Biology Reference
In-Depth Information
A CRITICAL OVERVIEW OF MEASUREMENT THEORY
Traditionally, morphometric data were measurements of length, depth and width, such
as those shown in
Figure 1.1
, based on a scheme presented in a classic ichthyology text
(
Lagler et al., 1962
). Such a data set contains relatively little information about shape and
some of it is fairly ambiguous. These kinds of data sets contain less information than they
appear to hold because many of the measurements overlap or run in similar directions.
What may be most obvious is that several measurements radiate from a single point so
that their values cannot be completely independent; any error in locating that point affects
all of these measurements. Such a data set contains less information than could have been
collected with no greater effort because some directions are measured redundantly and
many measurements overlap. For example, there are many measurements of length along
the anteroposterior body axis and most of them cross some part of the head, whereas there
are only two measurements along the dorsoventral axis and both are of post-cranial
dimensions. In addition, because most of the measurements are long, it is difficult to local-
ize shape differences to any region, such as any change in the proportions of the pre- and
postorbital head or the position of the dorsal fin relative to the back of the head. Also,
some of the information that is missing from this type of measurement scheme, but which
is necessary for morphological analysis, concerns the spatial relationships among measure-
ments. That information might be in the descriptions of the measurements, i.e. the line
segments, but it is not captured by the data. The data consist solely of a list of observed
values of those lengths. Finally, the measurements may not sample homologous features
of the organism, making it difficult to interpret the results. For example, body depth can
be measured by a line extending between two well-defined points (e.g. the anterior base of
the dorsal fin to the anterior base of the anal fin), but it can also be measured wherever
the body is deepest, yielding a measurement of “greatest body depth” wherever that
occurs. That second measurement of depth might not be comparable anatomically from
species to species, or even from specimen to specimen, so it provides almost no useful
information (except for maximal depth). Considering these many limitations of traditional
measurements, it is clear that the number of measurements greatly overestimates the
amount of shape information that is actually collected.
FIGURE 1.1
Traditional morphometric measure-
ments of external body form of a teleost, adapted
fromtheschemein
Lagler et al., 1962
.
