This table gives indices for all the trees used in the paper.
Alpha Tubulin
Data Set  Chars  MP steps  Cons. steps  Trees  C.I.  R.I.  Isym 

411

1346

1354

36

0.657

0.760

0.485


398

1206

1219

60

0.661

0.773

0.482


385

1092

1147

612

0.642

0.757

0.489


365

931

949

24

0.683

0.797

0.481


343

776

783

96

0.719

0.826

0.469


314

615

617

16

0.754

0.855

0.475


264

395

402

65

0.836

0.903

0.431


188

160

179

882

0.788

0.883

0.337


111

32

48

42

0.625

0.833

0.270

EF1alpha
Data Set  Chars  MP steps  Cons. steps  Trees  C.I.  R.I.  Isym 

388

1541

0.592

0.630



326

833

843

10

0.637

0.686

0.485


308

691

693

3

0.659

0.711

0.557


281

514

529

40

0.711

0.729

0.486


250

349

364

297

0.769

0.774

0.459


220

230

231

2

0.866

0.868

0.422


168

92

97

31

0.907

0.924

0.318


109

15

15

3

1.000

1.000

0.229

Small subunit RNA (transversions only, except first row)









875

5043

5120

3432

0.29

0.628

0.302


875

2200

2208

1128

0.254

0.659

0.356


801

1369

1436

> 10000

0.329

0.702

0.300


771

1143

1245

8671

0.368

0.717

0.245


743

972

1021

7964

0.403

0.733

0.199


697

747

787

1062

0.463

0.772

0.206


630

502

524

2076

0.556

0.822

0.158


526

231

232

479

0.758

0.906

0.122


376

25

25

2

1.000

1.000

0.063

The common symmetry index from Heard et al. (Evolution 1992, 46:18181826) could not be used in our study because it has to be computed on perfectly dichotomic trees. We thus had to develop another index, in order to evaluate the symmetry of our many multifurcated trees.
We defined the order of emergence of a taxon as the number of nodes between that taxon and the root. For the purpose of our study, we defined the index of symmetry as the sum of the order of emergence of all taxa. This sum was then normalized (divided by n(n+1)/2  1, where n is the number of taxa) so that the maximal value is 1 (perfectly asymmetric tree).
We performed a comparison between the two indices, for 10,000 random dichotomic trees of 50 taxa. The result showed a strong positive correlation between the two indices, meaning that they provide a similar order relationship for dichotomic trees. As can be observed, our index does not reach 0 for dichotomic tree, hence the negligible plateau in the lower left corner.
Though less intuitive than Heard's, our index allowed
evaluate the symmetry of multifurcating tree. We nevertheless had to postulate
that a radiation of 2^{n} taxa (index 0) is more symmetric than
the perfectly symmetric 2^{n} taxa tree (index 2(n1)/((2^{n}+1)1)
). Another disadvantage of our index is that one cannot compare the symmetry
of trees with different numbers of taxa (as our index does not reach 0
for dichotomic trees).
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