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--Original Message-- From: Philidor11@aol.com Date: 06 November 1998 05:01

>>'Say the ratio of maniraptorans living in the K to those living in the J
>Say the ratio of the chances of an indiv living in the K ever being found
>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/ ((A/B) * (C/D)) ).
>The chance of N maniraptoran fossils all appearing after Archaeopteryx is
>this expression raised to the power of N.'

>It'll take me a while to untangle the parentheses and confirm what I think
>you're saying.
>However, remember that small proportions of small samples have huge ranges
>that any detail of the group you're looking at has approximately no
>at all.

Small samples are less statistically significant, but according to that well
known statistical principle, "Many a mickle macks a muckle".  You can add up
small samples to make any degree of confidence required, so long as you have
enough small samples.  The "Law of Averages" refers to this kind of
situation.  (The phrase has passed into idiomatic folklore, but it's still
proper stats.).  Of course, the fact that *any* large and statistically
significant sample could be notionally fractured into smaller segments each
of no useful significance, shows that having small stat. insignificant
segments on its own says nothing about the significance of the whole.

>Awhile ago I was analyzing the results of a 1,000 response telephone sample
>which found a less than 1% rate of probable pathological gamblers.  Guess
>valid the demographics of that subsample are.  To approach useful numbers
>you'd need 6 or 7 times as many samples (at about $70 apiece) and
>stratification (does not mean under rocks).

That's because the original 1000 was not core data you were interested in,
only a population containing it.  However, fossils identified as members of
the maniraptora have a likelihood considerably greater than 1% of being

>Aside from this issue, remember that fossils are found not only where they
>be preserved but also where they can be looked for comparatively easily.
>If you wanted to be sure of getting a valid sample of a world population
>have to look in a lot of randomly selected places.  You might end up in my

My term C:D is defined to include not just the relative likelihood of
fossils existing, but also of being found.

>In re birds, are you satisfied that the gap between archaeopteryx and the
>'bird' is short enough to disprove the assertion that archaeopteryx was an
>anticipation of birds, but not necessarily even a close relative of the

But your position requires that a gap many times that size *before* Archae
was no problem.  A gap of five million years tops with no small fossil of a
particular type found?  Look at the Gasosaurus gap: until ten years ago a
gap existed of 25mys with no theropod of any kind, even large ones.

As for proofs, no-one is ever going to positively prove any family tree in
vertebrate palaeontology.  It is all a question of a feel for likelihood, of
'the general feeling by the community'.  (Positive evidence *is* useful for
this - positive evidence is used in legal cases (in practice, even in
criminal cases), and by animals, because absolute certainty is not
required - which in real life is generally the situation.)

>Seems like this type analysis has rules for validating hypotheses I'm not
>I understand.

Well, of course I'm up against the operating limit myself in this as far as
statistics goes; however, if you could find six proper statisticians, who
were equally au fait with these dinos, how many opinions would they have
amongst them?!

My position is "We ask not for proof, only for recognition.  Though the 'All
from Archae' idea seems to us (well me, anyway) to be preferable, it surely
requires at least equal acceptance as a hypothesis until a lot more
consideration has been given to the issue".

Taking rough but conservative data from TMKeeseys excellent website:
http://www.gl.umbc.edu/~tkeese1/dinosaur/genera.htm , totals of individual
specimens found so far for all the subgroups can be estimated as:

Tyrannosauroidea: 70
Troodonts: 28
Ornithomimos: 24
Oviraptors: 20 (assuming 5 _O_ sp.)
Protarchaeopt+Caudipt.: 4+
Deinonychs: 25

Total: 171

So, 171 (at the very least) Arctometatarsalia + Maniraptora have been found
after _Archaeopteryx_ and none before (if we discount the Segno J Jaw).
This is a lot more than I thought, and is going to give some strong
opposition to any hypothesis claiming any (Arctos/Mani's) occured before
Archae.  The 170th root of 0.001 is just over 0.96 .  This means that if you
toss a coin 170 times and it comes up heads every time, even if the null
hypothesis is that the coin is weighted to land heads 96% of the time, the
result is *still* so unlikely that you have to discard that idea in favour
of the notion that it has heads on both sides, ie that it doesn't have a
tails... which in our terms means that even if there are 24 times as many
Arctos/Mani's to be found in the Cretaceous as in the Jurassic, there is
only a 1000:1 chance of this evidence appearing.  You may say "Well, there
*were* 24 x as many - even 100 x - even 10,000 times.  It was just at the
start of the group's evolution".  The trouble is, the further along that
line the argument is taken, the more my point is made.

That looks like 'it', chaps.  Anyone mentioning the idea that any
Arctos/Mani's preceded Archae without also mentioning the possibility that
Archae was the first is really being a long way short of 'scientifically' .
. . 'fair'.

So much for "none pre-Archae".  But Archae was one.  If we are looking for
something that *gave rise* to such an illustrious line, wouldn't we be
looking for something rather unusual?  Might not Archae be a good candidate?
Perhaps as an idea that deserves better coverage than a total blackout?