Department of Biological Sciences, Monash University, Melbourne, VIC, 3800, AUS

Abstract

Background

The range of potential morphologies resulting from evolution is limited by complex interacting processes, ranging from development to function. Quantifying these interactions is important for understanding adaptation and convergent evolution. Using three-dimensional reconstructions of carnivoran and dasyuromorph tooth rows, we compared statistical models of the relationship between tooth row shape and the opposing tooth row, a static feature, as well as measures of mandibular motion during chewing (occlusion), which are kinetic features. This is a new approach to quantifying functional integration because we use measures of movement and displacement, such as the amount the mandible translates laterally during occlusion, as opposed to conventional morphological measures, such as mandible length and geometric landmarks. By sampling two distantly related groups of ecologically similar mammals, we study carnivorous mammals in general rather than a specific group of mammals.

Results

Statistical model comparisons demonstrate that the best performing models always include some measure of mandibular motion, indicating that functional and statistical models of tooth shape as purely a function of the opposing tooth row are too simple and that increased model complexity provides a better understanding of tooth form. The predictors of the best performing models always included the opposing tooth row shape and a relative linear measure of mandibular motion.

Conclusions

Our results provide quantitative support of long-standing hypotheses of tooth row shape as being influenced by mandibular motion in addition to the opposing tooth row. Additionally, this study illustrates the utility and necessity of including kinetic features in analyses of morphological integration.

Background

The evolution of morphology is limited by the complex interactions of various selection pressures and constraints, which can be extremely difficult to quantify

Morphological integration is both a cause and product of constraint and refers to how certain structures vary more closely with each other than with other structures because of various constraints

Teeth

Opposing mammalian teeth interact in a very precise manner, with specific tooth features occluding with each other, and the molars of mammals have specialized shapes related to diet

Because Carnivora have a highly variable number of molars and Dasyuromorphia consistently have four molars (Figure

Comparison of upper and lower tooth rows in Carnivora and Dasyuromorphia

**Comparison of upper and lower tooth rows in Carnivora and Dasyuromorphia.** 3-dimensional renderings of upper tooth rows of **A**) and **B**) and lower tooth rows (**C, D**). Scale spheres are 1 mm in diameter.

While OPC is a quantification of the complexity of a tooth row, it is not a statement of the direction of occlusion for the tooth row and there has been no evidence to indicate that tooth row complexity is related to occlusal direction or mandible motion. While it is logical that opposing tooth row complexities of a taxon would be highly correlated

Carnivora and Dasyuromorphia are good systems for comparing hypotheses about similarities in tooth shape and movement during occlusion because of ecological similarities, gross morphological differences and because mandibular movement is constrained to being only rotation and mediolateral translation with extremely limited anteroposterior movement. In this study, we compare biological hypotheses of tooth-mastication integration in carnivorous mammals. Statistical models of tooth row OPC as a response solely to opposing tooth row OPC may be the most parsimonious explanation of tooth row shape, which would mean that jaw movement does not affect the correlation between upper and lower tooth complexity. If tooth row shape is best explained by not only the opposing tooth row but also some measure of motion during occlusion, then tooth row shape is constrained by a suite of features and not just the opposing tooth row. Operating under the assumption that mandibular motion, as controlled by specific muscle action, is at least a partially heritable trait because of the limitations imposed by the organism’s musculoskeletal system this result would suggest integration of static and kinetic cranial features.

Methods

Specimens

16 species of Carnivora and 8 species of Dasyuromorphia were sampled, with a total of 34 specimens (20 and 14 specimens respectively; Table

**Order**

**Family**

**
Genus
**

**
species
**

**Collection**

**Number**

**upper tooth row length**

**lower tooth row length**

**upper OPCR**

**lower OPCR**

**t**

**d**

**a**

**w**

The number of teeth in upper and lower tooth rows is reported, along with OPCR values for each tooth row. Other measurements are lateral translation (

