Methods of determining cranial and postcranial character

congruenceBy Ross Mounce* and Matthew Wills

@RMounce http://about.me/rossmounce

Acknowledgements: Many thanks to all the Macroevolution group @UoBathReferences: 1. Grant & Kluge, 2003 Cladistics 2. Kluge, 1989 Syst. Zool. 3. Kluge & Farris, 1969 Syst. Zool. 4. Hoyal Cuthill et al, 2010 Cladistics 5. Archie, 1989 Syst. Zool. 6. Grant & Kluge, 2008 MPE

7. Bremer, 1988 Evol. 8. Mickevich & Farris, 1981 Syst. Zool. 9. Farris et al, 1994 Cladistics 10. Mounce, 2011 http://bit.ly/ILDreview 11. Ketchum & Benson, 2010 Biol. Rev. 12. Smith, N.D. 2010 PLoS ONE

* ross.mounce@gmail.com

Except where otherwise noted* this work is licensed under http://creativecommons.org/licenses/by/3.0/

*Many of the images displayed on this poster are not my creative

works, and may not be compatibly licensed.

Supplementary materials inc. code + data + more refs: http://bit.ly/palassposter

Optimal estimates of phylogenetic inference work on the basis of Total Evidence1. We do not contest this.However, using methods of 'data exploration' to examine subsignals within datasets, can be both a justified and useful means with which to gain quantitative support for more detailed evolutionary explanations2.

Molecular systematists routinely compare and contrast data sourced from different genes e.g. nuclear, mitochondrial & plastid markers. We think morphologists could stand to gain much insight from similar statistically-explicit comparisons of different anatomical regions. e.g. Do vertebrae make 'good' characters?

Does my soft tissue data agree with my osteological data?

What influence do dental characters have on the cladogram?

Have different parts evolved at different rates?

4. The Incongruence Length Difference TestThe ILD8 test9 is perhaps one of the most routinely used methods for comparing sequence data in molecular phylogenetics; with at least 2500 citations to the paper describing it, most of which do use the test10. Given its long history, we feel this test is under-utilised in palaeontology, but see some recent uses11,12.

2. What methods should one use?One would not recommend the consistency index3 – despite its popular usage, as it is known4 to be a poor measure of homoplasy – affected by number of taxa, characters, character states of characters, and the rate of evolution of characters in cladistic matrix.

Torvosaurus_ tanneri

Syntarsus_ kayentakataeLophostropheus_ airelensis

Liliensternus_ liliensterniDilophosaurus_ wetherilli

Coelophysis_ rhodesiensisCoelophysis_ bauri

Ceratosaurus_ nasicornisCarnotaurus_ sastrei

Baryonyx_ walkeriAllosaurus_ fragilis

Herrerasaurus_ ischigualastensisEoraptor_ lunensis

0,9,0,5,

0,1,0,1,

0,2,

-1.0,4,

0,8,

4.5,4.5,0.5,3.5,

1,0,

3. Partitioned Goodman-Bremer SupportAnother method relatively unused in palaeontological systematics is that of partitioned Goodman6-Bremer7 support (GBS). Using this method one can assess not just the number of characters that support each node in a strict consensus cladogram, but also from which partition those supporting characters came from. Negative support indicates otherwise 'hidden' character conflict between partitions.

Fig. 2 Re-analysing data from Ezcurra & Cuny 2007, JVP, to compare support contributed by cranial & postcranial character partitions (cranial,postcranial, GBS values on each node).

Postcranial elements from UCMP 77270

(Dilophosaurus)

Skull of D. wetherilli

Fig. 1 Data from re-analysis of 163 vertebrate-only cladistic matrices published 2000 – 2011 (Mounce & Damary-Homan, unpublished) further

details in ESM. A) The inverse relationship between CI & characters. B) The inverse

relationship between CI & taxa. Admittedly, taxa & character number are highly correlated.

0 50 100 150 200 250 300 350 400 4500.000

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1.000 f(x) = -0.0006274738x + 0.6109492765R² = 0.1635139213

0 10 20 30 40 50 60 70 80 90 1000.000

0.100

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f(x) = -0.0041252873x + 0.6669527033R² = 0.4040262399

1A)

1B)

Ensemble Consistency Index

Ensemble Consistency Index

Number of characters in dataset

Number of taxa in dataset

Figure 1 (above) empirically demonstrates some of the problems of using CI as a comparative statistic. We agree with Cuthill et al.4 that multivariate approaches are needed to adequately control for covariates such as these in comparative analyses. A better comparative measure of homoplasy may well be Archie's Homoplasy Excess Ratio5 (HER) which is more computationally-demanding. However, if there is a high proportion of non-randomly distributed missing data in the matrix it can lead to negative HER values.

Note in figure 2 (above) the conflict in GBS from cranial characters to the strongly postcranially-supported node (indicated by the arrow) – the distribution of states in one cranial character is incongruent with the topology supported by postcranial characters. Also there is strongly 'lop-sided' partition support for this cladogram – most nodes are only supported by postcranial characters – despite there being 68 cranial characters in this matrix relative to 77 postcranial.

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

Whole dataset

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

Part A(only)

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

Part B(only)

Length=25MP

MP

MP

L=11

L=12

Summed length of the cranial,postcranial partitions

Number of replicates

Length

Only 3 random reps were as shortILD p-value = 0.004 (4/1000)

Fig. 3 A toy matrix example of ILD value8 calculation. In this instance the length

difference between these partitions is 2 (25-23)

Fig. 5 Re-analysing Ezcurra&Cuny'07 using the ILD

test to compare cranial and postcranial partitions

Fig. 4 Example randomised partition replicates, with which one can use to determine the

significance of the length difference between the

partitions you are interested in.

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

Calc. ILD

ILD=1

Calc. ILD

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

ILD=3

… at least 999 times, and compare with the ILD you originally got, to get an ILD p-value

Having performed the ILD test, and others on 63 vertebrate data matrices, to compare cranial and postcranial partitions, we find many datasets like figure 5, appear to have unexplained significant incongruence (figure 6; p-values < 0.005).

16

7 40

10

6

164

14

13'Fish'AmphibiaMammalsBirdsDinosaursReptiles (other)

Fig. 6 A) Group composition of the datasets analysedB) ILD p-values: red=0.001-0.01 (highly significant),

grey=0.011-0.1 (significant or borderline), blue=0.101-1.0 (not significant)

We conclude the explanation for this phenomenon might be modularity; allowing observable difference in the rates of morphological evolution to be seen.

A) B)

1. Why compare subsets of cladistic data?