Draft by Clark Chapman of a Letter or Technical Comment for Science magazine:
Comment on Ward et al.'s Paper on
"Abrupt and Gradual Extinction..." in the Late Permian
There is a body of suggestive, but inconclusive, evidence that the Permian-Triassic (P-T)
boundary and associated mass extinction occurred suddenly (1), as would be plausible if it were due
to impact of an asteroid or comet, as is known to be the case for the Cretaceous-Tertiary (K-T)
boundary. Ward et al. (2) draw two important conclusions concerning extinctions and origination of
new species associated with the P-T boundary, both of which — if true — would tend to contradict
the impact hypothesis. First, while acknowledging that some species went extinct suddenly at the
boundary, they argue that others died out gradually before the boundary. Second, they argue that "it is
probable that at least some species originated" before the boundary. We believe that neither
conclusion is supported by the data they present.
Ward et al. carefully define a zero-level (Level A in their Fig. 3, also called "base of Unit II”),
which is a plausible level to assign to a hypothetical sudden P-T mass extinction. In what follows, we
accept exactly Ward et al.’s correlation of time horizons across different unit, as well as their
assignments of found fossils to specific taxa, although a complete statistical analysis would have to
consider uncertainties in these phases of the research, as well. We ask whether the vertical
distribution of collected fossils plotted by Ward et al. plausibly negates, or renders unlikely, the
hypothetical sudden mass extinction. They collected 126 skulls assigned to 21 vertebrate taxa, which
we refer to numerically from left-to-right as depicted in their Fig. 3. In this figure, they plot "errorbars", which are not formally defined. They are not what they appear to be (statistical limits on when
each of the taxa went extinct or originated) but instead have an arcane, non-intuitive meaning (3);
plausible ranges for extinction extend far above the “error bars” for taxa 1-13, for example.
The entire case for gradual extinction rests on the vertical distributions, with respect to the
zero-line, of at most 16 skulls representing taxa 1-6. Ward et al. mostly rely on just 9 skulls
representing taxa 1, 2, and 3. These three taxa are the ones about which they express confidence that
they went extinct below (before) the zero-level. Taxa 4-6 (based on minimal data) are those
acknowledged by Ward et al. as going extinct “at or near” the zero-level. As for the remaining 15
taxa, the data are wholly consistent with these interpretations: taxa 7, 8, and possibly 10 (the latter is
represented by only a single skull) went extinct essentially at the zero-level; 9, 11, 12, and perhaps 13
made it through the zero-level, but went extinct later, often considerably later; and taxa 14-21
originated above (after) the zero-level, which is consistent with the idea that empty ecological niches
(due to the mass extinction) fostered speciation (below we discuss Ward et al.'s second conclusion
that some taxa among numbers 14-21 originated below the zero-level).
Taxa 1-3 are those for which the uppermost skull was found 10 or more meters below the
zero-level. (Here we exclude taxon 5, which is represented by a single skull, about 26 m below the
zero-level: who can tell, from a single example, when this species originated or became extinct,
although Ward et al. inexplicably plot an “error bar” (confidence interval) about 25 m above the
height of the single fossil [3].) Although Ward et al. do not state the lower-level of sampling, we take
it to be at -60 m, based on the distribution for the abundant taxon 7. The 9 skulls are distributed
vertically as shown in column 0 of Fig. 1. The case for gradual extinction before the boundary rests
solely on whether there is a statistically convincing tendency for the skulls in these three taxa to be
missing as the zero-level is approached. Columns 1-10 show ten random distributions for 9 items
distributed between 0 and 60. No formal statistics on just 9 data points are necessary to see that there
is no robust case for a gradual extinction. Three of the ten random trials show an even stronger
avoidance of the zero-level than the actual data (the data even avoid the -60 m level more than do 9 of
the 10 trials). Thus, the data are wholly consistent with the hypothesis that taxa 1-8 and 10 went
extinct at the boundary. (Taxon 1, taken alone, is actually indeterminate. It is represented by 2
skulls, found at almost exactly the same height, about -52 m; as with taxa 5 and 10, such data provide
no evidence about origination or extinction, though Ward et al. plot an extinction confidence interval
at -50 m, just 2 m above the location of the only two skulls representing that taxon!)
We now briefly discuss the second major conclusion of Ward et al., namely that it is probable
that "some" species originated below (before) the zero-level. For these taxa (14-21), not a single
skull is located below the zero-level. Indeed, the one closest to the zero-level is 10 m above it. As a
test of the hypothesis of a sudden extinction, in which a sudden radiation (origination) of new species
must occur afterwards, to fill the ecological niches left by the species rendered extinct, we assert that
there must be a skull identified below the zero-level to negate the hypothesis. The height
distributions above the zero-level may be predictive of the probable extent below the zero-level only
in the case where nothing has changed in earlier times (3); it is certainly allowed that the data are
consistent with a more complex history. But in no way do the data make it "probable" that the
hypothesis of a sudden extinction is wrong. It is simply a non sequitur. Any non-randomness in the
height distributions of taxa 14-21 above the zero-level cannot logically predict anything about
whether a dramatic event happened below the first skull; any such non-randomness may well reflect
real changes in the ecological environment in this particular South African environment, or sampling
biases.