Carnivora

Canidae

Alopex

lagopus

FMNH

1345

3

3

154.25

96.75

3.22

8.71

22.21

56.20

Carnivora

Canidae

Canis

mesomelas

NMV

C32235

3

3

147.25

124.38

5.90

7.54

38.05

64.82

Carnivora

Canidae

Canis

aureus

ZMB

52447

3

3

172.62

132.88

3.37

10.16

19.73

70.00

Carnivora

Canidae

Vulpes

vulpes

NMV

C25076

3

3

153.38

111.38

4.44

9.75

24.49

65.48

Carnivora

Canidae

Vulpes

vulpes

NMV

C25077

3

3

150.12

113.62

4.10

8.43

25.93

66.88

Carnivora

Felidae

Acinonyx

jubatus

FMNH

U31

2

1

52.62

36.50

4.80

11.41

23.39

108.60

Carnivora

Felidae

Neofelis

nebulosa

NMV

R11997

2

1

42.62

18.38

4.71

14.04

18.55

97.48

Carnivora

Herpestidae

Herpestes

ichneumon

ZMB

83028

3

2

144.25

101.12

2.87

6.04

29.46

41.70

Carnivora

Herpestidae

Mungos

mungo

NMV

R1555

3

2

120.25

80.62

2.70

4.46

31.16

32.81

Carnivora

Herpestidae

Suricata

suricatta

NMV

R2454

3

2

162.62

64.12

1.12

1.24

42.18

38.63

Carnivora

Herpestidae

Suricata

suricatta

NMV

R2486

3

2

143.12

77.25

0.76

1.67

24.43

38.57

Carnivora

Hyaenidae

Crocuta

crocuta

FMNH

30.196

2

1

76.12

55.88

4.77

18.92

14.76

123.00

Carnivora

Mustelidae

Mustela

putorius

NMV

C22360

2

2

73.38

42.88

0.93

3.58

14.56

31.02

Carnivora

Mustelidae

Mustela

putorius

NMV

C32788

2

2

76.38

37.25

1.30

2.96

23.72

32.84

Carnivora

Mustelidae

Mustela

frenata

NMV

C11225

2

2

75.25

41.38

1.17

2.61

24.11

25.76

Carnivora

Mustelidae

Mustela

frenata

NMV

C31304

2

2

60.50

38.88

1.23

2.41

27.03

18.32

Carnivora

Mustelidae

Mustela

lutreola

ZMB

94308

2

2

119.25

71.25

0.92

3.31

16.36

34.70

Carnivora

Mustelidae

Vormela

peregusna

SMNH

A91 5107

2

2

113.25

56.75

0.94

2.94

19.05

28.90

Carnivora

Viverridae

Genetta

genetta

SMNH

A58 042

3

2

143.88

139.50

2.21

3.60

40.45

34.90

Carnivora

Viverridae

Viverra

zibetha

NMV

C1845

3

2

129.62

83.88

2.83

5.36

27.82

37.51

Dasyuromorphia

Dasyuridae

Dasycercus

cristicauda

NMV

C5364

4

4

251.88

188.25

1.34

1.80

36.59

22.65

Dasyuromorphia

Dasyuridae

Dasycercus

cristicauda

NMV

C5356

4

4

238.38

180.50

1.42

1.55

42.40

22.83

Dasyuromorphia

Dasyuridae

Dasyurus

geoffroii

NMV

C31515

4

4

212.12

170.62

2.03

3.67

28.93

38.99

Dasyuromorphia

Dasyuridae

Dasyurus

geoffroii

NMV

C31560

4

4

218.50

158.62

2.04

4.70

23.45

42.60

Dasyuromorphia

Dasyuridae

Dasyurus

maculatus

NMV

C6108

4

4

240.62

165.25

3.77

4.91

37.49

43.68

Dasyuromorphia

Dasyuridae

Dasyurus

maculatus

NMV

C29669

4

4

224.50

152.50

2.52

5.54

24.45

49.65

Dasyuromorphia

Dasyuridae

Dasyurus

hallucatus

MUZ

4735

4

4

214.88

162.25

2.43

3.30

36.38

31.62

Dasyuromorphia

Dasyuridae

Dasyurus

viverrinus

MUZ

5737

4

4

214.88

168.75

5.98

9.26

32.86

39.72

Dasyuromorphia

Dasyuridae

Phascogale

tapoatafa

NMV

C27059

4

4

292.88

204.88

1.84

2.27

38.99

28.73

Dasyuromorphia

Dasyuridae

Phascogale

tapoatafa

NMV

C34784

4

4

301.62

190.25

1.37

2.20

31.91

24.13

Dasyuromorphia

Dasyuridae

Sarcophilus

harrisii

NMV

C6232

4

4

169.75

114.62

4.83

11.01

23.69

83.50

Dasyuromorphia

Dasyuridae

Sarcophilus

harrisii

NMV

C6233

4

4

162.88

116.00

5.21

11.92

23.61

87.68

Dasyuromorphia

Thylacinidae

Thylacinus

cynocephalus

NMV

C5748

4

4

133.38

98.75

6.01

11.44

27.73

86.76

Dasyuromorphia

Thylacinidae

Thylacinus

cynocephalus

NMV

C5747

4

4

144.38

102.62

8.79

12.72

34.65

108.77

Three-dimensional scanning

Specimens were scanned with a Laser Design DS 2025 3D scanner with a RPS-120 probe (Laser Design Inc., Minneapolis, MN) scanning at 620 nm wavelength. Upper and lower tooth rows from the same side of the jaw were scanned. Additionally, as in Evans and Fortelius _{4}Cl) to aid scanning.

Depending on the size of the specimen, specimens were scanned at resolutions ranging from 50 μm to 10 μm. Tooth rows were saved as point cloud files, which were imported into Geomagic 12 (Geomagic Inc., North Carolina, USA 2010) and extraneous information was reduced using custom macros (available in Supplementary Information). Point clouds were aligned and then combined. Following this, each point cloud was transformed into a polygon surface at a triangle size greater than point cloud spacing by approximately 5 μm.

