858 THE STRUCTURE OF EVOLUTIONARY THEORY
the standard stratigraphic study). In an initial study of rank correlations between
stratigraphic position and values of unit characters at a standard shell length
estimated from bivariate regressions, she found no directional change for 82
percent of characters within species of 8 lineages. Of the 18 percent showing
significant rank correlations with time, most directional changes either become
reversed later in the same sequence, or run in a direction opposite to the net
transformation between the measured species and its descendant. In other words,
such changes, however genuine, should be read either as mild fluctuations within a
pattern of stasis, or as intraspecific temporal variation unrelated to the trend of the
larger lineage. For example, shells of the bivalve Lucina anodonta become
gradually less inflated from the Calvert into the overlying Choptank Formation.
But the same species then regains its ancestral degree of inflation in the succeeding
St. Mary's Formation (p. 587). Kelley (1983, p. 596) concluded with both
substantive and methodological comments: "Within these middle Miocene mollusc
species, then, changes are more commonly oscillatory than unidirectional... Most
variables follow a pattern of fluctuation within a narrow range of values through
time ... In order to approach the goal of unbiased assessment of entire faunas, I
examined all taxa of the mollusc faunas which were abundant enough for statistical
analysis. Because no other bias controls the taxa chosen for study, these data
provide strong evidence for punctuated equilibria."
Kelley's subsequent study (1984) affirms these patterns from a multivariate
perspective based on discriminant analysis of 10 characters through 14 to 20
stratigraphic levels. Figure 9-23 (from Kelley, 1984, p. 1247) shows the
stratigraphic distribution of centroids for each lineage at each level, as projected
upon the first discriminant axis. Stasis prevails within most species (shown as
unbroken vertical plots), while the four lineages composed of two or more
successional species through the sequence generally show a stairstep pattern across
transitions, and stasis within the bounds of species. In a very few cases, notably the
transition from the lower to the middle species of Anadara, a trend within an
ancestral species does move gradually towards the descendant's mean value. But
even in this case, the third and uppermost species of the lineage then reverses the
trend and moves back towards the beginning value.
Kelley (1984) also used patterns of misclassification for individual specimens
to illustrate the character of predominant stasis. In the three successive species of
Astarte, for example, 96.7 percent of specimens fall nearest the centroid of their
own species—thus indicating sharp and clear division between successive species.
But variation within species showed the opposite pattern. Only 42.1 percent of
specimens fell nearest the centroid for their own stratigraphic level. Most
remarkably, only 36.7 percent of misidentified specimens fall closest to centroids
for samples of either the same or an immediately adjacent stratigraphic level. In
other words, nearly % of misidentified specimens stood closer to the centroids of
stratigraphically distant populations than to the centroids for samples adjacent to
their own time. This pattern of nondirectional