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Re: Mass Extinction Statistics



<Suppose there are twenty million mammals in a given environment (ten
million placentals, ten million marsupials).  The K/T bolide strikes, and
90% of them, chosen randomly, are killed.  Then we know statistically that
the remaining distribution will still be very close
to fifty-fifty: that is, five million each would survive, give or take a few
hundred thousand or so.>

(Just a little math, 10% of 20 million equals 2 million total survivors.
End of math; concepts have to be explained in clear, non-technical language,
whether in stats or paleontology itself.)

Ah, Mike, you're making a bunch of assumptions.  Let's make some alternate
assumptions:  #1, all the placentals live in the East and all the marsupials
live in the West.  A bolide strikes and, assumption #2, the effects are so
intense in the East that not a living thing survives.  In the West, the
effects are less intense, assumption #3, and 20% of mammals survive; which
individuals are in the 20% and which in the 80% killed is decided randomly.
They're all marsupials.  10% of all mammals have survived, and they're all
marsupials.
You made the assumption:  chosen randomly, which could apply only if the
effects attempting to kill the animals were equivalent everywhere.  As I
mentioned earlier, it seems pretty unlikely that the impact affected every
square inch of the Earth in exactly the same way.
And you're making another assumption, that secondary effects are equivalent.
I used only primary effects in the example I gave:  animals are alive, the
bolide hits, animals are dead.  However, I think that the assertion that
secondary effects are important is reasonable.  As an example of secondary
effects, the death of a certain type of plankton can cause the extinction of
a whole group of land animals years later.  When you have a chain of
causality, the opportunity for randomness, even random events after the
impact, to influence the outcome is huge.  (I think HP Pigdon also made this
point in a post I encountered while this was in draft.)

The original issue here was whether it is possible to assume that there is
an identifiable cause for disproportionate survival.  I'm saying that even
if we exclude aspects of the animals involved and everything about
fossilization and other problems with the record of those animals, the
bolide is so likely to have differential effects that survival could be
disproportionate; that you still couldn't draw unarguable conclusions from
what lived.

One more:  if the bolide effects were the same everywhere in both primary
and secondary effects, you still could have random events occur well after
the impact which become highly significant for a reduced population.  For
example, more placentals survive than marsupials, but then the excess are
killed by a forest fire.

I'm a practical statistician; I calculate gambling odds and sometimes devise
prize structures at work.  This issue doesn't seem to me to require much
more than a simple recognition of the existence of significant randomness
after the bolide impact, the results of which cannot be isolated from other
factors in a single trial.