out 000000000 A 001110011 B 001110000 C 001100011 D 110000000 E 110001101 F 110001100

Out 000000000A 000000011B 000001100C 000111111D 001111100E 111111101F 111111100

L=25 L=11

L=12ILD = 25 – (11 + 12)

= 2

Determining the significance of ILD

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Cranial | Postcranial

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Randomized partition 1

Random. Partition 2 … Random. Partition 999

4 3 2 1 00

50

100

150

200

250

300

350

400

450

ILD

ILD = 2 ILD = 1

ILD = 1 ILD = 3

Cran | Post

The ILD of cranial and postcranial partitions

10

6

16

4

14

13

'Fish'AmphibiaMammalsBirdsDinosaursReptiles (other)

N = 63

Source data used in this study

16

7 40

0.001 - 0.0100.011 - 0.1000.101 - 1.000

ILD significance p-values

* 999 random reps, heuristic search, TBR-swapping, maxtrees 10000, hold 1000, RAS 10

Topological ILD

Original Matrix MPT(s) MRP matrix

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

AB 0110000ABC 0111000DE 0000110DEF 0000111ABCDEF 0111111

L = 4

Out 000000000 A 001110011 B 001110000 C 001100011 D 110000000 E 110001101 F 110001100

Out 000000000A 000000011B 000001100C 000111111D 001111100E 111111101F 111111100

Cranial

Post-cranial

AB 0110000ABC 0111000DE 0000110DEF 0000000ABCDEF 0111111DE 0000110DEF 0000111BDEF 0010111BCDEF 0011111ABCDEF 0111111

L = 11

TILD = 11 – 4 = 7

(excluding uninformative characters) MSY Lee, 2001

P-value = 0.113

TILD is not suitable for testing morphological data partitions

Regardless of exactly how one partitions morphological datasets, the very process of partitioning means that the smaller partition will have only 50% (or less) of the characters in the whole matrix

This has a negative effect on the % topological resolution (nodes) of the MP solution(s)

Which in turn reduces the number of parsimony-informative characters of the MRP-matrix of the MP solution(s)

Indeed, for many datasets I tested; the Strict Consensus (SC) of the MP solutions for one or both of the individual partitions was completely unresolved or very poorly resolved.

TILD (>50% maj-rule)

46

6

73

0.001 - 0.0100.011 - 0.1000.101 - 0.3000.301 - 1.000

TILD significance p-values

Cranial | Postcranial'apparently'

Significantly incongruent

N = 63

These results CANNOT be interpreted as support for hypotheses of incongruence of phylogenetic signal between cranial and postcranial data.They are an artefact of incongruence (character conflict) within each data

partition, NOT between the partitions as originally intended.

Incongruence Relationship Difference

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Cranial | Postcranial

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Randomized partition 1

Random. Partition 2 … Random. Partition 999

4 3 2 1 00

50

100

150

200

250

300

350

400

450

RF = 2 RF = 4

RF = 2 RF = 2

Cran | Post

IRD (Robinson-Foulds)

17

244

0.001 - 0.0100.011 - 0.3000.301 - 1.000

IRD(RF) significance p-values

16

7 40

ILD significance p-values

IRD(RF) provides similar but not the same conclusions as ILD

Partition Distance Correlation

Transform each partition into a (phenetic) distance matrix

Compute the difference between the two distance matrices using:– a) Mantel's permutation test (Mantel, 1967)– b) Spearman's coefficient of correlation

Determine significance p-values by comparing with randomly partitioned replicate matrix scores (~ILD)

Out 000000000 A 001110011 B 001110000 C 001100011 D 110000000 E 110001101 F 110001100 Out 000000000A 000000011B 000001100C 000111111D 001111100E 111111101F 111111100

-0.66 -0.44 0.44 -0.22 0.44 0.44 -0.55 0.55 0.55 0.55 -0.44 0.44 0.66 0.44 0.33 -0.55 0.33 0.11 0.55 0.44 0.55 -

Mantel: 0.36

Spearman's: 0.41 -0.44 -0.11 0.33 -0.33 0.33 0.44 -0.66 0.66 0.55 1.00 -0.55 0.33 0.66 0.44 0.55 -0.55 0.88 0.44 0.44 0.55 0.66 -

Which partition most resembles the whole tree (a fair test)?

Out 000000000 000000000A 001110011 000000011B 001110000 000001100C 001100011 000111111D 110000000 001111100E 110001101 111111101F 110001100 111111100

Non-parametric bootstrap resample the larger partition down to the size of the smaller partition

Calculate MP solutions for each (now equally sized partition)

Find Tree-Tree distance (partition<->whole) for each

Significance: Mann-Whitney U test each pool (partition) of replicates

Recap & Conclusions

'Apparent' significant incongruence of phylogenetic signal between cranial and postcranial data partitions is not uncommon, however one choses to measure it (ILD, IRD or “phenetic” ILD)

At present, there appears to be no obvious pattern to the distribution of significantly incongruent datasets (but since overall sample size is low, things may change with more data)

Further work needs to be done to properly distinguish between 'global incongruence' and strong 'local incongruence' (Baker ea., 2001)

To this end, further development of character compatibility methods (sensu Meacham & Estabrook, 1985) would be ideal, so that one can get informative statistics per-character rather than per-partition

AcknowledgementsFunding Computational Resources

Help and Guidance

Matthew WillsSylvain Gerber

Biodiversity Lab 1.07Ward Wheeler

All authors who kindly provided me their data(Marie Stopes Travel Grant)

...and now for something a bit different!

“Science is based on building on, reusing and openly criticising the

published body of scientific knowledge”

http://pantonprinciples.org/

Mounce, Butler, Davis, Dunhill, Garwood, Lamsdell, Legg, Lloyd, Pittman, Warnock, Wolfe+ ~150 signatories inc Benton, Ruta, Rannala, Wagner, Upchurch, Sutton, Farke, Dunlop...

The Next Step...

Publish your underlying data (set a good example!)

If you spot a paper in which the results cannot be replicated from the data given, because

a) necessary data is missingorb) data given doesn't give the results they say it does

DO SOMETHING ABOUT IT!

(you may get rewarded with a Nature paper!)