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Re: Mass Extinction Statistics




Mike,
You have a real talent for boiling down debates to the real "nitty gritty" important stuff. The size of individual kill rates is unavoidably a major source of contention, even among those who agree that a bolide caused most of the K/T extinction (even if other factors already had some groups in decline).
I think the kill rate was well over 99% for virtually all land vertebrates, as well as a large majority of marine vertebrates (although many sharks and other marine fishes may have had a huge scavenging "party" for a while). Certain insect populations (some "flies" for instance) probably exploded to plague proportions, so it was probably party-time for many groups of spiders as well. Therefore the kill rate for invertebrates was probably extremely variable: 100% for specialists (like ticks that only fed on tyrannosaurs or dromaeosaurs), but relatively low for some "acidotolerant" insects in the Southern Hemisphere.
No simple answers, but I am definitely among those that think it was a horrid global disaster from which only the fittest generalists emerged (among those having the "dumb luck" to be some distance from Yucatan). But what is most "fit" is relative to varying times, places, and situations, and so there is always some element of "dumb luck" and/or randomness at work---ready to throw a monkey wrench of uncertainty into our best thought-out scenarios and speculations. Sometimes it amazes me how much agreement biologists can come to (in spite of the obstacles, such as the fragmentary nature of the fossil record).
--------Ken
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From: Mike Taylor <mike@tecc.co.uk>
Reply-To: mike@tecc.co.uk
To: philidor11@snet.net
CC: jbois@umd5.umd.edu, dinosaur@usc.edu
Subject: Re: Mass Extinction Statistics
Date: Fri, 25 May 2001 11:38:24 +0100

> 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.
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