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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
Longicauda Like
Lucifuga Like
Spelae Like
Multiplicata LIke
Dorsalis like
Dermatemys like
Generalized Tracks
Taxogeny
Nodes
Edges
Distributions
Propositions
CREADer
Areas
Main Massings
Geology
Track Analysis and MetaCo
Martitrack Panbiogeograph
Applications
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Multimodel Selection
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Cenomanian
TinkerPopPanbiogeography
Track Analysis beyond Pan

 Individual Track Formation


"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).

The individual track is a spatial representation of the evolutionary space of a particular genetic continuum.

The minimal spanning criterion is applied in the absence of other information such as phylogenetic relationship where the line graph may first connect points between most closely related taxa."
John Grehan (Introductory Panbiogeography)











Constructing tracks.

"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.


Tracks are simply a graphic representation of the spatial structure present in a distribution.




Where different taxa are concerned, the track provides a representation of the spatial structure relevant to the evolutionary differentation of those taxa.


In other words, space and time are integral to the evolution of physical or biological form."



Another characterization of track constuctability is:


"The "tracks" are lines connecting areas which contain many disjunct species in unrelated taxanomic groups"


Since tracks represent both a spatial representation of a genetic continuum and may connect points areally of most closely related taxa, tracks with a defined width may express differences in biogeographic congruence differentiated (often by vicariance)  in multiple groups in the same graph,  provided the generalization of individual tracks have different relationships to nodes, masses and baselines in the generalized track thus presented as it crosses the region.




There seems to be a trend but also an outlier that is not nested. Is this one individual track, a generalized track with a node or something else? or from Terrepene c. carolina below.  Are other semantics that related individual tracks to masses through nodes associated with baselines possible? (not pictured)




Here I will show a use of a (Conway)nim sum (find same locations for compared tracks and delete, then find the sum or minimal span of the remaining localities) like function of multiple individual tracks (where different scales are considered for deletion). This  provides a estimate of track width and an outline of the geography of the nodes (beyond the individual track towards the genearlized one).







 Published Tracks:
Geographic information systems and spatial analysis:
a combined method for panbiogeographic studies by Jonathan Liria





- construct Individual Tracks given any two Collection Localities -