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Re: Diversity after divergence--pre-K/T modern orders. (fwd)

The following is a message from John Hunter, who asked me to forward it to
the list.


Scott D. Sampson, PhD
Department of Anatomy
New York College of Osteopathic Medicine
New York Institute of Technology
Old Westbury, New York
11568, USA

Phone:  (516) 686-3807
Fax:  (516) 686-3832 
E-mail: ssampson@iris.nyit.edu

---------- Forwarded message ----------
Date: Mon, 22 Mar 1999 13:26:04 -0500 (EST)
From: John Hunter <jphunter@iris.nyit.edu>
To: Scott Sampson <ssampson@iris.nyit.edu>
Subject: Re: Diversity after divergence--pre-K/T modern orders. (fwd)

John Hunter
Department of Anatomy
New York College of Osteopathic Medicine
New York Institute of Technology
Old Westbury, New York
11568, USA

Phone:  (516) 686-3802
Fax:  (516) 686-3832 
E-mail: jphunter@iris.nyit.edu

>Subject: Diversity after divergence--pre-K/T modern orders.
>Marshall states that analyses of fossils cannot assume a "uniform
>potential" since "many higher taxa had long early histories with
>relatively low diversities."  Therefore, he says, confidence intervals
>must be extended back into the Cretaceous. 
>Then Foote et al 1999 Evolutionary and preservational constraints on
>origins of biologic groups: Divergence times of eutherian mammals Science
>283:1310-1314  argue (I think) that rapid divergence times of early
>might be the reason for not being able to find fossil evidence of
>divergence in the Tertiary.
>Then they [Foote et al.] give and reject
>the following alternate hypothesis: "Modern eutherian lineages existed
>through the Cretaceous, but their preservation rates were generally lower
>than those of species in other mammal groups.  This difference in
>preservation rates would have to be more than an order of magnitude, for
>which we can offer no support...".
>But Marshall's point above re birds would seem to apply to mammals as
>well.  That is if it is true that species in their early fossil record
>have low,diversity.
>Thsi leads me to the question: do species sometimes, always, never, have
>low diversity at their first divergence point?


Certainly, if the group in question is monophyletic (i.e., from a single
ancestor) then it must begin at standing richness equal to one lineage.
And clearly the total probability of preservation of an entire group
increases with diversity.  We recognized this and the issues raised by
Bleiweiss and Marshall in our footnote 29, where we discussed why we did
NOT adopt Bleiweiss's approach, that is, why we did not extend confidence
limits, based on Cenozoic occurrences, back into the Cretaceous.  Because
Cretaceous preservation rates were much lower than Cenozoic rates, we felt
it more justifiable to use rates calculated on Cretaceous occurrences,
that is, based on mammalian groups other than modern eutherians. 

Two things that need to be distinguished are (1) the total probability of
preservation of a group of organisms over a given time and (2) the
instantaneous probability (or rate) of preservation characteristic of a
group. Total probability of preservation (i.e., the likelihood that at
least one member of the group is preserved and recovered from fossils)
must increase with diversity.  Total probability also increases with time
(i.e., the amount of time that the group has existed) as more
opportunities for preservation occur.  But instantaneous rate is an
average rate of preservation and recovery for a typical species of the
group over a set interval of time, say one million years (i.e., number
of preervation events per lineage-million year or Lmy).  Various factors
might affect this instantaneous rate such as having a hard skeleton or
being of large size. 

The relationship between total probability and instantaneous probability
is found in our footnote 17.  If one thinks of fossil preservation and
recovery as a rare and random event, then one can express it as a Poisson

P (preservation) = 1 - exp (-rS), where 

P = total probability of preservation (i.e., at least once)
r = instantaneous rate of preservation (per Lmy), and 
S = total amount of diversity (Lmy) of the group over the time of interest

We estimated S, or total diversity, as the area under a diversification
curve. As such, it is in units of standing richness (number of lineages)
multiplied by time (millions of years) or lineage-million years (Lmy).  As
diversity increases, time increases, or both, S must increase resulting in
an increase in total probability of preservation.  If the total
probability of preservation is high and we still haven't recovered a
fossil of the group from that time period, then we have to question our
initial assumptions.  Because we used such conservative parameters for
diversity (start at just one species, end at no more than 15 species) and
for models of diversification (including exponential growth, which
actually minimizes S, the area under a diversification curve), then we
argued that the most likely faulty assumption is probably time.  That is,
if the majority of the lineage splitting events occurred just before the
first fossil records of modern eutherian orders, then the amount of
missing time of the group is minimized, as is S, the amount of missing

Thus, in answer to your question, diversity affects total preservation
probability of a group (P), but not the per-taxon rate of preservation


>Lastly, Foote et al make the following statement and I ask if it is
>strictly true: "..there are no unequivocal modern eutherians in the

We elaborated on this point in our footnote 22.  Basically, there is not a
single claim of a member of an extant order of placental mammal, or member
of a superordinal group of extant orders, from the Cretaceous that is
without controversy.  However, even giving these claims the benefit of the
doubt (i.e., we assume a start to the fossil record of modern placental
mammals at 85 ma, corresponding to the appearance of ?ungulatomorphs in
Uzbekistan), we still find that deep splits such as those postulated by 
the molecular clock are unlikely.