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*To*: dinosaur@usc.edu*Subject*: Re: Diversity after divergence--pre-K/T modern orders. (fwd)*From*: Scott Sampson <ssampson@iris.nyit.edu>*Date*: Mon, 22 Mar 1999 20:52:35 -0500 (EST)*Reply-to*: ssampson@iris.nyit.edu*Sender*: owner-dinosaur@usc.edu

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 >recovery >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 >orders >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? Response: 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 process. 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 diversity. Thus, in answer to your question, diversity affects total preservation probability of a group (P), but not the per-taxon rate of preservation (r). ******************************************************************************** >Lastly, Foote et al make the following statement and I ask if it is >strictly true: "..there are no unequivocal modern eutherians in the >Cretaceous..." 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.

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