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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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Hyper Graph Creation
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Multimodel Selection
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Track Analysis beyond Pan

Hypergraphs - a structure on which panbiogeography functions

Here are some steps I am going through to create a hypergraph for what appears so far to be a serially bicoupled network between Plethodon and Desmognathus distributions.  The hypergraph that is being created below is the structure on which the Croizat method is applied.  By creating a index over the edges of the graph distributed into tracks, nodes, masses and baselines it is possible to de rive the phylogenetic structures of both general from the panbiogeographic divisions of the species distribution.  While this example was somewhat subjectively developed it shows that joint complex hierarchical  bfiurcation sequences can be convergent for different clade lineages and might be thought objectively as a complex dynamical system formatted as in this a serially bicoupled  edge network analyzed by panbiogeographic controls.

After becoming somewhat familiar with the individual species distributions and the joint common disjunction among the Desmogs, Plethodons and Euryceas....

I used a couple of published phylogenetic syntheses to couple the Plethodon phylogeny to the Desmognathus phylogeny spatially and demonstrated where in that match the Eurycean panbiogoegraphic track could be ordinated.

I then began to create a graphml representation

 to present the species as verticies and the common biogeography as edge congruences after sketching two versions of which are by definition - HYPERGRAPHS ( many species may have the same edge). The matching was designed with a view to being able to form a panbiogeographic index on the edges that both moves through both clades hierarchically and through geography at least vicariantly if not by simple spatial sequencing.

Missing connections are due to lack of defined relation between track width and node shape projectability.

Thus the graphml representation can be a multihypergraph where the  panbiogeographic concepts provide an index that graph traversals might enable one to create supersets of clade trees supported biogeographiclly - a goal of panbiogeography!  Furthermore panbiogeography can offer the graph visualization community with whole new classes of layout algorithms.  It may be that we will see panbiogeographically named (polyphyla -track,node,mass,base) clustering of social network data where other graphs have the same structure that biogeoghraphic spatialization visualizes in multiple phyla. Panbiogeography has unique ways to sparate edges and thus display node clusters across multiply coupled dynamic iterations reproduced naturally. A simple algorithm could be made by repulsing the nodes and attracting the edges which are grounded to their respective goegraphies but are further repulsed increasing track width into node projections to densities per mass into volumes by baselines!!

Wow a practical application for a discipline not even on the standard radar!

A panbiogeographic control graph layout algorithm is clearly needed