Spatial packing, cranial base angulation, and craniofacial shape variation in the mammalian skull: testing a new model using mice

Abstract

The hypothesis that variation in craniofacial shape within and among species is influenced by spatial packing has a long history in comparative anatomy, particularly in terms of primates. This study develops and tests three alternative models of spatial packing to address how and to what extent the cranial base angle is influenced by variation in brain and facial size. The models are tested using mouse strains with different mutations affecting craniofacial growth. Although mice have distinctive crania with small brains, long faces, and retroflexed cranial bases, the results of the study indicate that the mouse cranial base flexes to accommodate larger brain size relative to cranial base length. In addition, the mouse cranial base also extends, but to a lesser degree, to accommodate larger face size relative to cranial base length. In addition, interactions between brain size, face size, and the widths and lengths of the components of the cranial base account for a large percentage of variation in cranial base angle. The results illustrate the degree to which the cranial base is centrally embedded within the covariation structure of the craniofacial complex as a whole.

Fig. 1

Midsagittal sections through human (H. sapiens), pygmy chimpanzee (Pan paniscus), and mouse (Mus musculus) crania showing differences in orientation between prechordal and postchordal cranial base (CBA1). Note that the mouse is retroflexed (CBA1 is greater than 180°). See text for landmark details.

Fig. 2

Models of spatial packing. A simple two-dimensional packing model in which a larger brain in B compared with A is accommodated by a more flexed cranial base. The more complex three-dimensional model, C, considers that cranial base in terms of the anterior, middle and posterior cranial fossae (ACF, MCF and PCF), each of which has its own length and width. The brain and neurocranium grow above and laterally from the ACF, MCF and PCF. The face grows inferiorly, anterior and laterally from just the ACF and MCF. See text for further details of the models.

Fig. 3

PCA analysis of variation for PCs 1 and 2 for entire sample (following Procrustes superimposition).

Fig. 4

Landmarks used. For further details on landmarks, see Hallgrimsson et al. (2007).

Fig. 5

Regression of basicranial angle (CBA) against the index of relative encephalization (IRE, endocranial volume^0.33/cranial base length) and the index of relative facial (IFL, face length/anterior cranial base length) at the individual and strain levels.

Fig. 6

Results of randomization analyses. Top, angles with higher correlation to CBA generated by 1000 randomized angles within sample. Note that almost all these angles are cranial base. Bottom, random sets of 12 interlandmark distances that explain a higher percentage of CBA in the constrained spatial packing model Note that most of these distances relate to the length of the cranial base.

Fig. 7

Analyses of Mceph (more encephalized) mutants vs. wild types. A, CBA vs. IRE; B, CBA vs. IFL; C, comparison of means.

Fig. 8

Analyses of brachymorph (shorter cranial bases) mutants versus wild types. A, CBA vs. IRE; B, CBA vs. IFL; C, comparison of means.

Fig. 9

Analyses of pten mutants (longer anterior and shorter posterior cranial base lengths) vs. wild types. A, CBA vs. IRE; B, CBA vs. IFL; C, comparison of means.