Biology Reference
In-Depth Information
digitize it and then check its error. You can always delete it if you find that the error is
biased.
In some cases, it is not that the landmarks themselves are difficult to measure but rather
that they are subject to other sources of error, some of which are biased. One potentially
important source of measurement error is preservational artifact. One study of preserva-
tional artifacts affecting the variation of landmarks of the trilobite cephalon found that
compaction of shale-preserved specimens tripled the scatter of the landmarks around their
mean positions, but not randomly ( Webster and Hughes, 1999 ). The more lateral land-
marks were most affected, as were the most convex forms. The technology used to capture
images and also to record the data can be important sources of measurement error. Even
very subtle variation in the orientation of a three-dimensional specimen can have visible
effects on the shape when it is projected onto the photographic plane. The distance
between the specimen and the camera can also be a source of measurement error; the pro-
jection of three-dimensional objects onto a plane may distort points at different
perpendicular (normal) distances from the plane, especially when the camera is too close
to the specimen ( Mullin and Taylor, 2002) . Parallax is always a concern when three-
dimensional specimens are projected onto a plane but three-dimensional measurement
systems (including computer tomography, laser scanning systems and articulating arm
digitizers) can also introduce error. One study of repeated measurements of a single
specimen (mounted in fixed position) found that the Polhemus 3Space digitizer produced
the same errors along all three axes, but the authors note that other approaches, such as
computer tomography, might differ in their resolution along the Z axis because that is the
axis on which the slices of the scan are stacked ( Corner et al., 1992 ).
At the outset of any study, as part of the process of selecting landmarks, it is a good idea
to capture multiple images of the same specimen, repositioning it between each session,
and to measure each image multiple times so that you can assess the error introduced by
the image capture and measurement process. Because the magnitude and distribution of
measurement error may be related to the size and/or shape of the specimen, it is useful to
examine several specimens that span the variety of sizes and shapes that you will be analyz-
ing. If you have more than one instrument available to use, you can also check whether they
differ in the magnitude or distribution of measurement errors. We will return to the analysis
of measurement error, more specifically, of how its various sources can be decomposed by a
multivariate analysis of variance (MANOVA) in Chapter 9. If your preliminary assessments
of measurement error suggest that variation due to measurement error is large relative to the
variation of biological interest, we recommend imaging and measuring each individual
several times so that you can use the average value as your data.
Consistency of Relative Position
The issue, in this case, is landmarks that switch their position relative to each other.
This can occur even when changes in shape appear to be very modest, such as when a
foramen near a suture is sometimes anterior and sometimes posterior to it. These two
landmarks may thus move past each other. From the anatomy, it may not look like there
is much variation in shape because the bones do not differ in their proportions, what
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