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Axiomatic Panbiogeography

offers an application of incidence geometry to historical biogeography by defining collection localities as points, tracks as lines and generalized tracks as planes.
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Incidence Geometry
Composite Construction
Quaternion Algebraic Geom
Primate Vicariances
Individual Track Construc
Generalized Tracks
Main Massings
Track Analysis and MetaCo
Martitrack Panbiogeograph
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Panbiogeography is growing and becoming clearly distinct within biogeography.

"He (Heads) does not continue the long-standing dispute over dispersal versus vicariance but rather commits to a consistent mode of interpretation (p. 7):In the vicariance approach, the focus is on tracing the originary breaks between groups, not on locating a point center of origin within a group. In a dispersal analysis, the first question is: Where is the center of origin? In a vicariance analysis, the first question is: Where is the sister group? The focus is not on the group itself or on details of its internal geographic/phylogenetic structure, but on its geographic and ecological relationship with its sister group and other relatives

Panbiogeography is poised to change the way macroevolution is investigated.  Patterns are visible. It is just a matter of time before they appear to those not already attuned to looking for vicariances. Axiomatic panbiogeography attempts to situate this activity within a formal framework that is philosophically broad enough to even consider life off Earth but mathematically rigorous enough to permit intuitive constructions. It combines both geometry and algebra to link geography and taxonomy and offers a system that may prove useful to other disciplines. I was looking for the geographic component of evolutionary theory and found it pretty much only in the work of Croizat in 1986.

In 1987 I set up a series of independent studies on the biogeographyof the worm snake in the undergraduate College Scholar Program at Cornell.  In November 1987 I gave a graduate seminar on Croizat that was well recieved and since Robin Craw has encouraged my interest in this discipline that continues to receive less attention than it deserves. Continued attention to the topic has helped me to refine my own thoughts on how  evolution might work.  I think It might also be soon possible to explain adaptation by a new means that utilizes a Lamarkian-Croizatin base on which selection operates.  I am much less certain of things like that  than the simple use of geography to discern/dissect past splitings of lineage trajectories.  The commonality of distribution patterns continues to astound me every day.  MY thought is that macroevolution must soon take charge of these "wandering star distributions" and recover a heritage from the generalized track "planets" they ential. It is obvious to me that Gould who could not be bothered to substantially oppose panbiogeography early on  failed to find this context.

Nelson distinguishes an older and a newer "panbiogeography".

"In the old panbiogeography, key concepts are track and node, a track being a taxon's distribution (and internal relationships), represented most simply by a line on a map, and a node being an area where several different tracks overlap or intersect. In Heads' account, matching Croizat's method and result, there is scarce mention of track (“set of nodes,” p. 408), and a node is only that of a cladogram. Still his account, cloaked in the findings of molecular systematics, continues the spirit of the old and amply confirms Croizat's prediction (1964, p. xvi): “my work shall live.”

This is a newer node notion.  Seberg 1986 wrote: "panbiogeography is to be viewed, especially in Craw and Weston's version, as an adjunct to historical geology, rather than as a biogeographic theory..." but criticism confounds the simultaneous use of forces vs substances in both geology and historical biogeography either concurrently or in different time series.  It fails because infinite sequences of divergences that converge can.may be spatially separated in the same temporality (or not).

Axiomatic panbiogeography is approach to the Croizat method which relies on incidence geometry to direct  mathmatical applications onto the biogeographic data within Panbiogeography.  Algebraic manipulaton becomes possible both within and amongst generalized tracks.  New formats for the formation of individual tracks that vary with reciprocal relations of track width to node shape, mass density and baseline volume are developed within this discipline so as to enanhace classifications of historical biogeograhy.  Graphdatabase traversals provide a technology within which proposed patterns of relationship can be tested and recovered.

Software for track construction and display


From the links page, Craw, Grehan and Heads wrote in "Tracking the History of Life" on page 4 that, "Panbiogeography is an attempt to reintroduce and reemphasize the importance of the spatial or geographical dimension of life's diversity for our understanding of evolutionary patterns and processes.  It is an approach to biology that focuses on the role of locality and place in the history of life.  Its goal is to recover the importance of places and localities as direct subjects of analysis in biogeography.  Central to the panbiogeographic project is the acknowledgment that an understanding of locality is a fundamental precondition to any adequate analysis of the patterns and processes of evolutionary change. Panbiogeography emphasizes the role of place in the past as understood from the perspective of the present."


