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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
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Quaternion Algebraic Geom
Primate Vicariances
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Main Massings
Track Analysis and MetaCo
Martitrack Panbiogeograph
Replies to Criticism
Multimodel Selection
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Track Analysis beyond Pan

Last week I attended a Spatial Capture Recapture workshop at Cornell.

It appeared to me that by analogizing home ranges to individual tracks and using a generalized track of track parts,nodes, and masses for the detection devices, the work of axiomatic panbiogeography can be embodied such that geology as density covariates can be incorporated in towards future changes to generalized track delineations. I have only been able to think of this in an ad hoc way before. I had at first thought that the techniques of modeling search-encounter data converted into search encounter panbiogeography could be used to produce an unbiased example of Croizat's idea that life and earth evolve together by using the set of individual tracks to serve as the encounter devices (red lines below) but Andy Royle had a hard time cognizing that proposal as I first presented it because of a lack of clear independence between the "traps"  or search paths and the available "activity centers" in the analogy as displayed in the image below.

Recent developments in spatial mark –recapture offer a glimpse of how panbiogeography may become relevant to the day to day working of ecologists as well as providing a frame from within which differences of Panbiogeographic discipline may b e worked out.  First we demonstrate how the general approach of using parameters of observered AND unobserved (probability of detection) in standard mark recapture can be used to demonstrate Croizat’s idea that Earth and Life evolve together. And then we show how spatial technquies including search encounter methods as well as grouped activity centers can be used to  integrate individual tracks into generalized tracks and also provides a means to use release cohorts to map vicariance to track width.  The use of a limit of N for a best model as more data are added offer a statstic that is property of the track. Ascertaining how form-making reaches this limit when any number of taxa are used is now a positive prospect for panbiogeography. Does it happen by internal vicariance of some kind of metacommunity co-evolutionary kinematics or a coordinatable multiple species dynamics caused by competition and/or cooperation.  Panbiogeography is thus not detrimental at all.  Further it is explained that Darwin’s thought on geographic distribution is not counter to panbiogeography in this application indicated here since the mark recapture notion of extinction with no speciation forward being equivalent to speciation with no extinction backward can be read out of the Origin.

Darwin suggested that space usage is not as  powerful as natural selection in correlation to changes in populations with respect to a given area (page 109), in other words that natural selection of biotic potential determines space usage which will exclude others not in the evolving lineage that is experiencing the current increase and not that space itself through vicariant splitting determines some aspect of actual biotic increases.  Panbiogoegraphy allows for this possibility and SCR modeles adapted provide a means to relate this actual space usage in ecological realities that are then subject to natural selection and possible competitive exclusion based on space or habitat area or some other resource. The new modeling environment makes it possible to realize Darwin’s view that spatially correlated (density covarties of activity centers) may be synced with historically achieved vicariant speciations so as to result in utter extinction going forward which is the same thing as all speciation going forward but und er the vicariant rather than dispersal view of the filling of the space.  Darwin supposed but did not seem to believe that the number of specific forms could go on “perpetually and almost indefinitely increasing” but the formations of spatial usage can if heritable.  By demonstrating how space usage may increase in salamander lineages we go towards showing that while Darwin was in the need explain why we don’t see  a lot of transitional forms in thegeo record it need not be because the  variation in specific forms  OF SPACE USAGE can not be larger than he supposed.  What Darwin could have done is to recognize that space usage as a trait greatly increases the kinds of forms per phenotype but only if form-making is not soley conceived as a biotic competition predation but may be cooperation in space and or seem to have mis thought because of the way he thought of speciation itself (blending) which would decrease the form-making specification possiblites relatve to any model that diverges with motion in space. Fisher however misempahsized the possibilities for discrete inheritance which may include some kinds of Darwin’s blending under specific assumptions about the relation of the vicariance to form-making which may or maynot be true. Sotheing that can be investigated later.  Thus under Darwin’s view given lack of indefinite increase in spatial forms and limited  number of Earth places per surface area rather than the vicariant increase spatial trait possibilities through increased survival time he supposed that while there was likely still time for more increases in species numbers this number had to be limited.  The model approach here shows that number as N per track when tracks are constructed for the entire globe but how to realize the possible indefinite increase in space usage remains the ongoing project.  This will also inform our estimates of how many other species different supposed densities of human populations will allow (provided extra terrestrial development does not alter this space usage function). It may not be as Darwin supposed that the species most numerous in dividuals have the best chance of producing per given future period the most favourable of variations.  Some speices are pandistributional and thus might be thought to fit this description but as the globe gets filled and we assume not life off the Earth intereacting with us,  those space usages that can fill places where environmental fluctuations (lots of hot or cold, no water or too much water) are largemay be those that can stochastically evolve (perhaps with our help) through space usage oscillations into forms able to survive on those places not already filled and/or off Earth.

