Biology Reference
In-Depth Information
adding lines to show the relative positions of the landmarks early in ontogeny (dotted
lines connecting the bases of the arrows) and late in ontogeny (solid lines connecting the
tips of the arrows). Now we can see that the profile of the head is initially fairly shallow
(nearly a straight line across all three points), and becomes much steeper (particularly
between the tip of the snout and the second landmark
the one that was circled). All
three superimpositions show this same change in profile. Despite apparent discrepancies
in the displacements of individual landmarks, the relationships among the landmarks are
consistently represented. Before we can interpret the results in terms of these vectors of
relative landmark displacement, we must become accustomed to what these vectors repre-
sent. The individual vectors do not show changes at landmarks; rather, the differences
between vectors show changes between the landmarks.
GPA can yield some visually unsettling results, such as rotated axes of symmetry.
For example, in analyses of rodent skulls ( Zelditch et al., 2003 ), the coordinates of the bilat-
erally homologous landmarks on the right and left side were averaged to avoid inflating
degrees of freedom. When the results are shown by a GPA ( Figure 3.17A ), the midline of
the skull appears to rotate, but that cannot happen; the midline is the midline regardless
of variation in shape. Not only is this apparent rotation of the midline visually troubling,
it also complicates the interpretation of the results. One superimposition method that is
designed to overcome such a problem is the “Sliding Baseline Registration” ( Figure 3.17B ).
The sliding baseline registration (SBR), developed by David Sheets in collaboration
with Mark Webster ( Webster et al., 2001 ) and Keonho Kim ( Kim et al., 2002 ) reduces the
FIGURE 3.17 Superimposition of forms with an axis of symmetry ontogenetic changes in a cotton rat skull.
Dotted lines connect landmarks on the mid-sagittal axis. (A) Landmark displacements inferred from GPA which
appears to indicate translation and rotation of the midsagittal axis; (B) landmark displacements inferred from SBR,
which does not appear to suggest translation and rotation of the mid-sagittal axis; (C) landmark displacements
inferred from GPA on symmetrized and back-reflected configurations, which also does not appear to suggest transla-
tion and rotation of the mid-sagittal axis.
Search WWH ::




Custom Search