Biology Reference
In-Depth Information
majority of this chapter focuses on this issue because understanding
why
a method fails is
as important as realizing that it does fail, particularly when the aim is to avoid making the
same kind of mistake again. Thus, we have kept this chapter in the second edition primar-
ily to make a stronger and clearer argument against the use of this and related methods
(see also Adams and Rosenberg, 1998; Rohlf, 1998; Adams et al., 2011).
TAXONOMIC DISCRIMINATION
The fundamental taxonomic question can be divided into two parts:
1.
Are the samples different enough to warrant judging them to be different species?
2.
In what do they differ?
(For the sake of simplicity, we focus on discriminating between species; however, com-
parable challenges may arise at any level of the taxonomic hierarchy.) To answer the first
part of the question, one must decide what would be “different enough”. Having stated
that criterion, it is possible to ask whether the data meet it. For example, “different
enough” might be that no more than 2% of the specimens are misclassified, or that the
means of the samples differ statistically significantly, or even that the Procrustes distance
between the means is minimally 0.03 (or any other favored value). Choosing a criterion
also determines which method will tell if the data meet it, which could be MANOVA,
CVA, computing Procrustes distances between means, or other valid method of evaluating
the difference between species.
The more difficult decisions that need to be made concern the handling of the various
potential sources of within-group variation, including geographic variation, ontogeny, and
sexual dimorphism. Any of these factors could complicate distinguishing species.
Obviously, you do not want to claim to have evidence for two species when the samples
differ only in average developmental age or body size. If that might be the case, it would
be useful to design the sampling scheme to ensure that the samples are homogeneous and
comparable, or else to standardize the data to a common age or size using regression. The
results can be very different. For example, Figure 13.1 shows results from three analyses:
(1) samples are compared without standardizing by ontogenetic stage (Figure 13.1A); (2)
samples are compared at a common juvenile stage (Figure 13.1B); and (3) samples are
compared at a common adult stage (Figure 13.1C). In all three analyses, all eight CVs are
significant and, with one exception (the unstandardized data), the misclassification rate
is extremely low. For the unstandardized data, out of 390 specimens as many as 12 are
misclassified, all of which are
Pygocentrus nattereri
that are classified either as
P. cariba
or
P. piraya
. However, for both standardized data sets no more than four individuals are mis-
classified (also
P. nattereri
). Not surprisingly, all species differ from all others significantly
(in all pairwise comparisons,
P
0
.
002). In general, species differ by a Procrustes distance
of more than 0.030, except for the three
Pygocentrus
, whose adults differ from each other
by Procrustes distances as small as 0.027
,
0.028 (and by even less in comparisons of
unstandardized specimens). Thus, the same conclusion would be drawn from all three
analyses about the taxonomic status of these samples, but the results still differ because
the variables discriminating among the species are different.
