Evolution__3rd_Edition

656 PART 5 / Macroevolution
Extinction rates could show a
continuous or a two-peaked
distribution
In fact, they look fairly continuous
...
. . . and may fit a power law
Mass extinctions may not have
distinct causes
p per time unit. Then, many time intervals have a small number of species going extinct,
and a few have many species going extinct. (Because if the chance that one goes extinct
is p, the chance that two go extinct is p 2 , the chance that three go extinct is p 3 and so on.)
The different extinction rates observed at different times are simply due to chance effects.
Alternatively, mass extinctions could be a distinct kind of event, with a distinct kind
of cause from extinctions at other times. Then the extinction rates at times of mass
extinction should be unpredictable, and distinct from the extinction rates at other
times. For instance, suppose mass extinctions are caused by large asteroid impacts.
Extinction rates would then occur at a certain rate between large asteroid impacts, and
at a distinct, higher rate during and immediately after an impact. Unlike the random
model, the frequency distribution will not be continuous. Mass extinctions will (or might)
have a distinct peak (Figure 23.6b). When Alvarez’s explanation for the Cretaceous–
Tertiary mass extinction became widely accepted in the early and mid-1980s, some
paleobiologists suggested that there are two macroevolutionary regimes. Evolution
may alternate between “normal” periods with a “background” extinction rate, and mass
extinctions. Extinctions would have different causes at the two times: asteroids (perhaps)
for the mass extinctions and competition (perhaps) for the periods in between.
The distribution of extinction rates can be used to test between these ideas. Figure
23.6c shows one early study by Raup (1986). The extinction rates appear to fit the random,
Poisson distribution. The rate during the Cretaceous–Tertiary mass extinction may be
an exception, however, being above the curve. The generally good fit to the Poisson distribution
supports the view that variations in extinction rate are mainly random, and
that the history of life does not have two distinct macroevolutionary regimes.
More recently, the frequency distribution of extinction rates has been analyzed
further to see whether it fits a “power law.” A power law here refers to a family of
mathematical equations that describe distributions like those in Figure 23.6. In particular,
paleobiologists are interested in whether the distribution of extinction rates
is “fractal,” showing “self-similarity.” “Self-similarity” and “fractal” are two ways of
saying the same thing. A distribution shows self-similarity if its pattern on a large scale
is an expanded version of its pattern on a small scale, that is the pattern is the same at
all scales. For instance, the frequency distribution of extinction rates between 1 and
10 species per million years will show some pattern. If the pattern for extinction rates
between 10 and 100 species per million years is the same, but multiplied up by a certain
amount, then the whole distribution shows self-similarity.
Solé et al. (1997) performed an analysis of this sort. They found that the distribution
of extinction rates in a large compilation of fossil data appeared to be fractal a to show
self-similarity. Extinction rate data are noisy, however, because of the many sources of
error in the data. Tests of this sort are not all that strong.
If the distribution of extinction rates does show self-similarity, it is tempting to take
the reasoning a step further. If extinction rates are fractal, the differences in extinction
rates between different times are random and unpredictable. It would then be a mistake
to ask what the “cause” or even “causes” of mass extinctions is, or are. Mass extinctions
may not have a different cause from the periods when extinction rates are lower.
Consider, for instance, a simple model of extinctions that gives rise to fractal extinction
rates. The species in an ecosystem have a certain degree of interdependence.
Predators depend on prey; herbivores depend on food plants. If a food plant goes
..