Panbiogeography Gate

John's Panbiogeography

Axiomatic panbiogeography permits one to keep track quantification independent of actual causal association during composite construction.

The reciprocal incidence geometries of points to lines OR lines to points enables this,  when the/a third (motion) is involved.

Computer programs are facilitating acquisition of this "pure" intutition.

I first discovered the huge volumes of Croizat's work on the shelves of Mann Library at Cornell. In my senior year there, I managed to have Amy McCune advise an independent study, on Croizat's work. I gave a graduate seminar on the subject to entomologists interested in the notion of "tracks." One of the graduate students said at the time that, "It was one of the best we have had in a long time." I was told that the presentation (which situated Croizat's work within biology as a whole) got people talking who normally did not. 


Since then, I have spent quite some time trying to discover how to apply THE METHOD of Croizat. The work still seems to be done too much in isolation across the globe for any instruction to have been developed from it to have much of an impact. The recent discussions on Panbiog-L have helped to change this situation.  The issue of "chance dispersal" vs. "vicariance" seems to have obscured the present dissemination of Croizat's seemingly post-modern contribution to evolutionary theory.

Gary Nelson's participation on Panbiog-L has helped me to realize that Gould has covertly used geographic information in his notion  of exaptation. I found that the mathematical ideas present in Principa Botanica could not be gainsaid to the extent that Panbiogeography could but this was due to my failure to incorporate symmetry as deeply as Michael Heads has done.  Croizat's attempt to use multiple languages does not seem yet to be of a more considerable influence than technology may, to assist distribution of the ideas.


In this Space, Time and Form is not part of some curriculum as much as 'vicariance biogeography' is because the removal of teleology has not worked itself out beyond the history and philosophy of panbiogeography (Heads 2005 as quoted  here). This (removal)  is possible however within a restricted application of a particular genetic instantiation of a constraied notion of vicariance.

"What is panbiogeography? Difficult to characterize panbiogeography considering the diversity of viewpoints.To PATTERSON (1981) is "phenetic" because would be based on overall similarity.To MAYR (1982) is "eccentric".NELSON (1989) sees it as an "evolutionary metatheory".Stace (1989) defines it as "vicariance in global distribution patterns."Grene (1990) considers "capricious".For some authors, is a precursor of cladistic biogeography (Nelson & Platnick 1981; BIG 1990; COX 1998).For others it is an alternative research program (CRAW && WESTON 1984; HUMPHRIES & SEBERG 1989; Platnick & Nelson 1988; MORRONE & CRISCI 1990, 1995; VARGAS 1992b; ZUNINO & ZULLINI 1995; MORRONE et al. 1996; Colacino 1997; CRISCI et al. 2000; Grehan 2001d).Finally, there are those who propose that panbiogeography has important implications for evolutionary studies (Grehan 1984, 1988a, 2001b; Grehan & AINSWORTH 1985; HEADS 1985, Gray 1988, 1992; MORRONE 2000c)."

Robin Craw

The missing David Hull reference is :
D.L. Hull 2008 Leon Croizat : A Radical Biogeographer, pp. 194-212 in O. Harman & M.R. Dietrich (eds) Rebels, Mavericks and Heretics in Biology, Yale University Press, New Haven & London.
This is a very biased and inaccurate account that again “idealises” Gary Nelson and the New York school, and ignores completely the considerable influence that panbiogeography has had in Argentina, Brazil, Chile,Columbia, Cuba, Mexico and Venezuela. Hull also misses the point that mid-late 1970s New York school vicariance biogeography “evolved” into New York school “area cladistics” in the 1980s. Far more papers are published in peer reviewed journals using quantitative panbiogeographic methods originally developed by New Zealanders than are published using Nelson’s area cladistic method, so Hull gets it completely wrong once again.
He also misses completely the key issue that Croizat was trying to think through “the colonial difference” and “decolonize” biology