Biology Reference
In-Depth Information
which is one of the most visually obvious ontogenetic changes in shape. Because we do
not want to sacrifice that information, we place points marking the anterior and posterior
boundaries of the structure. In effect, to obtain that information, we sample the same geo-
metric points in all specimens. In other cases, we cannot sample complex curves that lack
landmarks, as exemplified by the jaw (see
Figure 2.1C
). Thus, to obtain adequate coverage
of the form, we sample those curves with semilandmarks (see
Figure 2.1D
).
Repeatability
The third criterion for selecting landmarks is that they can be found reliably. If they
are difficult to locate even on the same specimen measured multiple times, they can
induce measurement error. Sometimes, these difficult points are easy to recognize even
before digitizing them; for example, the landmarks on the mandibular notches mentioned
above (see
Figure 2.3
). These landmarks are difficult to locate reliably for two reasons:
first, the landmarks are defined in terms of a change in curvature along curves that change
curvature more than once, so finding the landmarks requires assessing curvature by eye,
and recognizing which particular changes in curvature are the ones to digitize. Second,
the curvature (and where it changes) varies among individuals of the same species and
sometimes even between the two sides of the same individual. In the case of landmarks
such as these, the definition of the landmark may migrate over the course of digitizing
many specimens
the precise point that is recognized as the right change in curvature
may differ between the first and hundredth specimen digitized. Sometimes, the reliability
of a landmark is not so easily anticipated in advance of measurement. For example, some
points seem as though they ought to be difficult to find repeatedly, such as the anterior
and posterior points on the piranha eye, but they may actually be less prone to error than
points that are more discrete and well defined. Also, points that seem very fuzzy (such as
blurs on x-rays) can sometimes be more reliable than you might imagine. In the case of
landmarks that are obviously difficult to locate, such as those points on the mandibular
notches, it is important to check and recheck your digitizing, going back to the beginning
of the file and scrolling through to see if the definition of the landmark migrated. But for
others,
it may be best
to avoid prejudging them, and checking their repeatability
empirically.
Some landmarks are prone to measurement error in only one dimension because the
landmark is easy to locate along an axis, e.g. the anteroposterior axis, but difficult to locate
along another. This ambiguity along one direction can be a real problem for points that
might otherwise be well defined, such as those on a suture. Sutures that generally follow
a body axis sometimes wander, taking a complex path. It may be easy to pin down the
anteroposterior location of a point along the suture, but more difficult to decide its medio-
lateral position. When a landmark is difficult to find in only one direction, the error will
be concentrated in that direction, inducing biased rather than random error. Biased error
is a more serious problem than a large random error because biased error will look like
something that merits an explanation. However, the difficulty that you perceive in the
course of digitizing may not be reflected in the actual variability of the point. At the outset
of the analysis, before deciding that a point is unrepeatable in one or both directions,
