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Methods of determining cranial
and postcranial character
congruence
By Ross Mounce* and Matthew Wills
* [email protected]

3. Partitioned Goodman-Bremer Support

1. Why compare subsets of cladistic
data?

Another 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.

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.

Eoraptor_ lunensis
Herrerasaurus_ ischigualastensis

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
Doanatomical
vertebrae regions.
make 'good'
different
e.g. 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?
2.
What
methods
should
one
use?

Ensemble Consistency Index

1A)

f(x) = -0.0006274738x + 0.6109492765
R = 0.1635139213

0.900

Carnotaurus_ sastrei

4.5,4.5,

Torvosaurus_ tanneri

0.5,3.5,

Baryonyx_ walkeri

1,0,

0,8,

Allosaurus_ fragilis

Postcranial elements from UCMP
77270
(Dilophosaurus)

Dilophosaurus_ wetherilli
0,9,
0,5,

Liliensternus_ liliensterni
0,1,

Lophostropheus_ airelensis
0,1,

Skull of D. wetherilli

Syntarsus_ kayentakatae
0,2,

Coelophysis_ rhodesiensis
Coelophysis_ bauri

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).

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.

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.
1.000

Ceratosaurus_ nasicornis

-1.0,4,

4. The Incongruence Length Difference Test

0.800
0.700

The 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.
Only 3 random reps were as

0.600
0.500
0.400
0.300
0.200
0.100
0.000
50

100

150

200

250

300

350

400

450

Number of characters in dataset

Whole
dataset

1B)
Ensemble Consistency Index

Part A
(only)

1.000
0.900

Out
A
B
C
D
E
F

000000000
001110011
001110000
001100011
110000000
110001101
110001100

000000000
001110011
001110000
001100011
110000000
110001101
110001100

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

0.800

Part B
(only)

0.700
0.600
0.500

000000000
000000011
000001100
000111111
001111100
111111101
111111100

Out
A
B
C
D
E
F

MP

Length=25

MP
000000000
000000011
000001100
000111111
001111100
111111101
111111100

L=11

MP

L=12

Fig. 3 A toy matrix example of ILD value8
calculation. In this instance the length
difference between these partitions is 2
(25-23)

0.400
0.300
0.200
0.100

Out
A
B
C
D
E
F

000000000
001110011
001110000
001100011
110000000
110001101
110001100

000000000
000000011
000001100
000111111
001111100
111111101
111111100

Out
A
B
C
D
E
F

000000000
001110011
001110000
001100011
110000000
110001101
110001100

000000000
000000011
000001100
000111111
001111100
111111101
111111100

Calc.
ILD

Calc.
ILD

ILD=1

ILD=3

Number of replicates

0

Out
A
B
C
D
E
F

short
ILD p-value = 0.004 (4/1000)

Summed length of
the
cranial,postcranial
partitions

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

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.

Length

Fig. 5 Re-analysing
Ezcurra&Cuny'07 using the ILD
test to compare cranial and
postcranial partitions

Having performed the ILD test, and others on 63 vertebrate data
matrices, to compare cranial and postcranial partitions, we find many
Number of taxa in dataset
Fig. 1 Data from re-analysis of 163 vertebrate-only cladistic matrices datasets like figure 5, appear to have unexplained significant
published 2000 2011 (Mounce & Damary-Homan, unpublished) further incongruence (figure 6; p-values < 0.005). A) B) details in ESM. A) The inverse relationship between CI & characters. B) The inverse We conclude the relationship between CI & taxa. Admittedly, taxa & character number are explanation for this highly correlated. Figure 1 (above) empirically demonstrates some of phenomenon might be the problems of using CI as a comparative statistic. modularity; allowing 4 We agree with Cuthill et al. that multivariate observable difference in approaches are needed to adequately control for Fig. 6 A) Group composition of the datasets analysed the rates of B) ILD p-values: red=0.001-0.01 (highly significant), covariates such as these in comparative analyses. A grey=0.011-0.1 (significant or borderline), morphological evolution better comparative measure of homoplasy may well blue=0.101-1.0 (not significant) to be seen. 5 be Archie's Homoplasy Excess Ratio (HER) which is more computationally-demanding. However, if there is Supplementary materials inc. code + data + more refs: http://bit.ly/palass a high proportion of non-randomly distributed missing Acknowledgements: Many thanks to all the Macroevolution group data in the matrix it can lead to negative HER values. References: 1. Grant & Kluge, 2003 Cladistics 2. Kluge, 1989 Syst. Zool. 3. [email protected] & Farris, 1969 Syst. Zool. 4. Hoyal Cuthill et al, 2010 Cladistics 5. Archie, 1989 Syst. Zool. 6. Grant & 0.000 0 10 20 30 40 50 60 70 80 90 100 10 13 16 6 14 16 'Fish' Amphibia Mammals Birds Dinosaurs Reptiles (other) 7 40 4 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. *Many of the images displayed on 2010 PLoS ONE @RMounce Except where otherwise noted* this work is licensed under this poster are not my creative works, and may not be compatibly http://about.me/rossmounce http://creativecommons.org/licenses/by/3.0/ licensed.

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