Skip to main content

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.
About Us
Contact Us
Site Map
Member Login
Incidence Geometry
Composite Construction
Quaternion Algebraic Geom
Primate Vicariances
Individual Track Construc
Generalized Tracks
Main Massings
Track Analysis and MetaCo
Martitrack Panbiogeograph
Replies to Criticism
Multimodel Selection
Search Encounter
Track Analysis beyond Pan
Help anticipate a perception,develop an intuition
and systematize a reading of
Croizat's contribution to biogeography with axioms

                            "Imagine three systems of THINGS, which we will call points, straight lines, and planes."Hilbert

                   What these things are we do know - they are specimen collection localities, individual panbiogeographic
                    tracks and the generalized track they can compose.

Incidence Axiom #1
For every point P and for every point Q not equal to P there exists a unique line l that passes through P an Q.  A collection locality is considered the most local level places of endemism asserted (therefore) in a main massing there is no unique line that connects two localities outside the main massing - through its -main massing

Incidence Axiom #2
For every line there exists at least two distinct points  incident with l, one point or which may be in the mathematical neighboorhood of a main massing if present, one point  being the original collection locality and the other point deriveable from th etopology of the ancestral higher order pinpoints with the parameter the specific data point of original collection locality.

Brad McFall
Phone  (607) 256-0308

Incidence Axiom # 3 There exists three distinct points with the property that no line is incident with all three of them.  One of these points is A NODE, the phylogenetic and biogeographic nodes.

If you would like to work on/in axiomatic panbiogeography and join this team please contact us. The team site will include conversations on abstract panbiogeography.

228 Linden Ave #B1
Ithaca, NY USA

Computer tools are permitting biogeographers to search for and discover (Maps and map-making)
Earth's geographic distribution patterns
simply by plotting and connecting collection locaties. (Maps and map-making)
(areally co-extensive sets, Creader, virtual exploration, graphdatabases, panbiogeographic atlas)

Early astronomers searched the skys for patterns and later discovered laws-of-force that bound the dynamic connection amongst observed points of light. Today, panbiogeographers use the concept of vicariance to reveal substantially the same kind of thing, except form-making rather than simple inertial motion divides the temporalities recovered,  not from light sources at some distance, as in astronomy, but rather by speciation as-it-appeared back further in geological time now translated biogeographically into the present. Historical biogeography is based on contingent events within a definite homogeneity.  So despite the the historical nature of this process rules determined by the forces involved can be "exhumed" in a kind of analogical distributional taphonomy called panbiogeography. (Panbiogeography Today)

Panbiogeography is different from other forms of historical biogeography in that it is possible to use a generallized panbiogeographic track's geography to predict or recapitulate what older evolutionists discerned as mutally exclusive descent and deviations from a primary form. This unique aspect of current panbiogeography is indicated by the trend to understand the node not simply as a connecting link between two individual tracks but rather as much akin or sister with, the phylogenetic node as discussed by cladists. There is much more that can be thought-through with this innovation that is poised to change the way macroevolution is evidenced. Multimodel statistics applied and developed for panbiogeographic track atlas data establishes a new eminence for panbiogeography hetetorfore relegated to negative remarks and the soured opinions of others. (Nodes)

Leon Croizat founded the discipline and method of Panbiogeography and its modern practioners are developing his orginal insights for the times and towards the places when and where  that revolution in biogeography he forged in pen and paper may reveal indeed not only divided places of a humanly created continuum displayed through his many volumes but additionally into modern formats from original form-makings made and thus  inherently classify the very forces behind those differences in the susbsistant patterns so stoichiometricallly uncovered.  I hope he would be proud of where panbiogeography has gone and is going. The latest book by Micahel Heads details that aspect to which panbiogeogphy is essential to those atempting to know the past tracks on/in which life has moved as the Earth rotated and revolved. (Blog)

Already, molecular panbiogeography of the tropics challenges the instituational legacy of traditional phylogentic heritages, eschews needless debate, and marshalls a strong case for vicariance as a force as well as the substance behind the innovations panbiogeographers make on a daily basis.  With that context in mind the essential elements of the science of panbiogeography​ follow.