We wish to comment on two other matters relevant to these widely publicized conclusions. In
many sciences, three-sigma confidence levels are adopted as the standard of proof. Logically,
anything less than fifty-fifty chance is unproven. Simple examination of Ward et al.'s Fig. 3 shows
that their "error-bars" typically extend beyond the last datum by less than the average distances
between the data for the taxon in question. In any "confident" interpretation of when a taxon goes
extinct (quoting the authors), an error bar should extend beyond the 1-, 2-, or 3-sigma levels, which
are far beyond the plotted 20% confidence “error bars”. Ward et al.'s Table 1 presents similarly
dubious numerical estimates of "confidence". They ascribe a "confidence" of 0.875 (three significant
figures!) to the extinction of taxon 1, which (as mentioned above) is represented by only 2 skulls,
both located at essentially the same height. There is simply no probative value in estimating
origination or extinction of a taxon represented by just 2 skulls at the same height, let alone to 2 or 3
significant figures. And this taxon is the only one to which Ward et al. attribute a confidence of early
extinction significantly greater than 0.5. Fig. 1 and common sense, as opposed to any number of
formal statistical tests of just 9 data points, tell us that there is no basis for ruling out an abrupt mass
extinction at the zero-level or for favoring a gradual component to the extinctions.
In view of the profound implications of the Ward et al. conclusions, namely that the greatest
known mass extinction could not have been caused alone by an asteroid impact, we emphasize
another factor — minimally acknowledged by Ward et al. but which may dominate these statistics of
hard-won, in-the-field collections of skulls. Unlike marine fossils, which may be representative of
oceans world-wide, the presence of fossils in a terrestrial locality — in this case the Karoo in South
Africa — may not represent anything more than the evolving ecology of that particular region. That
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several skulls of one taxon are found at one level but not at a later level may merely reflect that
environmental or other ecological circumstances forced the migration of that species to some other
part of Pangea. It may, but certainly does not necessarily, imply extinction.
Therefore, the minimal or absent statistical significance for gradual extinction is rendered
even more dubious by the fact that any perceived hint of declining representation of skulls below the
zero-level might as well be explained by local circumstances in the Karoo, rather than any
hypothetical causes of global extinctions. It must not be forgotten that, based on astronomical
evidence, the impact of one or more asteroids or comets larger than the K-T boundary extinctor is
statistically likely in the past 0.5 Gyr (4), and the Earth can hardly have avoided the inevitable and
horrific environmental consequences that would have resulted (5). Thus, in the absence of any
countervailing evidence or alternatively energetic and sudden modifier of the ecology, the
presumption must be in favor of the inevitable asteroid or comet impacts to explain mass extinctions,
unless proven to be false. Ward et al. have not met that standard.
References
1. D. H. Erwin, S.A. Bowring & J. Yugan 2002. End-Permian mass extinctions: A review. In
Catastrophic Events and Mass Extinctions: Impacts and Beyond (ed. C. Koeberl & K.G. MacLeod),
Special Paper 356 (U.S. Geological Survey), 363-383.
2. P.D. Ward, J. Botha, R. Buick, M.O. De Kock, D.H. Erwin, G.H. Garrison, J.L. Kirschvink & R.
Smith 2005. Abrupt and gradual extinction among late Permian land vertebrates in the Karoo Basin,
South Africa. Science 307, 709-714.
3. S.C. Wang & C.R. Marshall 2004. Improved confidence intervals for estimating the position of a
mass extinction boundary. Paleobiology 30, 5-18. This paper, and others cited therein, define
mathematical approaches to interpreting fossil heights in a uniformly sampled stratigraphic sequence.
We believe that these procedures have been misused by Ward et al. in several ways. For example,
what appear to be “error bars” in their Fig. 3 actually represent the range of 20% confidence; there is
an 80% chance that the range extends beyond the plotted “error bar”. From the formalism in Wang &
Marshall, it should not be possible to plot such confidence intervals for taxa like 5 and 10, which are
based on just one fossil find, since the formula involves a division by (H-1) where H is the number of
fossils. The plotting of a 90% confidence interval for the extinction level in Ward et al.’s Fig. 3
cannot be right; the claim is that the calculations are for “the nine taxa,” (presumably those with last
occurrences at or below the zero-level, although C values are tabulated for 12 taxa in Table 1,
including several that extend well above the zero-level), but only 7 have 2 or more occurrences,
required for calculating confidence. And, according to Table 3 of Wang & Marshall, treatment of 7
(or even 9!) taxa requires use of confidence levels appreciably greater than the 20% used. Moreover,
Wang & Marshall are clear that their methodology for estimating the extinction level applies only if
all taxa are known to have gone extinct at that horizon; Ward et al.’s belief that at least 3 taxa went
extinct “gradually”, beforehand, would invalidate that assumption. Actually, many of Wang &
Marshall’s simulations graphically show apparent “gradual” extinctions, even though all taxa in their
simulations are defined to have gone extinct simultaneously. Application of Wang & Marshall’s
method to disproving an hypothesized origination horizon violates the stated assumption that “fossil
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horizons [must] be distributed independently and uniformly throughout the taxon’s stratigraphic
range;” the distribution can hardly extend “uniformly” below the assumed horizon.
4. C.R. Chapman 2002. Impact lethality and risks in today's world: Lessons for interpreting Earth
history. In Catastrophic Events and Mass Extinctions: Impacts and Beyond (ed. C. Koeberl & K.G.
MacLeod), Special Paper 356 (U.S. Geological Survey), 7-19.
5. O.B. Toon, K. Zahnle, D. Morrison, R.P. Turco & C. Covey 1997. Environmental perturbations
caused by the impacts of asteroids and comets. Revs. Geophysics 35, 41-78.
3 March 2005
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Figure 1. The dotted line represents the zero-level of Ward et al., which we hypothesize to be the
time of an abrupt mass extinction. Trial 0 shows the actual data of Ward et al., representing the
locations of 9 skulls representing the three taxa about which Ward et al. express confidence of
extinction well below the zero-level. Trials 1-10 represent random selections of 9 integers between 0
and -60. Trials 1 and 8 seem to show much more dramatic avoidance of the zero-level than do the
actual data, but they are as likely to result from random chance as trials 5 and 7, which closely
approach the zero-level.
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