Not sure yet if this linearization works (guessing locations, not in a line, steps not necessarily even with geology etc. but this is the idea.

Panbiogeography can thus be not only an historical biogeographic discipline but a prospective  evolutionary instruction.


Conclusion : the non constructive criticism of panbiogeography is uncalled for as it undermines the prospect of expanding our knowledge of time based on space as well as our understanding of the the interaction of form-making as a whole when considered outside the origin of life issue.

While thinking about the analogy between spatial mark-recapture and the Croizat "method," it is possible to realize (that for/with a constant intensity function ) panbiogeography with an indeterminate number of baselines (axiomatic panbiog off Earth) a Poisson point process is appropriate while in Croizat's time and using the records he considered only a binomial homogenous point process would be thought.

There has been criticism of Croizat’s work and that developed since his time but none has been as strong as Waters et al who state, “we argue that “panbiogeographic” studies of spatiotemporal biological history (e.g., Craw 1988; Heads 2010a, 2010b, 2011, 2012a, 2012b) are detrimental to the progress of biogeography as a discipline.”

They attempt to say what panbiogeography “usually is” without showing differences of opinions within panbiogeography  such as Marti Track vs Others ().  The issue of congruence in track analysis is embedded in this different use/representation  of state-space.  With no nodes the number of individual tracks in a generalized track is likely to be less.


The criticism suspects that the ontology arises only within the narrow confines of assumed ancient vicariance. While this is surely possible and appears often the easiest way to intuit organizationallly it is only that as masses are added that N may be better thought of random rather than fixed per the Earth's present number of ocean basins ( when the intensity varies).  It is easy to visualize a recursive ancient (beyond our current knowledge) between the baseline point and the project space it implies.

Here by the use of modern statistical techniques it is possible to see how panbiogeography can proceed without having to rely only on old vicariances as the basis of inference.


They say it is misleading but not why or how it misleads.


They say panbiogeography lacks the ability to present alternative hypotheses.  Here I suggest that viewing historical biogeography as hypothesis testing (of) a null hypothesis is wrong headed.  A multiple model approach is necessary and a means to select from them is sufficient.  By showing how spatial mark recapture can be expanded to landscape scales,  it becomes possible to  present multiple model s  (based on/with panbiogeographic parameters) some models of which may not be totally panbiogeographic in the Nelson-Croizat sense in which dispersal from centers rather than splits between centers can be modeled as well. This need not be done necessarily however as it will depend on....

The lack of use of alternatives is not the fault of panbiogeography per say, but is due to failure to use frequentist positions for all of evolution but probabilistic ones for unknowns within a given biological change.


As presented in recent studies, the panbiogeographic approach involves little more than mapping species distributions and drawing lines (tracks) connecting them.


We show how the drawing of lines connecting species distributions is all that is needed when creating models that demonstrate earth and life evolve together.

When less space is involved it becomes a matter more likely to use a binomial process since there may be dependencies on N. This will continue until generallied tracks across the globe are agreed on.

 It is role of metapopulation and suprapopulation biology that needs to present the alternatives that may involve  some other technicque not panbiogeography.

The statistical approach still is qualitivae in the sense of needing to select distributions to be compared but the congruence in the generalized track is all that is needed to make it more quantitative.


Waters et al say

If tracks are meant to indicate paths of dispersal or

vicariant events, there is also no apparent reason why they should take the minimal distance

(although indeed they are rarely depicted as great circle distances).

While this may seem like a valid prima facie criticsm there is a clear reason why minimal spanning trees (  or great circle distances under correction).  This enables one to limit the track “width” to an infinitesimal relative to its length when combining multiple distributions.


This shows up search encounter system as the a dimensionless search  encounter path that probability of encounter falls off from unity from the least path between points (as if reduced to  a point process).

The generalized track  or state space plus individual track encounters with the generalized track may not be a line but in the ideal case it is. The dispute over the congruence and how to understand the node depends on how this generalized path varies geographically (lat /long etc).

The reason that panbiogeography focus currently mostly on ancient vicariance is that no general way of constructing the entire state space individual track have been composed.

That is not a reason to say that panbiogeography is detrimental but a reason to suggest how to do it.


Here I show how geological covariates on the generalized track specdies densitites can contain  variable shape generalied tracks that may be found to be analytically resolved into nodes and masses per baselines such that  pushing out in space as well as back in time can be means to further make Panbiogeographic consensus.