Mandibular movement

To manipulate the surface reconstruction in three dimensions and simulate the chewing sequence, surface polygon files were exported as PLY (Stanford Triangle Format) files. The PLY files for the mandible and skull were then imported into Blender v. 2.5 (The Blender Foundation, 2011) where they were positioned as in life. The dentary condyle was placed in the glenoid fossa and the mandible was positioned with protocones of the upper molars placed in the talonid basins of the lower molars (i.e. centric occlusion). The mediolateral axis through the center of the dentary condyle acted as the center of rotation during chewing, remaining stationary in the sagittal plane. In life, synovial joint tissue is present between the bones, so the condyle was positioned with a small space between it and the glenoid fossa.

To simulate the process of occlusion, we used techniques described in Evans and Fortelius

S_harrisii_circle.avi avi [

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S_harrisii_condyle.avi avi [

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S_harrisii_teeth.avi avi [

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Four measures were taken for each specimen to quantify mandibular motion: distance of mediolateral translation by mandible (lateral translation,

Prior to analysis, lateral translation distance and ventral rotational distance were divided by glenoid fossae width, then natural log transformed. These ratios are measures of the relative amount of mandibular motion. Sagittal occlusal angle was also natural log transformed. These measures were compared between the two sampled orders for significant differences in medians using the non-parametric Mann–Whitney U test.

Tooth shape

Tooth shape was measured as the number of discrete orientation patches on the teeth in a row (OPC). This measure provides a good estimate of the complexity of a morphological surface, which corresponds to the number of orientation-delimited functional surfaces ^{4}/m_{1} and posterior, while for Dasyuromorphia the tooth row was defined as M^{1}/m_{1} and posterior. For each specimen, the occlusal surfaces of the upper and lower tooth rows were isolated and saved as vertex files. These files were converted in Surfer for Windows (Golden Software, Inc., Colorado) and custom GIS software was used to measure the OPC value of the reconstructions (Surfer Manipulator

OPCR measurements were natural log transformed prior to analysis. The relationship between upper tooth row ln(OPCR) and lower tooth row ln(OPCR) was determined using an ordinary least squares regression. Average tooth OPCR values were calculated as the tooth row OPCR value divided by the number of teeth in that tooth row, then natural log transformed.

Model comparisons

Generalized least squares (GLS) models were constructed for two hypothesis groups: upper tooth row OPCR as a response to lower tooth row OPCR and measures of mandibular motion, and lower tooth row OPCR as a response to upper tooth row OPCR and measures of mandibular motion. GLS is an extension of ordinary least squares (OLS) estimation, but allows for correlation between the predictors, an assumption of OLS

Five different models were constructed for both responses of upper and lower tooth row complexity. Each model represents a unique hypothesis of morphological factors controlling tooth shape: tooth row shape is only controlled by 1. opposing tooth row shape; 2. opposing tooth row shape and relative lateral translation (

Models were compared using the second order Akaike’s Information Criterion (AICc)

All analysis was performed in the R statistical programming environment

Results and discussion

Morphological measures

Carnivoran upper tooth row OPCR values range from 42.625 in

Comparison of natural log transformed OPCR values for sampled Carnivora and Dasyuromorphia

**Comparison of natural log transformed OPCR values for sampled Carnivora and Dasyuromorphia.** (**A**) Upper tooth row OPCR, (**B**) average upper tooth OPCR, (**C**) lower tooth row OPCR, (**D**) average lower tooth OPCR.

