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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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 On Wright's account of orthogenesis, the use of the term is bounded by random variations accidentally acquired not attributable to what the organism already is and organization already attained by evolution that restricts the possible lines of variation. There seems to be claims that ordered relations such between organs, organisms and organizations have not been established, that there is no organon even for instruction of the same on the horizon of practicality.

In Evolution in Mendelian Populations Wright wrote, "The probability arrays of some genes will travel to the right and close up as their selection coefficients stiffen, while some of the genes which have been nearly fixed will come to be less severely selected and their probability arrays will shift to the left and open out or even move to the extreme left under displacement by another allelomorph.  A continuous and essentially irreversible evolutionary process thus seems inevitable even under completely uniform conditions.  The direction is largely random over short periods but adaptive in the long run.  The less the variation of gene frequency about its mean value, the closer the approach to an adaptive orthogenesis" (page 150).

About 30 years later Croizat wrote in Space, Time, and Form: The Biological Synthesis

A simple interpretation could be that Croizat's "structural inception" is causally prior to an effect which is a decrease in variation about a mean value, mean values.  The orientation is less variation in gene frequency at an already organized mean value unless that organization was due to selection itself. This structurality however according to Croizat,  depends on the "kind of organ" so a more intricate rendering of the texts (between organism and organization) is necessary and Wright also provides suggestions in this directum. Darwin did tend to fall back into a teleological judgment rather than make a transition to physics as Kant did (WHILE using the work of Darwin's grandfather within the Linnean notion that existed in systematics at the time) in the Opus Postumum. Mayr appears to have confounded the digital advances for "infinite"(very, very  large) analog differences (depending on the mechanical machine analogically) and failed to make the transition to physics across the subtle sublime differences that Aristotelian thought always logically leads to and judgements as opposed to appears always rest at no matter the taste.

Gould's confusion on orthogenesis appears to be related to a need to decouple the prior evolutionary organization (whatever that is) from the/a relationship between the levels of organization between the tissue /cell type(organ) and the individual organism (vs gene vehicle (Dawkins)) which he solves by a theory of levels of selection WITHOUT offering an means to instruct how to attain a direct intution empirically of the structural relationships between the level of selection and level of organization. This attempted solution (in Structure of Evolutionary Theory) seems motivated to take into account Williams' idea that no actual biotic adaptation (there is a difference between the structure of an extant adaptation and an ideal adaptation AND a perfect adaptation) exists but this will be argued further along (on math and philosophy in biology). The notion of downward causation is not adroitly nor adequately applied.

Modeling the Panbiogeographic Track as a Complex Dynamical System

The case for orthogenesis from vicariance as a general bifurcation


There has not been a uniform way to understand track analysis and there has been a shift away from creating tracks to simply visualizing sister-sister breaks.   Here I show how the notion of the track as a complex dyamical system that moves lineages over evolutionary time through a bifurcation sequence containing point, cyclic and strange attractors divergenetly per vicanance event or sister-sister splits suggests  unifying Wright’s idea for othorthogenesis with Croizat’s by havin g vicariance be a general model bifurcation.

Orthogenesis is a general context-dependent constraint which is orthogonal to the forces that cause system construction and can be represented algebraically even when there is no indication of its existence (since the complex dynamical system can be understood as bifurcating vector field, a field which contains said forces, whatever they are..)  Panbiogeography is a method that can conscript the signature proabilites associated with vicariance as bifurcation.

Here an imaginary scenario of the forces behind higher plant and vertebrate evolution is presented that enables one to represent the orthogonality that Wright thought and Croizat sought to cartographically represent.

Plants – force is seed  gravity fall to earth as a fall to the Sun  = growth of the particular (maximized photosynthesis) plant


preFish (cilia to rhythm of moon tides as lateral line = food ingestion)

Fish (lateral line to (whole body – spinal cord) motion(relation of  concussive forces to other forces (electric-magnetic)via ear)

Amphibians (body part motion independent of  spinal chord directum (creates different reproductive modes)

Permian forms – catastrophe of  predadtor prey and relation to ear

Modern Amphibians – move food into gut via catastrophe optimized

Mammals – use of bone for Permian eating into good nose and vibration to eye

Modern Mammals (different manipulation to ear of different appendages)

Vertebrates show an orthogenetic trend with independent orthoselections, independent in the sense that Plants also have an orthoselection which depends on motion sexually  into the horizontal (to gravity).


