offers an application of incidence geometry to historical biogeography by defining collection localities as points, tracks as lines and generalized tracks as planes.

Species can have different edges if the nodes are simply shaped differently. On Using Graphdatabase Traversals to define the
Panbiogeographic Node

Panbiogeography is a discipline of historical biogeography
begun by Leon Croizat (1952, 1958,1964,1976). Various theoretical papers that
attempt to quantify a process of doing panbiogeography have been published
(Henderson, Page,). Software to assist in implementations of various stages in
the praxis have also been created (Croizat, Martitracks).

It has been noticed that the Panbiogeographic
concept of the node was used primarily as a link between two tracks (Nelson,Morrone,
as implemented in Martitracks).This
interpretation has led comparative biogeographers to criticize the
epistemological value of panbiogeography (Ebach and Parenti).Here a graphdatabase traversal representation
of the Panbiogeographic node is scoped in such a way that the slightly
different concept of the node (as used by Heads (MPT) and reviewed by
Nelson(x)) is supported. Its
presentation with respect to creating generalized tracks permits both a further
quantification of panbiogeography and better comparison to the cladogram node.

The rise of big
data and the establishment of the NOSQL landscape has led to the solidification
of graph databases as a viable option for storing and retrieving data.Panbiogeographic tracks have always been thought
to be related to graphs (Page, --Craw, Grehan, Heads) and the possibility of
utilizing graphbasedtechnology within the graphic basis of panbiogeography calls for
incorporation just as much as Page’s thought that Google Earth should be able
to reinvigorate panbiogeography. Rodriguez- - Reasoning can be gainsaid with "an algorithm by which implicit knowledge is made explict" in the process of understanding. Graph traversals permit the implicity knowledge embedded in maps by Croizat to become explicit and extends an authentic extermalized panbiogeographic sense with the incorporation of new data not used by Croizat and those immediately following him.

With the node
being possibly not simply the connecting collection locality between two
minimal spans but rather is used in panbiogeography as the node of a cladogram
is (some logical junction between sister clades) it becomes possible to
consider the Panbiogeographic node as an edge between two verticies where the
verticies are the tracks themselves.This might not have seemed a likely lexicology for track graphs before
the creation of graph databases able to implement single relational algorithms
but with the creation of transforms from multirelational graphs to
singlerelational graphs the multiple nodes that any analysis must produce both
become representable and analyzable.Software permits synthesis with graphic presentations that can enhance
the publication value and semantic content of Panbiogeographic works. More than
one node per track requires multiple edge types (one per node).

Under this new
demonstable Panbiogeographic node the older published nodes can be
reinterpreted. Graph traversal with graph map statistics permit
reinterpretations. It is also possible that graph traversals may permit
geographic distributions to serve as predictors of species collection locality probabilities
contrary to the opinion of Ebach and Parenti.

Panbiogeographic
nodes as graph database edges

Articles that
published Panbiogeographic nodes – reinterpretations

Panbiogeographic Nodes

The area where two or more generalized tracks intersect is called node.

This
area is a focus for historical biogeography but if vicariance is the
supposed means, the breakage locations rather than the area can
nontheless inform the development of further knoweldge. This place
earlier thought of only as an area of endemism can be concieved in more
complicated ways using morphometry where a bifurcation is proposed to operate vicariant time.

Heads has pointed out that vicariance can still explain a distribution to an island even when there is no monophyly.

Panbiogeography
has seen a conversation that has moved from point by point comparisons
of geographic distributions considered as areas of endemism where tracks
connecting them as lines had nodes in between to one in which the node
was thought more “like” a root or node as found in cladograms.
Vicariance splits the direction to sisters there-through. This change
from "older panbiogeography" depends crucially on how the individual
tracks compound into the generalized tracks and thus how the notion of a
node as the junction between two different tracks whether individual or
general changes when a certain number of drawn indiviudal tracks
combine to form the generalized track,

Axoimatic
panbiogeography is an attempt create a sophisticated mathematical
organon to organize these new panbiogeographic insights.

This
conversation is poised to continue to transfigure itself with a
further incorporation of the mass and the baseline as the modern
discipline of graph databases is applied to Page’s 1987 proposal to
consider generalized tracks as an application of graph theory to
biogeography. In this direction, authentic panbiogeography (whether
supported by one notion of congruence or not) can clearly differentiate
itself from other techniques in historical biogeography. It will be
possible to query the node’s attributes directly and find how related
they are to masses and baselines of others.

This
conversational clinanmen can be illustrated simply from Fig3 in Page’s
paper (below) which displays the difference of the Steiner and Minimal
spanning trees.

Nodes were majorly disussed
simply as the collection locality (third) between two others – as the
vertex of a graph but since they have begun to take on properties of
their own, as in the the average between two collection localities as
defined in the steiner tree.

The
next stage will consider drawing the node around multiple collection
localites polyphyletically and creating a graph database of the species
and nodes.

Axiomatic
panbiogeography contains a large enough theoretical space for this
conversation to proceed and search encounter panbiogeography offers a
means to statstically show how geology interrelates with the new
generalized track nodes with masses.

