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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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Track Analysis beyond Pan

Martitrack Panbiogeography 
 
"This project uses well documented geometrical functions to evaluate congruence between tracks (=MST) and therefore perform a Panbiogeographical analysis. Although the origin is Panbiogeography, the program could be used to evaluate common patters as Areas of Endemism or Design of Conservation reserves or Primary Homology (in a biogheographical context).

"Therefore, the spatial congruence among MSTs is the criterion to define whether a generalized track exists; if a species is not congruent with the remaining species, no generalized tracks are generated. Once, all species are compared and some levels of congruence are detected, a generalized track is created."

There is some need to be able to construct generalized tracks even in cases when these functions do not pinpoint a generalization.

Any program that attempts to implement Croizat's method (by any name) will come up against Kant's "The composition of motions, in order to determine their relation to others as quantity, must take place according to the rules of congruity, which is only possible, in all three cases, by means of the motion of the space that is congruous with one of the two given motions, whereby both are congruous with the compound (motion)."






By copying and pasting the url for these above files (click on the links and copy the url) into the search box on google maps one can obtain the map below for instance.


Axiomatic panbiogeography offers authentic panbiogeographers a larger mathematical/logical unity from which to extend constructions of hierarchical relationships within the domain of historical biogeography than that described by Daniel Rafael Miranda-Esquivel and Susy Echeverria. 


Although qualified as to “approach” the authors  wrote:“The Panbiogeographic method involves basically three main steps (Morrone, 2004): Firstly, construction of two or more taxon individual tracks (minimum spanning tree from distributional localities).  Secondly, delimitation of generalized tracks through geographic congruence between individual tracks.  Finally, determination of nodes within the intersection areas between generalized tracks.”

In axiomatic panbiogeography the notion of the generalized track is more general than this.

One begins with the notion of the point or collection locality, the line or individual track and the generalized track or incidence geometrical equivalent of the plane. The intersection “areas” between generalized tracks can better be cognized as a 3-dimensional entity if the hierarchical relationships among the distribution patterns becomes complex. How complex this needs to be for the benefit of axiomatic panbiogeography to apply is likely to be found to be in those cases where simple catastrophes fail to topologize the mathematical range of the points in the domain.

The three-fold method of: individual track construction,  composite track interpolation  and node junctioning, results in hierarchies only so deep


but is useful in investigations where multiple baselines are not needed or where there is little relationship between nodes and masses conceptually.

This methodological procedure does not divide out the third phoronomic (angle) case from the first two amongst the points.


So pictured for instance(of lizard, snake,and salamander ("with two nodes")) is a map with a  generalized track , two nodes and individual tracks that could not be used to elucidate the catastrophe model of the same track suggested( below) if the hierarchical relationships where only expanded under the three fold implementation of Martitracks with Pantracks,as applied

in the case of the junction between tracks from Plethodon and Eurycea in the same area suggested again below where the node itself takes on different "shapes".

This is about the most complex type of pattern one can reliably use the Martitrack program with- 

The Martitrack program may help to identify otherwise obscured endemic areas.

A small difference in the general track is seen with a cut value of .01 rather than the default .25 showing a closer representation to the projective origin

 

 

 

 




Systematics and Biodiversity

Volume 11, Issue 3, 2013

DOI:
10.1080/14772000.2013.834488
Augusto Ferraria, Kim R. Barãoa & Felipe L. Simõesa

pages 285-302


"Panbiogeography represents the spatial congruence among species distributions by means of generalized tracks. Some critics have suggested the method fails to objectively evaluate congruence, being neither repeatable nor falsifiable. The MartiTracks software was proposed to address spatial congruence using geometric properties as a counterpoint to the manual procedures so far employed in generalized track obtainment. To evaluate whether MartiTracks is a reliable alternative to the congruence problem in the quantitative panbiogeographic approach, we tested the software parameters with three analysis schemes under two real datasets. Then, we proceeded to a comparison of the results to those produced from Parsimony Analysis of Endemicity (PAE) and Clique Analysis, two quantitative methods which are based in predefined biogeographic areas or in the employment of grid cells. For PAE we used both analytical units, while Clique Analysis was restricted to grid cells. Through this, we aimed to comparatively evaluate the criteria of spatial congruence in different approaches. For each dataset and method, significantly different tracks resulted, highlighting the disparate congruence criteria among panbiogeographic approaches. Despite PAE ending up as the most reliable of the tools tested, it is still far from solving panbiogeographic congruence. The main focus of this paper, MartiTracks, is indeed a tool that makes minimum spanning tree construction a repeatable and easy-to-visualize process, but stumbles upon its obscure procedures of generalized track obtainment, congruence criteria, subjective parameter definition, the unclear implications of employing said parameters, and dubious results. Our results suggest that the subjectivity of the parameter setup process substantially influences the results, biasing them to the user-desired level of congruence. That the software produces fast and easy-to-visualize results does not make it a definitive solution to the problem of quantitative panbiogeographic approaches."

 



The code is available here

The Martitrack Manual

 

croizat0.kml

croizat1.kml

track1-joint2.kml

join1-track1-joint2.kml

By copying and pasting the url for these above files (click on the links and copy the url) into the search box on google maps one can obtain the map below for instance.

 

If you are interested in this website hosting kml files created with Pantrack of Martitracks please use the contact form.

