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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
Planar Chaos
Graph Rewriting
Main Massings
Track Analysis and MetaCo
Martitrack Panbiogeograph
Replies to Criticism
Multimodel Selection
Search Encounter
Track Analysis beyond Pan

Panbiogeographic typing and Graph rewriting
Bifurcation type
1- track width
2- track length
3- track nodes
4- track masses
5- track baseline
6- attractor areas (track antinode foreground)
7- repeller areas (track anitnode background)

Here we show how to use panbiogeographic concepts as an graph rewrite interface to glue two spatialized phlyogenetic graphs from tracked subgraphs (LHS->RHS)  and thus "re-write" the geography into a larger  biogeography -- a "panbiogeography". Bisimulation thus captured axiomatic panbiogeographic congruence among (Plethodon - Desmognathus -Percina). Panbiogeography provides a new means to type graphs closed onto future phylogenetic tree possibilities as the panbiogeographic atlas database is increased in size. The process of doing this will result in a utilization of Croizat's idea of extensions of a centrally vicariant region practically multiply otherwise localized divisions as noted on page 135 of Space, Time and Form.

Node replacement grammars could be designed when different Linnean levels posses the same panbiogeographic
elements(subspecies has same as rest of Genus).  A species node might be replaced by a subspecies track structure with new edges that connect at the subspecies nodes maximally in its masses. They could also be used when different phyla posses similar biogeographies but again at different Linnean levels.

We do panbiogeographic graph grammars and rewriting to generate phylogenetictypes(trees) (via the three angles of Earth degrees of freedom relative solar system stability) using unlabelled edges from two nodes(species tracks) meaning that there might be a path between the  two nodes now or in a future where "future" means both a more comphrehensive panbiogegoraphic atlas graph as more taxa are incorporated and/or due to new paths created by ordindary means of locomotion via climate change etc. It obviously could be used to look into the origins of path creation and their community ecological evolveabilities and is perhaps the structure behind   Croizat's "dispersal from what dispersal" that has made even Gareth Nelson suspicious where new panbiogeographic substance is findable.

Axiomatic Panbiogeography is necessary both to investigate, "ancient" vicariances as well as to  assist in human interaction with ecological community structures as the  human population increases seemingly out of control.

Panbiogeographic graph rewrites (G->G') = f(grossone) metabiologically. Only now the transformations can include infinite alterations beyond the standard four (f((1))+grossone; (f((1)+groosone));groosone* f(1); f(grossone*(1) )
(1)=grossone).  This appears to be an open technology for interfacing an infinity computer to.

Sigref should also be applied to the Plethodon-Desmognathus hypoergraph coincidences. nly One need not have a representation of all collection localities but only some symbolized with Croizat concepts and a binary decision cycle about space useage alternating between genera which because of local differences may not be an artifact of the method but a method for the facts even on the smallest scale observable!

Subdue induction graph grammars seem possible in axiomatic panbiogeography.

Heads wrote, "In this book it is the evolutionary trajectory, not a particular point along it, that is of interest.  Whether a group is treated as a species, subspecies or genus is not relevant to the discussion; instead, the focus is on the process of differentiation in space and time."

Finding that the Genus of Hemidactylium may  match a three fold repeated clade structure of some of the Nothonotus species (with the others matched to Necturus), the matching of various other salamander genera to different groups of species of Etheostoma, and the fusing of both Plethodon and Desmognathus salamanders with most  of the Percina species indicates that pehaps indeed bismulation (with branching) rather than species numbers or branch lengths is able to  capture this trajectory panbiogeography features.

One can imagine using a graph grammar to replace a full multi-species distribution with a panbiogeographic representation creating a restgraph such that the native distribution subgraphs are replaced with panbiogeographic graphs g(r) via an embedding.

The grammar thus created for a particular genus, family, order etc. could then be bisimulated congruently to another to create a generalized track.

One can wonder if it is not possible to gather genetic support for ancient vicariances by using say a bismulated panbiogeographic track convergent graph grammar to search and find the same grammar pattern in molecular evolution variation say in the rather unique plant insect interaction of the Tasman arapods (Aganthis) with Agathiphaga and the beetle tribe Tomici. If the genetic and geographic grammars match this should lead to as  clear an evolutionary support than that found for any other explanation.

AGG permits node type inheritance (from its algebraic contruction) in which a node type can have one direct ancestor from which it inherits the attribute and edge types.  This behavior appears to be useful when a more biogeographicallymeaningful position (not at the arced midpoint)
for ancestor nodes of phylogenies need be graphed in Google Earth and are possibly panbiogeographically at odds
with the cladistic node relations on the higher levels(due to heterogenous mobilism/immobilism activity).