This
view of the node of the generalized tracks thus binds the notion of
center of origin of a hypothetical group to all 5 placements suggested
by Heads

(in
the region of the oldest fossil, in the area of the most advanced
"form", in the area of the most "primative" form, or in the area of the
basal group. Haeckel had the idea that evolution could be divided into
descent (areas of the basal groups viewed often where the oldest fossil
might have been found and migration or motion of the species as its form
deviated through time (primative vs advanced forms).

This
division is not logically necessary since semantically informed syntax
of math used panbiogeogrpahically can seperate that kind of kinematics
without the conceptual bagggage and cladistic difficulty of sustaining
primatve vs advanced or primary vs secondary forms. This is needed
because beyond this uniformity availabe mathematically lies the baseline
that directs the tracks, nodes, masses as a graph database in a certain
directionality. This appears to have been unavailable to Darwin
(focused as he was on natural selection and adaptation) but glimpsed by
the sublime insight of Leon Croizat who threw off many a concept to
sustain the intensity of creativity used to adroitly sustain what
certainly others had thought but none had managed to narrate in enough
detail to last.

So once
the antinode (Henderson) areas are clearly delimited then the effect of
the mass/density of tracks/points (as a covariate along with historical
geology data) can be used to designate track witdths throughout the
search encounter panbiogeography and the confluence of different
baselines into the same biogeography can be assessed. So one could ask
do the Rattites and Nothofagus share a common baseline geopgraphically
or not? This was not possible for Darwin.

Predictions of
species collection locality probability based on graph object abstraction data
egest where Panbiogeographic masses are used to constrain the node-anti node
self similarity a and distribute
probability of occurrence back to the track vertecies (all nearest neighbor verticies
of the nodes egested on mass input.)Nelson has
questioned the use of Croizat main massings as usable concept in
panbiogeography. Here the new notion of graph traversal node is applied to a
use case for the main massing that leads to constraint on the node anti-node
space with the graph database in such a way that species location predications
can be made from graph databases that contain heterogeneous phyla tracks subjected
to nodes as edges definitions applied.

Use of Panbiogeographic
graphdatabase traversals (node in clade
related to Panbiogeographic edge node )to compare phylogenetic trees. Alpha, Beta and Gamma angles per collection locality (which map the geography of V to V+E) are a part of description logics whereat inferable subsumption relationships in the structure exist. These relationships enable translation between the panbiogeographic track graph the clade/phlylogenetic tree.

Use of Panbiogeographic
subgraphs as patterns for other non-panbiogeographic domain searches. "The structure a graph takes in the real-world determines the efficiency of the operations that are applied to it." http://arxiv.org/pdf/1004.1001.pdf The structure of panbiogphlyo graphs may assist in the efficient applications of graphs in other ranges for the same "domain"

Guest Editorial:
Panbiogeography from Tracks to Ocean Basins: Evolving Perspectives Author(s):
John R. Grehan Source: Journal of Biogeography, Vol. 28, No. 4 (Apr., 2001),
pp. 413-429

to display the
new perspective for the node developed here. One takes a distribution map and
creates the minimal span on this set getting (b).A panbiogeographic node has been thought of
as one of the vertices in b that connects two other minimal spans.Here we will look at it as one of edges instead.

One simply
creates the minspans for a taxa collection localitity data of any degree in the
linnean hierarchy and maps it along with another taxa in the same general
geographic region/area.One defines the
collection locality 2-D place where these min spans appear to overlap (using
other programs such as martitracks if desired).The taxa minspans become the vertices in the graph database and overlaps
become the edges and are the now refined Panbiogeographic node capable of comparison
and use conjunction with the cladogenic node.

One can think of a Panbiogeographic Atlas combined with a
phylogenetic tree as a graph database traversal which structures the graph such
that the biogeography informs the ancestor-descendent linkages in which the traversal
assumed were already passed.One of the applications
of axiomatic panbiogeography through the Atlas will be in the creation of specialized traversals
that can used on arbitrary graphs to help locate particular data objects
namable panbiogeographically.Thus
Croizat’s Carribean Node may instruct the location of a comparably structured
path in some completely non-biological graph.There will classifications of part breadth and part depth first
traversals with known biogeographic baseline rooting otherwise treed
phylogenetically.These will represent
forces rather the forms purely. Robinson failed to relate genetic algebra to infintesimals but this possible to do in graph databases. The route followed by traversal can be the track^node^mass^baseline determined biogeograpically as the "root" that references the third party graph created duing the 'walk' over the graph. insofar as vicariance is incorporated into the panbiog concepts applied the traversal will be biased towards breadth first processing (unlees the geography matches the phylogeny used).

Finding a generalized track within a edge scaled graph database of distributions noded is precisely the problem of matching and de-duplication (Is Bill Clinton and William Clinton the same person?) -- a function presently unsupported by graph database vendors. An average path that converges as one scales can represent a "match" and any paths within a set standard deviation amount would be considered for "de-duplication".

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