Dasyuromorph upper tooth row OPCR values are significantly greater than carnivoran upper tooth row OPCR values based on a Mann–Whitney U test (p < 0.0001). This is also true for lower tooth row OPCR values (p < 0.0001). Dasyuromorph average upper OPCR values are significantly greater than carnivoran upper tooth OPCR values (Mann–Whitney U = 77, p < 0.05), while average lower tooth OPCR values are not significantly different (Mann–Whitney U = 104, p > 0.2). However, in the case of average upper OPCR values,

An OLS linear regression between upper OPCR as a response to lower OPCR in our samples reveals a strong and significant relationship (^{2} = 0.92, p < 0.00001). Additionally when upper and lower tooth row OPCR values of previously sampled Carnivora ^{2} = 0.86, p < 0.00001). Additionally, parameter estimates of the slope and intercept for both linear models are within one standard error of each other. Of all 58 carnivoran and dasyurid specimens from this study and Evans et al.

Lateral translation distance varies between under a millimeter for

Similar to lateral translation distance, there is great variation in ventral rotational distance ranging from 1.236 mm for

Sagittal occlusal angles range from 14.55° for

Because of the large degree of overlap in all morphological measures, instead of considering these two orders as distinct, we will consider Carnivora and Dasyuromorphia as part of the same morphological continuum. When there are few subpopulations, small sample size, and large overlap in value means, linear mixed-effects models, which take subpopulation effects into account, are numerically equivalent to the simpler generalized least-squares method. Preliminary comparisons made between mixed-effects and GLS models showed they were numerically equivalent with no major difference in likelihood, indicating no major subpopulation effects. These results are consistent with traditional morphometric and geometric morphometric analyses of skull shape in carnivorous mammals suggest that Dasyuromorphia and Carnivora are part of a continuum of carnivorous skull shapes

This is the first study to measure dasyuromorph, and marsupial in general, OPCR values and we find that OPCR values in Carnivora and Dasyuromorphia occupy an overlapping range of values. Tooth row OPCR values are larger in dasyuromorphs than carnivorans, although average tooth complexities are nearly identical. The marginally greater median average tooth OPCR in dasyurids than carnivorans may be a product of the sampled carnivoran diversity. This also applies to our measures of mandibular motion where the marginally significant greater relative lateral translation in dasyurids than carnivorans may be a product of sampling. Increased sampling in Carnivora may also negate these findings. Current carnivoran sampling does not include more omnivorous or herbivorous species, such as bears. Jaw movement in bears is not as constrained by tooth shape as carnivorans with more blade-like teeth and our methodological focus on centric occlusion cannot be applied in less constrained systems.

Model comparisons

The best performing model of upper tooth row OPCR is a combination of lower tooth row OPCR and relative ventral rotational distance (Table

**Model No.**

**Intercept**

**lower OPCR**

**
rt
**

**
rd
**

**
a
**

**
df
**

**logLik**

**AICc**

**ΔAICc**

**Akaike weight**

Models are presented in order of relative best to worst. Shown are parameter estimates, number of parameters (

3

0.98

0.77

−0.21

5

27.73

−43.32

0.00

0.757

4

0.87

0.78

−0.04

−0.18

6

27.84

−40.58

2.75

0.192

2

0.76

0.81

−0.17

5

24.93

−37.71

5.61

0.046

1

1.37

0.79

3

19.43

−32.06

11.26

0.003

5

1.36

0.74

0.07

5

22.03

−31.92

11.41

0.003

The best model of lower tooth row complexity is upper tooth row OPCR and relative ventral rotational distance with a log-likelihood of 20.214, AICc of −28.3, and Akaike weight of 0.446 (Table