Swaying by main massings is a function of particular density covariates and can be object tively added once the node and anti nodes are deteremined from a more exhaustive search of the space (rather than an individual track search encounter to node process).

Thus to say how panbiogeography “usually is” requires one to usually be doing it before one can criticize that practice.

Rather these authors attempted to judge a priori without  showing how panbiogeography can not grow.

When it comes to comparing ALL distributions in an area one can show how the  diversity but that speaks of reasons for the common distributions which is not a matter for panbiogeography but for the known molecular evolution correlate and that is not something that any field of biogoegraphjy is able to do  yet.  So it would be misplaced to use that reason to argue against  progressing with in panbiogeoghraphy.

What this criticism amounts to is a view that the “truth” of evolution can be known certainly.  This is not possible.  That panbiogeography might create multiple options for evolution should not be counted against it but rather for it since it permits various options for evolutionary research to pursue as it becomes more certain of its past contingencies.  That criticism can only hold weight in an atmosphere where evolution must be defensible as a unified view against non-evolutionary ones.  Evolutionary opinions abound and it would be unscientific to restrict it categorically this way.  One may have reasons to reject a conclusion of panbiogeography but this does not mean that the way it can any way be done is to be rejected.  Again it is a need to bring other kind of biologists into the use of panbiogeography that is needed not that panbiogeography should be rejected by null hypotheisis.  If these other disciplines can confirm/asupport the claims of panbiogeography then its conclusions become more likely.  If they cannot – then perhaps other reasons for the apparent similarity of species distributions need be created but to say they are spurious when they appear to the eye and the stats seems out of mind.

A non ancient vicariant process might be cooridinated home range changes within metapopulations driven by belt tricked synced intra specific competition under predation.


Again this seems more speculative than ancient vicariance to proceed with syntheisizeing multiple generalized tracks through Croizat;s nodes so it would be wrong to argue that because only ancient vicariance is used by current panbiogeographers that that is a good reason to reject it. 


So here we show how to use search encounter statistics to create  maps of generalized track species densities which if found to be better models when fitted with geological density covariates (or any other covariate such as home range expansion with in metacommunities etc, coordinatable  temporary emigration/permenant dispersal, etc).


The truth remains that many biologists just don’t think vicaraintly but when looking at a lot of distributions this splitting and seperability seems much a part of the phenononon that it is hard to ignore.

Spatial search encounters models are based on searches of  areas for individuals which are subsequently marked and released and rerecorded spatially when they are found on other searches.  This can occur when the survey path is laid out a priori independent of the activity centers of the individuals and that the collection of the data does not affect the path itself. This is only assumed however so allow one to assume that the activity centers are distributed uniformly in the bounding state-space.

Here we show how the individual movements and their activity centers can be replaced by minimal spanning tree of individual species’ distribution and the search path provided by the sum of encounters of other distributions from each individual track.  By searching along each and every individual track the entire state space is covered and no one “activity center” (centroid of the individual species min span) receives preferential treatment.

When there is uniform search throughout the enire geographic space independent of the biogeographic places the location of anti-nodes can be obtained but then the prescribed state space is undefined and it can not be said without further information whehtyher the activity centers are uniformly biogeographically distributed.

Ant nodes are places where the encounter probability is zero and requires a donut approach to the modeling from the individual track but is rather expressed as the node +mass relation which alters the line to density mapping.

As the number of individual tracks used increases the fixed search path = the uniform serach intensity search occasion number.

Location of species I on search k’s encounter probability pik==p(uik)=Pr(yik=1\uik).  The only species places athat are not observed are in the anti-nodes.

Relating this to ancient vicariance is a further division of the covariates model to create a different baseline.  In that case there is “movement” and potential phyolgenetic influence but this is not done without a coordinated change in all generalized tracks around the globe.


Because Pr(yik=1|uik that increases as one come close to the path line) it is the min span describes the connection in the individual track.

The total encounter probability to any individual track may be computed simply by the number of min spans crossed or by the number of collection localites within a given distance from the indivudal track line.  Because multiple min tracks of another species can be crossed by any one invidiaul track line search the  encounter probability is a sum of these crossings.



Elucidating mechanisms underlying amphibian declines in North America using hierarchical spatial models 

Muths et. al. propose a study of how climate change may affect amphibian occupancy.

“We will develop hypotheses for climate-induced shifts in occupancy dynamics, and test these hypotheses using a dataset representing many individual projects and regions from across North America. We will formulate the problem in hierarchical Bayesian models to examine multi-scale processes affecting patterns of species occupancy.”

The locations from which the models will be developed however appear to avoid salamander endemic areas. 