 

 

Axiomatic panbiogeography offers authentic panbiogeographers a larger mathematical/logical unity from which to extend constructions of hierarchical relationships within the domain of historical biogeography than that described by Daniel Rafael Miranda-Esquivel and Susy Echeverria.  Although qualified as to “approach” the authors  wrote:“The Panbiogeographic method involves basically three main steps (Morrone, 2004): Firstly, construction of two or more taxon individual tracks (minimum spanning tree from distributional localities).  Secondly, delimitation of generalized tracks through geographic congruence between individual tracks.  Finally, determination of nodes within the intersection areas between generalized tracks.”

In axiomatic panbiogeography the notion of the generalized track is more general than this. One begins with the notion of the point or collection locality, the line or individual track and the generalized track or incidence geometrical equivalent of the plane. The intersection “areas” between generalized tracks can better be cognized as a 3-dimensional entity if the hierarchical relationships among the distribution patterns becomes complex. How complex this needs to be for the benefit of axiomatic panbiogeography to apply is likely to be found to be in those cases where simple catastrophes fail to topologize the mathematical range of the points in the domain.

The three-fold method of: individual track construction,  composite track interpolation  and node junctioning, results in hierarchies only so deep but is useful in investigations where multiple baselines are not needed or where there is little relationship between nodes and masses conceptually. This methodological procedure does not divide out the third phoronomic (angle) case from the first two amongst the points.

So pictured to the right for instance(of lizard, snake,and salamander ("with two nodes")) is a map with a  generalized track , two nodes and individual tracks that could not be used to eluicidate the catastrophe model of the same track suggested below if the hierarchical relationships where only expanded under the three fold implementation of Martitracks with Pantracks,as applied

in the case of the junction between tracks from Plethodon and Eurycea in the same area suggested again below where the node itself takes on different "shapes".

This is about the most complex type of pattern one can reliably use the Martitrack program with- 

The Martitrack program may help to identify otherwise obscured enemic areas.

A small difference in the general track is seen with a cut value of .01 rather than the default .25 showing a closer representation to the projective origin

 

 

 

 

MartiTracks is helpful in promoting the idea of the generalized track in panbiogeography and useful when looking for potentially dense track areas or masses.

I have been using it on Windows.

Thanks for calling attention to the program
. Also, if anyone needs some space to host KML files let me know.
Brad McFall




A panbiogeographical explanation of the disjunct distribution of Fagus (Fagaceae) in the northern temperate zone
WANG Li-Na1, JIANG Xiao-Long2, LEI Yun1*, and ZHANG Ming-Li2,3*
Chinese Journal of Plant Ecology2012, Vol. 36Issue (5):393-402    DOI: 10.3724/SP.J.1258.2012.00393

Methods Distribution data of 581 records of 10 species were obtained from herbaria and monographs. Track analysis of panbiogeography and software MartiTrack were used for data analysis.

Important findings Results indicated that there was no generalized track linking the distributions among China, Japan, Europe and North America or even between China and Japan, two adjacent areas in East Asia. Two regional generalized tracks were only found within China and Japan. These facts imply that the Fagus distribution cannot be explained by dispersal. Dispersal probably only occurred in limited and/or local regions and not as dispersal across the northern temperate zone in the Tertiary. The disjunction most likely resulted from (1) geological historical events such as Tethys westward movement, Qinghai-Tibet Plateau uplift, and Asian monsoon action, (2) climate change since the Tertiary, especially climate fluctuation during Quaternary glaciation, and (3) Fagus biological characteristics with regard to humid and temperate climate and annual rainfall.



 The creation of this output appears to be motivated in the nameable Kantian expression (Metaphysics of Nature ("All geometrical construction of complete identity rests on congruity")).  There is no doubt that the martitrack project attempts to improve the intuition congruity brings to biogeography.  This is why it claims to have application in the general formation of generalized tracks, creation of areas of endemism and in the design of conservation reserves.  The program and project offers a meands to suggest similarity and equality. It may be helpful in discriminating between barriers and boundaries. One difficulty is the imposition of the moving cause within the program's coding but there is no doubt that this program works towards notions with unity in both the generalized trackline and direction but as for the totality of directions, as well as the plurality of directions in any one line or segment of a line, continued work will need to be conducted since as Kant said, "Geometrical construction demands that one quantity should be identical with the other, or two quantities in composition, with a third, not that they should pronounce the third as causes, which would be mechanical (as opposed to "phoronomic") construction."

 

 

 

 

 

 

 

 

 I expect as I work through all of the parameters, the martitracks representation of Desmognathus tracks

will be unable to sustain the reticulations otherwise suggested panbiogeographically, when compared with Plethodon and Eurycea in the same homologous area. It is not strictly the case that software and analyses must "evolve" together as the naked eye is capable of still significant insights.

 This is the "naked eye" structure that MartiTracks will likely be unable to sustain and support pantrackically.

 http://bioinformatica26.blogspot.com/2011/03/biogeografia-y-martitracks.html

requests one not to be negative but seeing how martitracks treats Plethodon glutinosis distributions it is hard to find only a silver lining.

Comparison of Panbiogeographic track creation

Figure 7. Panbiogeographical analysis of the genus Bomarea (Alstroemeriaceae).

A. The five generalized tracks obtained with the following parameters: cut value = 2, lmin = 2.5, lmax = 3. lmax.line = 4, and min-SI = 0.8 in MartiTracks. B. Generalized tracks from Alzate et al. [25].