Evolution__3rd_Edition

478 PART 4 / Evolution and Diversity
Different cluster statistics can give
different hierarchies
Phenetic classification is inherently
ambiguous
If we measured a third character, such as pulse interval between the sounds in the
courtship song, it could be drawn as a third dimension into the paper; now each species
would be represented by a point in the three-dimensional space. The aggregate distance
between the species could be measured as before by the distance between the species’
points. We could likewise measure dozens of characters and measure the distance
between the species by the appropriate line through hyperspace. Numerical taxonomists
recommend measuring as many characters as possible a even hundreds a and
classifying according to the aggregate similarity for all of them. The more characters
that are measured, the more likely it is that peculiar individual characters will be averaged
out, and the classification will be better founded.
Is a numerical phenetic classification objective or subjective? Objective classifications,
remember, must represent some unambiguous property of nature. The phenetic
classification itself represents the measure of aggregate morphological similarity for
large numbers of characters. The question, then, is whether there is some property of
nature, some hierarchy of “real” phenetic similarity, that the measurements of aggregate
morphological similarity may reasonably be said to be representing. (This topic is
discussed in a related way in Section 13.5, p. 363.)
We can start by looking more closely at the statistical methods used in numerical taxonomy.
In Figure 16.2 there were five species with two characters. To form Figure
16.2a, we grouped each species with its phenetically nearest neighbor. Two clusters a of
species 1–2 and 4–5 a immediately formed. But to which of these clusters should we
join species 3? The nearest species is 2. If we join species 3 to the cluster with the nearest
neighbor we put it with cluster A (the nearest neighbor to species 3 in cluster A is
species 2, whereas in cluster B it is species 4 and 5 equally) (Figure 16.2b). However, if
we had calculated the average distance of each cluster as a whole, the answer is the
opposite (Figure 16.2c). The geometry of Figure 16.2 is such that cluster B rather than
cluster A has the nearer average neighbor to species 3.
The nearest neighbor and average neighbor methods are both examples of cluster
statistics. They are not the only ones, but they are enough to make a point of principle.
We have here, within the phenetic philosophy, managed to produce two different
classifications. If the numerical phenetic claim to repeatability and stability is to be
upheld, it must have some way of deciding which of the two is the correct phenetic
classification. To do so, it would need some higher criterion to fall back on. The problem
is it does not have one. The higher criterion would presumably be “the” hierarchy
of aggregate morphological similarity, but that hierarchy does not exist in nature
independently of the statistics that measure it. And a as Figure 16.2 shows a different
statistics produce different hierarchies.
So there is an essential degree of subjectivity in the phenetic philosophy. If its
classifications are to be consistent, it must pick on one statistic, such as the average
neighbor statistic, and stick to it. Classification would then be repeatable, but at a price.
The consistency does not follow from the phenetic system itself; it is imposed by the
taxonomist a subjectively. In practice, numerical taxonomists have never been able to
agree on which statistic to use, and this is one reason why the school has lost much of its
influence since its origin in the early 1960s.
Moreover, the choice of cluster statistic is not the only subjective choice in phenetic
classification. The measurement of distance poses an analogous problem. The measure
..