Muths et. al. reasonably suggest a useful relationship in that they, “ will examine alterations in timing and availability of surface-water habitat (driven principally by climate change), as first order variables that control the probabilities of breeding, successful metamorphosis, and return rates of amphibians.

But given that significance of the change in occupancy is not great/huge for the time series they posses:

And the different  variations surface water habitat use by salamanders and space use by frogs and toads.  An examination of the changes in breeding behavior  needs to be supplemented by space usage models that take into account historical metacommunity –to landscape correlations and endemic to speciation rate possibilities.  If the models show declines in populations not near endemic areas then the ultimate response of amphians to climate change may be very different than the immediate proximate population genetic effects. It may even be that climate change could accelerate diversification while causing mass extinctions.  For that scenario however one needs to understand not individual species declines but coordinatated responses of groups of amphibian communities.  There is not much thought given to this possibility and the dire reports may not reflect the reality. Cyclical population dynamics might become a first order affect dominating genetically the naïve view that becaue of metamorphosis surface water extant supplies intellectually.  Further the effect of climate change may be to  open up current reproductive barriers to hybridization and permit greater recombination of characters as current barriers to biotic potential are changed into a new regime.  Amphibians offer the researcher these options that may not be available when analysizing othjer taxa data.

So we need to model the home range activity centers RELATIVE to the surface water extent before claims about return rates can be derived via successful metamorphosis to breeding probabilities.  Panbiogeography is poised to supply concepts helpful in this direction when home ranges are associated with individual tracks and the generalized track contains the state-space of surface water extent. This will provide a means to address group**/community responses to changes in temp and surface water since competition and cooperation can be abstracted there through which is only secondarily considered in terms of cyclical population changes.  If the occupancy at a particular location goes down – could it be that it goes up at another unrecorded locality?  And if the declines are all along the periphery of geographic space then could genetic load be released under some amount of disturbance that results in increased space usage and further coordinatable change in species population growths and developments.


Sound environments are different in space and frogs may use them differently.

"We hypothesize that this flexibility in mating calls

has evolved as a response to natural variability in space and

time in background noise levels because of waterfalls and

rapids, wind and noise made by conspecifics and other


Animal Conservation 16 (2013) 275–285 © 2012 The Authors. Animal Conservation © 2012 The Zoological Society of London

Mate attraction by male anurans in the presence of traffic noise

G. M. Cunnington & L. Fahrig

If this hypothesis is true then the evolution of the large ear morphology of the Asian fast stream frog to recieve ultrasonics is under the same general kind o f selective pressures as give rise to proposed plastic physiology otherwise.  Detailed study of these frogs biophysics may reveal (on this hypothesis) why flexibility rather than distributed dialects explains the differences in calls.

At issue is how noise can "mask" the natural calls.  An understanding of the physiology of immediate call alterablity can help to understand if for instance a long duration for a call makes it more "imnmune" to masking or not. Alternatively one might simply like to know if it is due to mere inensity/amplitue deafining  or simple frequncy difference phasing  or instead us a rest more complex choatic interactions.  Without understanding of the basic physiology that can be approached with components of rate, average amplitude and  dominant frequency measures.

If the immediate nature in the response is purely mechanically a physical constraint and not subject to  behavioral- neuological modifiability then  to the extent that anurans can not alter this biophysics either within or across generations is the extent to which dialects may develop regardkess of past speciation events even  where plasticity is now  being claimed of.

This hypothesis leads to the niave view that frog species difference in frequency channel seperation  was driven by increases in frequency mutations with increased exposure to sound (assuming waterfalls and wind were more likely than thunder (human noise has high low frequency componets relatively)) What it does not take into account is that frogs and toads may have evolved in the environment of deafining insect sounds and thus that not the environment drove the frequency seperability. Birds came later (maybe birds flew to eat frogs).

Did frogs and toads learn to sing to avoid the decade deafining sound of cicaddas. I mean at first pre-anurans learn how to approach and consume large masses of cicaddas(( but only ever decade or so) ) with the buzzing sound trembling the lateral line system)) and then these ancestors exhaust that info to find other insects. Could jump to flyers. Thus  was 10 or 20 years time difference  evolutionarily enough to space all the frog and toad frequency variation we see today? Is human sound pollution of the last 50 or so years beginning to take a toll on this balance and straining the frogs' ability to find more insects that it has found by seperating its sound reproduction from its energy consumption.

Could it be that frogs and toads cant jump to where insects explode populationaly as much anymore because they cant hear each other breed and so end up neuologically overbreeding when they need to be spending more time over eating?  When they eat less they are more susceptible to illness and extreme weather - aka BD and then they die??