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RE: Species & Giraffe necks (was Re: tooth counts in systematics)

        I'm glad to see someone on the professional side recognize the
undefinability of species. The Grants' work on finches shows the
problem in action - species can define and undefine themselves
by hybridization. 
        A mathematical note: If the definition of a species 
requires that a surface be drawn in either sequence space or 
design space that separates two species, then Turing's theorem 
and the Blum-Shub-Smale theorem on recursive systems both
show that "species" is, in general, undefinable. 
        That doesn't mean the concept isn't useful.
G. Derkits
> ----------
> From:         Thomas R. Holtz, Jr.[SMTP:th81@umail.umd.edu]
> Reply To:     th81@umail.umd.edu
> Sent:         Monday, April 12, 1999 11:14 AM
> To:   smithjb@sas.upenn.edu
> Cc:   dinosaur@usc.edu
> Subject:      Species & Giraffe necks (was Re: tooth counts in
> systematics)
> At 10:50 AM 4/12/99 -0400, Josh Smith wrote:
> >L Nyveen wrote:
> >> 
> >> And all that leads right back to the old clumper/splitter debate.  You
> >> can't decide what intraspecific/intrageneric variation is without first
> -
> >> often quite subjectively - deciding just what makes a species/genus.
> >> 
> >     BINGO.  You see why spending all ones time deciding what sits 
> >next to what on a cladogram is in my mind something best left to others.
> >We spent an entire semester seminar here just wrestling with the species 
> >definition question and came to very very few satisfactory conclusions.
> Seconded (not that I was in that seminar, but one similar enough).  Much
> as
> I like the Specific Mate Recognition Species Concept in principal (at
> least
> for sexually reproducing metazoans), there is just too much baggage and
> too
> little testable with it to apply it effectively to most of the type of
> material I work with.
> The more time goes on, the more I agree with Horner on this idea: species
> are unreal divisions of historical (natural) lineages.
> Oh, and by the way, to muddy the waters of yet another basic tenant of
> biology (in this case, homology), see Nick Soulunias' paper in the latest
> _Journal of Zoology_ (I'll post the whole citation later today).  Lots of
> nice stuff showing the decervicalization (or thoracization?) of the last
> cervical of _Giraffa_, and the intercalation of a new cervical somewhere
> between C2 and C6.  And all this AFTER the split between okapis and
> giraffes
> (and, for that matter, between _Giraffa_ and a lot of the other big
> extinct
> giraffids).
> Yeah, so this can happen within a traditional mammalian subfamily, but
> having the cuppage of _Opisthocoelicaudia_'s centra reverse modes is "too
> improbable" for it to be a titanosaur.  Uh, yeah.  Right.
> Thomas R. Holtz, Jr.
> Vertebrate Paleontologist     Webpage: http://www.geol.umd.edu
> Dept. of Geology              Email:tholtz@geol.umd.edu
> University of Maryland        Phone:301-405-4084
> College Park, MD  20742       Fax:  301-314-9661