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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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NODES







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.

two lined node.bmp

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.

Geographic Catastrophe Biogeography.bmp

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.​

                      Croizat64track.png


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.


beechratitie.png


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

One can use the Figure 1 of Grehan in

http://www.sciencebuff.org/content/files/science-pdf/grehan_pdf/Grehan2001TrackstoOceanBasins.pdf

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).





CROIZAT, L. (1952). Manual of Phytogeography. W. Junk, The Hague.

CROIZAT, L. (1958). Panbiogeography. Published by the author, Caracas.

CROIZAT, L. (1964). Space, Time, Form: The Biological Synthesis. Published by the author, Caracas.


CROIZAT, L. (1976). Biogeografia analitica y sintetica ("Panbiogeografia") de las Americas. Boletin de la Academia de Ciencias Fisicas Matematicas y Naturales35, 1-890.


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".