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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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Areas -What would a systematics of area names be qualified by?  Should it be based on forms (substances categorized) or forces (sets of moving possibilities)? How can multi-model inference get historical biogeography beyond null hypothesis testing, the simple difference of sympatric vs allopatric speciation models, and naive notions of a "node"?



 
If it is to be based on the moving forces involved,  then the forces (regardless of the forms) that are postulated to equilibrate in Island Biogeography are clearly fully criticizabld. Micael Heads has done this globally. One of the needed elucidations (there are a few) that Michael Heads provides in Molecular Panbiogeography of the Tropics is a demonstrable positioning of Island Biogeography in such a manner that further criticisms of it seem inevitable region by region. Croizat’s discussion of islands in the Caribbean and beyond can emplace that equilibrium (inspired from Darlington) into a different structure.





 

John Grehan was well aware of Michael Heads’ critique of Island Biogeography well back in 2009 at least.

http://mailman.nhm.ku.edu/pipermail/taxacom/2009-June/065517.html

 

“I also thought Robin's observations were on the mark. I have found that quite a few biogeographers think panbiogeographically and apply panbiogeographic principles and even methods even though they may not be aware of it.

 

I will be interested to see Michael Ivies comments on Heads' constructive posting about Caribbean biogeography, and island biogeography in particular.

 

[Taxacom] panbiogeography critique  John Grehan Mon Jun 29 07:35:08 CDT 2009


The general application of equilibrium is fully mis-taken in the foreground of thinking that links evolution (lexically Darwin’s) to the perspective of Earth and life evolving together whether in a metapopulation or across ecological communites or not.  Immigration and Colonization are different locomotions or translations in space. Current generalized attempts at thinking about equilibria (tracing back to Lotka in some way) are just talking past each other, failing to find a common voice and remaining plurivocal.


One may blame this on simple mispopularization but the issue is much deeper.



It involves not only a proper choice but  a needed biophilosophy that leaves room for methods that search for repeatable geographic patterns and propose “laws” or full explanantions for their existence.



Here are panbiogeographic elements needed to analyze the distribution of pit-vipers in the area of Middle America, recently reconsidered by Castoe et. al. (2009). The elements are purely geographic but read as panbio - geographic and yet the species distributions are not the geography contra comparative biogeography.  Carrying the synthesis farther implies one is able to differentiate the geographic congruence from the biogeographic congruence. This may be approached by further analzing the incidences in the difference of intra and inter species tracks as written by Croizat in Chapter 7 of Panbiogeography.
 
Thus panbiogeography may indeed contribute "clear evidence" or "consensus" for when and how the area of Middle America has broadly shaped biodiversity.  This has not emerged because the hierarchical implications in the flexible labeling of panbiog elements has not recieved significant attention in part due to faulty definitions of "station" and "habitation." Renewed attention by Heads has helped give clarity in the opening chapters of Molecular Panbiogeography of the Tropics.  Here he also writes, " Vicariance interpretations of phylogenetic sequences are given in some recent literature.  For example, in the New World snake Bothriechis, eariler studies deduced a process of dispersal from Costa Rica to southern Mexico.  Instead Casote.et. al. (2009: 98) interpreted the phylogeny as indicating " a more simplistic northward progression of cladogenesis that requires no inference of dispersal (italics addded).  A similar pattern is also seen in other snakes of the area, "suggesting vicariance as the primary driving force underlying speciation."  The Great American Biotic Interchange theory proposes dispersal across Central America, so the idea that evolution in the region may not have involved physical movement is of special interest....The same method of interpreting phylogeny used in these papers is used here." (page 19)
 
Parenti and Ebach stress repeatedly a supposed conceptual difference of area homology from spatial homology sensu Croizat (1952). There is no doubt that there are spatio-temporal relationships among geographic distribution localities that may be independent of true biotic relationships. 


 Showing that a concepts are distinct is not the same logically as having a distinct concept however. Parenti and Ebach do not indicate how area simillarity (based supposedly on "Croizat" spatial homology) and area homology may be cognized to grade into one another. This will come into play when panbiogeography may be applied off earth for sure.

 Their point of view is limited to some extent  by the way they intend geology and biology to be integrated in comparative biogeography. So as an example they offer eel distributions (east and west coast of the northern Atlantic Ocean) as to represent their interpretation of spatial homology : "we may draw a line, or baseline, to unite these two areas and propose that they were previously connected, either by land bridges or as formerly joined continents; they share a spatio-temporal relationship" (op. cit. page 43).
 
 Contrarily, area homologies are supposed to be a kind of space homology which depict explictly  "biotic' realtionships in the same space. This confusion is due to the general failure to appreciate Kant's point that compositions of velocities (which involved distance over time) need not necessarily compound in the same nested ways that spaces within spaces or areas do.  Comparative biogeography sought to found without natural law, a natural classification of areas where it was observed for the distance no matter the time that this need notnecessarily be thought of in terms of interbreeding.  While this is true, in the particular, it does not generalize in space for any possible velocity (no matter the 3-dimensionality) because soon as one is willing to give dimensionality to lines between one and two the confusion appears.  It may very well be  indeed that the various panbiogeographic concepts of track, node, mass, baseline compound differently for different taxa in the same area homology due to different overlaps of area similarities and area homologies within component monophylys.  I will try to make this clear by using another example Parenti and Ebah offer on both sides of the Atlantic, that of the salmon.

According to Parenti and Ebach the link between areas "a" and "f" indicate area similarity only. I will show various historical scenarios that will offer attributing connections among the boxed areas to different groups of the alpha, beta, and x angles diagrammed above. This will result in area similarities becoming restricted in the geographic latitudes and longitudes they can contain, as specific area homologies are constructed and historical biogeographic trajectories are proposed. Making a rigid demarcation constrains how space itself may assist the classification.
 
This issue is one of the relation of the grids used to outline the structure of the domains that may have congruent areas as discussed for instance by Henri Lebesque.  Area homology (domains and congruence) depends per similarity (unit square (lat/lomg) and grid per track, node, mass, baseline) on the conditions listed on the last page below. There is even a possibility of using transcendental numbers to do just what Lebesque "feared" thus the need to stick to the conditions listed.

Subjectively indetifying a node (as an angle) in a distributed mass collected from an area.



 Is there one node and two tracks here? Are there two tracks and three nodes or just one track with a large width?  Is this data of an underlying sequence of models collapsed into the present?