**Model No.**

**Intercept**

**upper OPCR**

**
rt
**

**
rd
**

**
a
**

**
df
**

**logLik**

**AICc**

**ΔAICc**

**Akaike weight**

Models are presented in order of relative best to worst. Shown are parameter estimates, number of parameters (

3

−0.86

1.21

0.25

5

20.21

−28.29

0.00

0.446

2

−0.26

1.11

0.24

5

19.73

−27.33

0.96

0.276

4

−0.47

1.16

0.13

0.16

6

21.21

−27.30

0.99

0.273

1

−1.23

1.17

3

12.78

−18.76

9.53

0.004

5

−1.34

1.16

0.04

5

14.48

−16.82

11.47

0.001

For both upper and lower tooth row OPCR as model responses, the numerically best performing model was the opposing tooth row OPCR and relative ventral rotational distance. However, in both cases these models do not greatly outperform the next two best models. We recommend the use of multimodel inference methodology, such as weighted parameter averaging, to take this uncertainty in parameter estimates and variance into account when making estimates from these models

For upper tooth row OPCR as response, our 95% confidence set is made up of our three best performing models. The only variables in these models are lower tooth row OPCR, relative ventral rotational distance and relative lateral translation of the mandible. Multi-model inference and parameter averaging would be best limited to just the best three models. Inclusion of the last two models in model averaging is most likely unnecessary, as they have large ΔAICc values and low Akaike weights. From the three model confidence set we find that upper tooth row OPCR decreases if lower OPCR is held constant and one of relative ventral rotational distance or relative lateral translation increases and the other is held constant (Table

There are similar results for lower tooth row OPCR as a response. The parameters in the three models of our 95% confidence set are upper tooth row OPCR, relative ventral rotational distance and relative lateral translation of the mandible. The second and third best performing models have ΔAICc values of less than 1, indicating these models are virtually identical is explaining lower tooth row OPCR. As such, the best model would be made weighted averaging of the estimated parameters of these three models. Inclusion of the final two models is unnecessary, as they both have high ΔAICc values and low Akaike weights. From the confidence set of these three models we find that lower tooth row OPCR increases if upper OPCR is held constant and one of relative ventral rotational distance or relative lateral translation increases and the other is held constant (Table

In both model selection cases, models with just OPCR or with OPCR and sagittal occlusal angle as predictors are the two worst performing models, by moderate difference in AICc values. The poor relative model support of OPCR as the sole predictor means that the best possible inference of the opposing tooth row OPCR should not be based entirely from OPCR values. Instead more complex models are advisable (see below). The poor performance of OPCR and sagittal occlusal angle is unexpected, as this value represents the angle of movement of the jaw during closing. While this angle measure is strongly correlated with both upper and lower OPCR, the use of GLS with a Gaussian spatial correlation to control for this multicollinearity leads to low likelihood models which perform worse than models including the linear measures.

Conclusions

The combination of kinetic and static measures has not previously been used in the context of integration, though represents an important part of studies of comparative anatomy

Additionally, the use of information theoretic model selection criteria also provides a method for quantifying the uncertainty between different hypotheses of constraint. Model selection uncertainty allows for better parameter and variance estimates by using weighted averages of values from the set of best models

Future analysis may wish to consider the interaction of relative lateral translation distance and relative ventral rotational distance as a predictor instead of the solely additive relationship between these two variables. This new variable is an alternative relation between the horizontal and vertical movement and may allow for a better understanding of tooth row shape. Preliminary exploratory post hoc analysis indicates the inclusion of this variable may be unnecessary, though increased sample size may recover possible tapering effects.

In conclusion, our results provide quantitative support of long-standing hypotheses of tooth row shape as being influenced by mandibular motion in addition to the opposing tooth row

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

PDS conceived the study. PDS and ARE gathered and scanned specimens. PDS measured mandibular motion. PDS conducted statistical analysis with input from ARE. PDS wrote the manuscript with input from ARE. All authors read and approved the final manuscript.

Acknowledgments

We thank NW Longmore and R O’Brien (NMV) for assistance with specimens and A Courtney for coordinating loans. PDS would like to thank G Hunt and the 2012 PBDB workshop for training in R. ARE is supported by an Australian Research Fellowship from the Australian Research Council. We would also like to thank PD Polly and an anonymous reviewer for helpful comments that improved the quality of this manuscript.