Paleobiology, 4(2), 1978, pp. 201-202
A test for evolutionary equilibrium revisited
Graham A. Mark, Department of Ecology and
Evolution, State University of New York at
Stony Brook, Stony Brook, New York 11794
Karl W. Flessa, Department of Geosciences,
University of Arizona, Tucson, Arizona
85721
Accepted: February 2,1978
Cowen and Stockton (1978) seem to agree
with one of our main conclusions (Mark and
Flessa 1977, p. 21): "Problems of ecological
classification, taxonomic consistency and temporal and geographic scale need resolution
before evolutionary equilibrium models can be
more than heuristic." Their discussion points
out other difficulties with hypotheses of evolutionary equilibrium and with tests for their
validity.
How much observed fluctuation is consistent
with the notion of "equilibrium"? We tried
to avoid this problem in our particular test.
Our version of "the" equilibrium hypothesis
postulated that "within biologically coherent
regions and during times of relatively uniform
environmental conditions, the number of taxa
is usually constant" (Mark and Flessa 1977,
p. 18). We stated the hypothesis this narrowly
because we hoped to distinguish it conceptually from qualitatively different models,
especially those picturing unlimited diversity
and those in which diversity fluctuates unsystematically. To expect exact constancy is
surely unreasonable, as Cowen and Stockton
correctly insist and, in fact, our test was not
this narrow. We tested for positive correlation,
not for equality, because we were unwilling to
specify just how constant an equilibrium must
be.
On a more technical level, Cowen and Stockton claim that the correlations that we found
were methodological artifacts. As a point of
formal statistical method, their "low number
effect" is real enough. Their use of it to criticize our analysis, however, is misdirected.
© 1978 The Paleontological Society. All rights reserved.
Their error stems from their confusion of
standing crop and turnover rates.
We generated our sets of "net" originations
and extinctions by eliminating short-ranging
genera from consideration. Consequently, as
Cowen and Stockton note, if our results indicate low diversity (as is the case throughout
the Mesozoic and Cenozoic), then correspondingly low levels of "net" originations and extinctions (low turnover) are also necessary.
Note, however, that actually existing low diversity does not require low turnover; low diversity can be maintained by high turnover if
the taxa are short-ranging. Eliminating the
short-ranging brachiopod genera prevented us
from detecting high turnover in low diversity
situations. We used this method anyway because, as we pointed out (p. 20), "By including
genera which arose and vanished within the
same time interval, the correlation of origination and extinction will increase, but this inflated correlation is not a consequence of a
true evolutionary equilibrium among different
genera." Evidently, an analysis of either gross
or net data sets will produce unwanted biases.
Cowen and Stockton incorrectly assume
that high diversity (as in the Paleozoic) requires high turnover rates. But in fact, in
either net or gross data sets, high diversity
can be maintained by low levels of originations
and extinctions (low turnover) provided the
taxa are long-ranging. Thus, although intervals characterized by low diversity are artificially constrained to show low turnover, intervals of high diversity are not required to
have high turnover. Cowen and Stockton's
attempts to discredit the other correlations that
we found are similarly incorrect.
Our present intention is not, however, to
defend the statistical or evolutionary importance of a correlation that explains, at best,
only 16% of the variation in extinctions and
originations. We are content to conclude that
our test failed to find substantial evidence for
evolutionary equilibria. Although Cowen and
0094-8873/78/0402-0009/$1.00
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202
MARK & FLESSA
Stockton are concerned that our test was "so
narrow that the predictions . . . [we] . . . made
from it are denied" (p. 199), we caution
against granting the hypothesis of an evolutionary equilibrium such flexibility that it is
immune to contrary evidence.
Literature Cited
C O W E N , R. AND W. L. STOCKTON.
evolutionary equilibria.
1978.
Testing for
Paleobiology. 4:195-200.
MARK, G. A. AND K. W . FLESSA.
1977.
A test for
evolutionary equilibria: Phanerozoic brachiopods
and Cenozoic mammals. Paleobiology. 3:17-22.
S T U D E N T CONTEST
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