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Re: Mass Extinction Statistics



> Date: Fri, 25 May 2001 00:11:18 -0400
> From: "philidor11" <philidor11@snet.net>
> 
> Take a more familiar example.  Any animal can be fossilized.  Does
> the discovery of 3 animals of a species who obviously died in
> different times and places mean that the animal was more likely to
> be fossilized than an animal represented by only a single fossilized
> individual?  Obviously not, if both animals were of similar size and
> other physical factors influencing the likelihood of fossilization.

Indeed, because your sample size (four animals) is too small to draw
any statistical conclusions.  But if the three-to-one ratio was
produced by finding (say) 3000 fossils of one animal and 1000 of the
other, _then_ you have some explaining to do.

A proper statistician (do we have one in the house?) could give you
the probability that this 3000-1000 distribution could occur randomly
if the animals have equal population and fossilise equally well, but I
can tell you it's minuscule, as is much less likely than 1:1000000.

> I know that it can appear a single strike gives sufficient
> opportunities for luck to balance out, but say for instance the
> bolide happened by chance to affect some areas more than others,
> though all areas are devastated.  And say that the most affected
> areas happened to have higher concentrations of placentals than
> marsupials.

I think that when people ascribe extinction patterns to "dumb luck",
that's more credible if we're assuming that truly tiny numbers of
animals survived.  Is that what we think happened?  Here's what I
mean.

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.

But if the kill-rate was 99.99999%, so that only four animals
survived, then there's a very good chance that the survivors would be
75-25 biased towards either placentals or marsupials -- and of course,
there's a one-in-eight chance that all four surviving mammals would be
of the same type.

So what was the individual-animal kill-rate at K-T?  "Merely" 90% or
something more like 99.99999%?  Because if the latter, the "dumb luck"
selection hypothesis makes much more sense.

(Er, substitute "breeding pairs" for "animals" in the rough maths
above if that makes things seem more sensible.)

 _/|_    _______________________________________________________________
/o ) \/  Mike Taylor - <mike@miketaylor.org.uk> - www.miketaylor.org.uk
)_v__/\  "Wagner's music is much better than it sounds" -- Mark Twain.