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re: EARLY EVOLUTION OF 'BIRDS'



Eek!  I knew someone would say something like this!


--Original Message-- From: Randy King <randyk@ims.com>Date: 09 November 1998
19:19


>I'm late in my emails again, hope this hasn't been beaten to death
>already.  I just can't leave it alone....
>
>At 11:52 PM 11/5/98 EST, Philidor11@aol.com wrote:
>>'Say the ratio of maniraptorans living in the K to those living in the J
was
>>A:B;
>>Say the ratio of the chances of an indiv living in the K ever being found
to
>>that of one in the J is C:D;
>>The ratio of the chances of a maniraptoran we have found coming from the K
>>to from the J is (A/B)*(C/D).
>>The probability of any maniraptoran we have found coming from the K is
1/(1
>>+ 1/ ((A/B) * (C/D)) ).
>
>I think this is incorrect.  I believe the ration of maniraptoran in K to J
>would be (AC:BD).

But that's the same as (A/B)*(C/D).

As for the rest of it, well, you may well be right, I'm not even going to
check it, because the chances of throwing heads 170 times in a row is still
incredibly small, even with a coin that lands heads 95% of the time.


>The probability of a given maniraptoran coming from K
>would be AC/(AC+BD).  The probability of N given maniraptorans coming from
K
>would be [AC/(AC+BD)]^N.
>
>>
>>The chance of N maniraptoran fossils all appearing after Archaeopteryx is
>>this _expression_ raised to the power of N.'
>
>Assuming Archie came from the JK border.

No, I did say much the same applies wherever you take the line, just a slightly
different question.


>There are too many assumptions
>being made to draw definite conclusions.  Starting with, distribution of
>creatures we've found from J or K isn't an independent variable, but very
>dependent on the geography.

It's the same planet!  And nothing's definite in probability - you still end
up with another probability.  The two assumptions I make are that,
worldwide, the fossilisation llikelihood ratio between J and K is such and
such (slot in your choice) and the actual number of animals-ratio was
(again, make your choice).  I don't think making those assumptions is
unreasonable.  The answer is just another probability.

>
>Where are you trying to go - and who was it that's going??

I'm going to prove the maniraptorans are birds - and you're all going
eventually!

>-Randy, mathematician at large.



BUT - thanks very much for taking the trouble to work through it.

Regards,

JJ