Are there periodic booms and busts in the diversity of life on Earth? Hear a tale of fossils and Fourier transforms
How to Date a Fossil
Even after dates have been assigned to the stratigraphic layers, the
lifespans of the fossil organisms are still not quite pinned down.
Consider again the genus Tellinimera. Under the GTS2004
calibration, its first appearance in the lower Campanian could have
been at any time between 83.5 and 77.05 million years ago (mya), and
its last gasp in the Danian was somewhere between 65.5 and 60.2 mya.
Depending on how the dates of origination and extinction are chosen
within those intervals, Tellinimera could have lasted for
anywhere from 11 to 23 million years.
For genera whose dates are known with the greatest
precision—to the substage level of detail—Muller and
Rohde adopt a simple convention: If a genus first appears within a
substage, they set its date of origination to the beginning of that
substage. By this rule Tellinimera is assumed to arise at
83.5 mya. Likewise a last appearance within a substage is assigned
to the end of that substage. Where the data specify only a stage
rather than a substage, Muller and Rohde follow a more complicated
policy, allocating fractions of a genus to each possible
subdivision. Thus the extinction of Tellinimera is shared
equally between the two substages of the Danian stage; half of the
genus dies out at the end of the lower Danian (62.85 mya) and half
at the end of the upper Danian (60.2 mya). For genera dated only at
the epoch or period level, an even more elaborate algorithm comes
The net effect of this procedure is to divide geologic time into a
series of nonoverlapping units, with an average duration of roughly
three million years. Although the fractional allocations spread some
events over several of these units, it is still the case that all
originations and extinctions occur at the boundaries between units.
Nothing ever happens during a substage.
The decision to locate all changes at stratum boundaries has a
plausible argument in its favor. The boundaries were defined in the
first place because they mark distinctive shifts in fossil biota,
and so originations and extinctions ought to be clustered there.
Still, it can't be true that all taxa began and ended their
existence at those selected transition moments. So I decided to try
distributing the events more evenly, a decision made in the spirit
of idle experimentation, to see whether it would have any effect on
For each genus I assigned a date of origination by selecting a
moment at random from within the whole interval in which the
earliest fossil was reported. For Tellinimera all dates in
the lower Campanian, between 83.5 and 77.05 mya, would be equally
likely. Extinction dates are chosen in the same way, by picking a
number at random within the interval of last appearance. (Special
care is needed when a genus begins and ends in the same time unit:
It must not die before it is born.)
Under this plan, the average longevity of a genus is halfway between
the minimum and the maximum possible. Moreover, the scheme has the
attractive property that greater uncertainty in the dating of a
fossil automatically translates into greater variance in the
randomly assigned dates. If all we know about a genus is that it
arose sometime in the Permian, then the randomizing procedure can
assign it any date in the 48-million-year span of that period.
The major drawback of a randomized date assignment is that it makes
the analysis nondeterministic. Every run of the program gives a
slightly different result. But the law of large numbers protects us.
Although any particular genus may be assigned quite different dates
in successive runs, the outcome averaged over all 36,000 genera is
The final step in converting Sepkoski's database into a chronicle of
biological diversity is to construct a histogram giving the number
of extant genera as a function of time. My histograms have bins 1
million years wide, so 542 bins span the interval since the start of
the Cambrian. Once the bins are set up, a program scans through the
list of genera, placing each of the 36,000 origination and
extinction events in its proper bin. Then a pass through the bins
from earliest to latest increments the number of extant genera for
each origination and decrements it for each extinction. The result
is the graph at the top of this column.
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