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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
Orthogenesis
Quaternion Algebraic Geom
Vicariance
Primate Vicariances
Individual Track Construc
Generalized Tracks
Taxogeny
Nodes
Edges
Distributions
Propositions
CREADer
Areas
Main Massings
Geology
Track Analysis and MetaCo
Martitrack Panbiogeograph
Applications
Work
Replies to Criticism
Multimodel Selection
Search Encounter
Cenomanian
TinkerPopPanbiogeography
Track Analysis beyond Pan

Edges

Can a graphdatabase edge traversal demonstrate a common vicariance in two genera that overlap?



Finding edges based on quantifiable overlap:
 

Panbiogeographic Tracks

A track is a representation of the spatial form of a species distribution and can give insights into the spatial processes that generated that distribution.

A species distribution may appear as a collection of localites mapped, an outline of an area inhabitated or an inline track.

The track graph is often drawn as a minimal spanning tree of the collection localites but other spatial track form  formats are possible. 

Tracks can be categorized into individual (when one speces or form is considered) and generalized (when more than one are combined in some way.

panbiog graph database setup.bmp

One can then use the graphdatabase of individual tracks to create the observation search path of different generalized tracks.  One then creaes a multimodel set and model average to find better panbiogeographic generators for tree c onstructions.


The distributional generator can include vicariant ramification at nodes connected by track segments.  Thus the world map by Croizat might serve to illustrate a representaion with five vicariant foci capable of distributing species into the geographies conneted by adjacent line tracks.

croizat ontology.bmp

Heads' last two books suggest that a small number of geographic nodes are responsible for a large percentage of the nested vicariant patterns retracted from history.

A graph traversal of the entire mutatble set of pigtail shaped graphs is the generalized track as a search en ounter path.

The panbiogeographic track can be seen as the search encounter path.  A more generalized track can be then considered as a better predictor for search encounter data and multinomial representation when melded with taxanomic data an hypothesis of trajectory.

That however is built up of many individual tracks which then posses definite track wdiths so as to accomodate the variance in the other Cc oncepts included in the then current database.

 If vicariance is considered the sole cause of the multiplication of the geogrpahy in to the biogeograpy the distinction of the node size and shape and the track width becomes one and the same concept. 

This is where the ecology of metacommunity dispersals and range overlap of evolutionary tectonicalteration meet and the SCR modeling of the geology and disperals as two different covariates can be used to further refine the taxonomic tree setssuffenicient for the data then provbisioned.

At this time in the understood panbiogeographic plexus/work the interface with phlylogeography as(This term was introduced to describe geographically structured genetic signals within and among species.) will be apparent.

It is the track and its widith which will be challenging phylogeographic scenerios not the node which addressesw entire metapopulation and metacommunity issues rather than smaller scale migrations and within population geneneti  popluation sgtructure of deme movoements.


 Panbiogeography is thus largerly about correlting tracks, nodes, masseses and baselines with patterns of speciation in space and time.


Panbiogeography originally proposed by the French-Italian scholar Léon Croizat (1894–1982),[1][2] is a cartographic approach to biogeography that basically plots distributions of a particular taxon or group of taxa on maps and connects the disjunct distribution areas or collection localities together with lines called tracks. A track is the graphic representation of the spatial structure present in a distribution with respect to the minimum distances between the individual localities of a taxon. The track identifies those sectors of space that are most closely associated with origin and differentiation.  The individual localites can be considered as incidence geometric points.

"The appeal, and perhaps the pitfall, of track construction is its simplicity. As a method it is so easy that 'anyone' can do it for any group of organisms.

The individual track is a spatial representation of the evolutionary space of a particular genetic continuum. Nodes exist between and amongst individual tracks.

Node kinds.bmp

"The most frequent form of track construction formalizes the track as a line graph called a minimal spanning tree in which the shortest possible line is drawn between disjunct localities (Page, 1987;Craw and Page, 1988).

A track is a representation of the spatial form of a species distribution and can give insights into the spatial processes that generated that distribution.  These process can include the vicariant formation of nodes connected by individual track segments.




Vicariant nodes.bmp


Individual Tracks

Generalized Tracks

The principal conceptual tools are the track, node, baseline, and main massing. There are a substantial number of publications where panbiogeographic methodology is described and explored. Craw et al (1999) provide an overview of methods applied up to that time. Subsequent efforts have focused on providing further algorthims for combining individual tracks into generalized (standard) tracks. This page will, therefore, present only a brief illustration of the principal descriptive steps in track construction.

Published Tracks​​