Biology Reference
In-Depth Information
FIGURE 2.6
Landmarks on a mouse mandible.
(A) Schematic showing the locations of landmarks; (B) two
measurements defined by Type 3 landmarks (represented
as asterisks). (After Atchley et al., 1985. Genetics of mandibu-
lar form in the mouse.)
the mouse mandible (
Atchley et al., 1985
). One of the measurements is the length of the angu-
lar process, which is the Euclidean distance of a line segment that extends from the midpoint
of a line extending from landmarks 1 and 2, to the midpoint of a line extending from land-
marks 3 to 19. These midpoints, shown as asterisks in
Figure 2.6B
are Type 3 landmarks.
Another measurement is of the incisive process, which is defined as the shortest distance
from landmark 8 to a line extending from landmarks 4 to 6. The point at which those two lines
intersect is also a Type 3 landmark. Type 2 landmarks are intermediate between these
extremes. They are locally defined, but not as locally as Type 1 landmarks, and they often
refer to geometric constructs, but these constructs are the tip of a structure, a bulge, or local
maxima or minima of curvature. All but two of the landmarks shown on the mandible are
Type 2 (the exceptions are the landmark at the emergence of the incisor from the alveolar
bone, and the point on the intersection between the posterior of the articulating surface of the
condyle and the condylar process, although both of these could be regarded as Type 2 land-
marks because their position depends, at least in part, on the orientation of the specimen.
As well as ranking these types according to the localization of their definining criteria,
Bookstein (1991, pp. 64
66)
also distinguishes them according to their explanatory role.
In his view, Type 1 landmarks can enter into familiar valid functional explanations, more
specifically, the accounts of a deformation, such as conservation or optimization of bio-
mechanical strength or stiffness under loading, or conservation of enclosing structures
under changes in their content. Type 1 landmarks allow you to identify directions of forces
that impinge on a structure, or to recognize the effects of processes moving the landmarks,
being surrounded by tissue on all sides. Type 2 landmarks lack information from sur-
rounding tissues in at least one direction. These are often the points at which forces are
applied but, in the absence of information from at least one direction, it is not possible to
distinguish displacements lateral to the boundary direction from a combination of inward
and outward displacements. Type 3 may not be meaningful as landmarks and their
