Quantitative Morphology
By joining biology and geometry, morphometric methods enable us to study form in three dimensions. In its broadest sense, morphometrics refers to any method that analyzes quantitative morphological variables using statistical techniques. Morphometric methods are applied to determine how samples of forms differ from one another, how they are similar, and how forms change during time as the result of a particular biological process (e.g., methylation, growth, evolution). The data sets analyzed by these methods are measures of morphology at nearly any scale from the molecular to the organismal. Three dimensional landmark data as well as the measures that derive from them (linear distances, angles, and volumes) can be collected directly from biological forms or from images of those forms.
3D Imaging
3D imaging techniques enable a quantitative 3D representation of any phenotype of interest. Images provide the following advantages over direct measurement of biological objects: 1) the image is a stable representation of a moveable object in a single coordinate system making measurement easier; 2) 3D reconstruction of images enable visualization of surfaces not typically visible (e.g., interior of bones); 3) images can be archived and data can be collected at a later time. In our particular application we use medical computed tomography (CT) to image baboon skulls and high resolution or micro-CT to image mouse skulls. Various software packages are available for creating 3D reconstructions of these images in order to visualize the skulls and measure dimensions of interest. Other imaging modalities useful to the quantitative study of craniofacial phenotypes include magnetic resonance imaging of soft tissue structure (e.g. muscle, brain) and photogrammetry that provides 3D surface information (e.g. skin surface).
Methods
Geometric morphometrics are methods that most usually use 3D coordinates of biological landmarks (Note: the linked page contains Java Applets) to quantify the similarities and differences between forms. In this study we are using 3D landmark data taken from baboon and mouse skulls for which we have genetic information to determine the phenotype-genotype relationships responsible for craniofacial variation, development and evolution. Figure 1 shows the 3D skull landmarks used in this study for both baboons and mice.
Figure 1. Example of 3D skull landmarks shown as red dots on CT images of baboons (upper row) and mice (lower row). Landmarks are shown from the front (far left), the right side (second from left), the base or bottom of the skull (second from right), and from inside the skull looking from the top (far right).
From these landmarks we can derive different measurements by calculating linear distances, volumes and angles. Multivariate statistics or morphometric methods can then be applied to these 3D coordinates or linear measurements to study the shape and shape variation in these baboon and mouse populations. These morphometric analyses enable us to define anatomical axes of variation within the skull and to identify how specific skull features vary along those axes. Coupling these phenotypic measures with genetic information (see Genetics) allows us to identify the potential genes and associated pathways that underlie the craniofacial shape variation observed in our samples. We will use similar morphometric techniques to study shape variation in fossil human and papionin skulls using the information gained from the baboon and mouse models as a basis of comparison. Including fossil specimens provides a gateway for determining the timing and order of major genetic and phenotypic changes in human craniofacial evolution.
Preliminary Results
We have collected 3D landmark data from medical CT scans of 432 baboons (127 males, 300 females) from the Southwest Foundation for Biomedical Research. We have begun to analyze these data using various geometric morphometric and statistical methods focusing first on sexual dimorphism of craniofacial shape differences in this population. Craniofacial form differences between the sexes are greatest for traits of the muzzle, with male faces that are longer and greater in height than females (Figure 2).
Figure 2. Distances with the greatest absolute EDMA difference between males and females. All distances were greater in males than in females. Note that form differences for males and females are greatest within the muzzle. Dotted lines indicate distances that traverse through bone.
While all distances were larger in males than in females for unscaled measurements, differences in relative size arise when the distances were scaled by the geometric mean. These shape measures show again that males have relatively larger muzzles than females (Figure 3), but females have relatively larger measures within the base of the skull compared to males (Figure 4).
Figure 3. Distances that are relatively larger in males than in females when distances are scaled by the geometric mean. Note that males have relatively larger muzzles than females. Dotted lines indicate distances that traverse through the bone.
Figure 4. Distances that are relatively larger in females than in males when data are scaled by the geometric mean. For their size, females tend to have relatively larger distances that join the upper face with the base of the skull as well as larger basicrania. Dotted lines indicate distances that traverse through the bone.
Contrary to the differences observed for skull form and shape between the sexes, phenotypic variation is not different between males and females and the structure or pattern of variation is similar between the sexes. Specifically, male and female skulls appear to be morphologically integrated similarly in that measures within the face, measures within the basicranium, and hafting measures between the basicranium and the face are more highly correlated within each region than with between regions (Figure 5 shows the division of the skull into these integrated units).
Figure 5. Illustration of the integrated bony elements in these baboon skulls. Facial structures (red), neurocranial structures (blue), and distances that haft the facial skeleton onto the neurocranium (green) were more highly correlated with themselves than with structures from other regions.
For both sexes, hafting measurements were the most highly correlated and measures within the basicranium were negatively correlated with each other (Figure 6).
Figure 6. Results from correlation matrices of male and female distance data with hypothetical matrices for the face, basicranium and hafting distances. Hypothetical matrices assume a correlation of 1 for distances within a morphological unit (in this case, the face, basicranium or hafting distances that connect the face to the basicranium). Male and female correlation matrices of our measured distance data were compared with these hypothetical matrices using Mantel’s tests. Note that males and females have similar patterns of integration within the skull and that hafting distances were the most highly correlated and therefore most integrated.
These preliminary results indicate that male and female baboons differ in craniofacial shape, but the phenotypic variation of shape and the structure of that variation are similar between the sexes.