Supplementary information Cranial ontogenetic variation in early saurischians and the role of heterochrony in the diversification of predatory dinosaurs



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Figure S5 Shape differences in ancestors when crested taxa are included or excluded. (a) Averostra, (b) Ceratosauria, (c) Avetheropoda, (d) Coelurosauria, (e) Tyrannosauroidea (clade including Dilong and Tarbosaurus with Guanlong as outgroup). Red dots mark (semi-)landmarks, which shows significant differences from each other. Skull openings are shaded in grey.
Table S10 Angles of ontogenetic trajectories in PCA against PC 1 when crested taxa are included in the data set.




PC 1-2

PC 1-3

Massospondylus

86.3695

73.9781

Coelophysis

43.1616

7.2269

Megalosaurid taxon

84.2163

60.9371

Allosaurus

5.8852

14.7089

Tarbosaurus

0.1579

59.0058



Table S11 Pairwise angles between ontogenetic trajectories in PCA when crested taxa are included in the data set.

PC 1-2

Massospondylus

Coelophysis

Megalosaurid taxon

Allosaurus

Tarbosaurus

Massospondylus

0.0000













Coelophysis

43.2079

0.0000










Megalosaurid taxon

2.1533

41.0546

0.0000







Allosaurus

87.7453

130.9532

89.8985

0.0000




Tarbosaurus

93.7883

136.9962

95.9416

6.0431

0.0000



















PC 1-3

Massospondylus

Coelophysis

Megalosaurid taxon

Allosaurus

Tarbosaurus

Massospondylus

0.0000













Coelophysis

81.2050

0.0000










Megalosaurid taxon

134.9152

53.7102

0.0000







Allosaurus

91.3130

172.5180

133.7718

0.0000




Tarbosaurus

165.0277

113.7673

60.0571

73.7147

0.0000





Figure S6 PCA when crested taxa are included. (a) Ontogenetic trajectories of terminal taxa for PC 1 against PC 2. (b) Ontogenetic trajectories of terminal taxa for PC 1 against PC 3. Theropod taxa are shown as black dots, while sauropodomorph taxa are shown as grey dots.

8. Influence of semi-landmarks on the results

After exclusion of the semi-landmarks from the data set the differences in the ontogenetic trajectories retains, but the courses of the trajectories changed relative to each other. This primarily impacts the diagnosis of heterochronic events in the regression analysis, which differs from the original data set with respect to the cranial evolution in early sauropodomorphs and tyrannosaurids. However, as less shape variation in dorsoventral dimension is captured after the exclusion of semi-landmarks, the results for early sauropodomorphs and tyrannosaurids are somewhat misleading. The mapping of the Procrustes shapes onto the phylogeny clearly shows a relative increase of the dorsoventral height of the skull in both groups.


Table S12 Angles of ontogenetic trajectories in PCA against PC 1 when semi-landmarks are excluded from the data set.




PC 1-2

PC 1-3

Massospondylus

81.1710

59.6961

Coelophysis

81.3625

32.3194

Megalosaurid taxon

52.1091

23.0962

Allosaurus

32.4126

7.4444

Tarbosaurus

1.1564

55.0223

Table S13 Pairwise angles between ontogenetic trajectories in PCA when semi-landmarks are excluded from the data set.

PC 1-2

Massospondylus

Coelophysis

Megalosaurid taxon

Allosaurus

Tarbosaurus

Massospondylus

0.0000













Coelophysis

17.4665

0.0000










Megalosaurid taxon

29.0620

46.5285

0.0000







Allosaurus

48.7585

66.2249

19.6965

0.0000




Tarbosaurus

80.0146

97.4811

50.9526

31.2562

0.0000



















PC 1-3

Massospondylus

Coelophysis

Megalosaurid taxon

Allosaurus

Tarbosaurus

Massospondylus

0.0000













Coelophysis

152.6233

0.0000










Megalosaurid taxon

82.7922

124.5844

0.0000







Allosaurus

52.2517

155.1250

30.5406

0.0000




Tarbosaurus

114.7184

92.6583

31.9262

62.4667

0.0000



Table S14 Angles of ontogenetic trajectories on plot of shape versus centroid size (log-transformed) when semi-landmarks are excluded from the data set.




Angle

Saurischia

4.2406

Massospondylus

3.4176

Neotheropoda

5.2886

Coelophysis

7.5316

Orionides

4.3657

Megalosauridae

4.3320

Avetheropoda

3.8961

Allosaurus

3.1168

Tarbosaurus

1.5063



Table S15 Heterochronies within Saurischia when semi-landmarks are excluded based on the regression analysis. The table shows the differences of Procrustes distances (ΔPD) between ancestor-descendent relationships of adult species from the regression analysis. Positive values* = peramorphic trends; negative values** = paedomorphic trends; values in brackets = non-significant trends




ΔPD

Saurischia-Massospondylus

(0.0088)

Saurischia-Theropoda

0.0579*

Neotheropoda-Coelophysis

(0.0114)

Neotheropoda-Orionides

0.0303*

Orionides-megalosaurid taxon

0.0430*

Orionides-Avetheropoda

-0.0229**

Avetheropoda-Allosaurus

(0.0210)

Avetheropoda-Tarbosaurus

(0.0033)




Figure S7 PCA and regression analysis when semi-landmarks are excluded. (a) Ontogenetic trajectories of terminal taxa for PC 1 against PC 2. (b) Ontogenetic trajectories of terminal taxa for PC 1 against PC 3. Theropod taxa are shown as black dots, while sauropodomorph taxa are shown as grey dots. (c) Ontogenetic trajectories of terminal taxa (solid lines) and hypothetical ancestors (dashed lines) against log-transformed centroid size (LogCS).

Table S16 Comparison of the results of the PCA and the regression test (shape vs. log-transformed centroid size) for all tree data sets.

PCA

Saurischia (original)




Saurischia (without semi- landmarks)




Saurischia (taxa with nasal crests)




PC 1

30.75 %




28.37 %




28.58 %




PC 2

23.94 %




19.98 %




22.73 %




PC 3

13.26 %




15.64 %




12.96 %

























Regression

Correlation

p value

Correlation

p value

Correlation

p value

All

15.32 %

<0.0001

14.98 %

<0.0001

14.71 %

<0.0001

PC 1

0.46 %

0.6735

4.80 %

0.178

0.30 %

0.7333

PC 2

45.68 %

<0.0001

51.23 %

<0.0001

48.82 %

<0.0001

PC 3

27.30 %

0.0007

19.66 %

0.0039

22.03 %

0.0016

PC 4

6.35 %

0.1183

0.79 %

0.5896

0.64 %

0.6143


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