By associating vicariance as generalizing of tracks it is possible to sketch the orthogonal directions from species distributions and present macrons (reduced dimensional attractors onto geography) of the larger fractal self-similarly organizing  systems of prior evolutions ( of blinking fractals).



The Panbiogeographic track has had a rather sparse acceptance. The idea of using a minmal span and of thinking of the node as the connection place between different ones or parts has given way to the use of vicariance rather than spatial track plotting as dominant Panbiogeographic application.

If one thinks of lineage formation through form-making as being a complex dynamical system (like the adaptive landscape as representing a vision of the same)(stability – instability)

Then in the heterogeneity of deme spatilization one might postulate vicariance as that direction orthogonal to Wright’s orthogeneis (represented as gene organizations also orthogonally organized) and think of this as a general bifurcation model as suggested by Abraham under the term morphodyanamics.  Determing the complex interactivity of these orthogonal domains as convergent parallels becomes one the and the same activity uniting panbiogeography, the shifting balance theory and macron alebgra.  It is this new discipline that is described herein.

Panbiogeography thus bifurcated offers a way to derive “successor states” of deme evolutions as an orthogonal algebra of indexed places by relating track width to node shape via transtioning from point, to cyclic to chaotic attractors as the lineage biogeographic fractal is ramified to maximal diversity per clade and is made of multiple blinking fractal processes.  Croizat’s claim was that the Earth’s oceans provide a base from which multiple overlaps of lineage changes can nonetheless be visualized (that the ocean oriented macron still can provide an interface on which to view past orthogonal splits of  cosets). This baseline is multiple basins of attractions separated by the aforesaid algebra within orthogonal algebra within orthogonal algebra! We are thus led to the possibility of developing a fractal dimension law of evolution for the entire globe as a correlation of different attractors and this is an orthogenesis in that it is not due to chance random differences within species but rather chaotic but unrepeatable order constantly splitting by space, time and form globally for all species which appears as chance probabilistically. Orthoselections provide random directions out of this spatial evolution but only in the bounded context dependent constraints of the absorbing area and basin of attraction with holes vicariantly bifurcated by the bi-quaternion of the vector field panbiogeograhicalized.  Wright’s network idea of evolution finds a helpmate in the graph theory dual vertex general model of Abraham between sister-sister breaks. Inertia physically is the outer bound of these constraints but because evolution works across gravity, and e-m within the strong and weak content as well a new math of infinity is needed to simulate the complexity that can be highlighted with  simple  existing computer tools.  The new field of technobiology will open up this new frontier of expanding knowledge of applied evolution.  Only the first slivers of light in this new point set is currently available. There is no mystery to any of this it simply a redesigned spatial mark and recapture probabilistic as macron probabilities where the home range is the species distribution and one species track serves as the “trap” for the other subspecies to higher form geographic distribution (search encounter panbiogeography) This probability is however written as a grossone distribution and as such is different than either the Bayesian or Multinomial representations of the same since practical complications prevent varying degrees of self-organization and self-similiarty heterogenous within form but homogenous in space no matter the time.  This is why macron algebras have not been uncovered until starting now.  Biology will provide a guide to chemical supramolecular interconnections as well as complex social regulation and may even offer a thought for deep physics to ponder.  Geology provides the final bound for the ability of panbiogeography to reveal past lineage divergences but that there is a bound and not a stochastic noise surrounding the future understanding is clear.

Today ( February 13 2014) Warren Allmon ( a student of Gould) confirmed my opinion of Gould and resolved a thought I had about Darwin during his Darwin Days lecture. Thursday, February 13 | 5pm | Kaufman Auditorium, Goldwin Smith Hall, Cornell University
  • Darwin and Paleontology with Dr. Warren Allmon Director of the Paleontological Research Institution

Warren argued that Darwin is not to be thought of as a "modern" but rather as a person trying to convince the world that evolution by descent had happened first and foremost and if one understands it to happen by natural selection also - all the better.  He presented fairly compelling quotes that suggested that the "law of succession of types" which for Darwin was largerly the change in situ on South America of large to small mammals was key in Darwin's thought.  This opens a way to see that because of a continuity in shape change in one continent but with the existence of the horse no longer there that Darwin's notion of dispersal from centers and failure to see othogenesis and vicariance is wholly possible to see as supported by Darwins own words.  Allmon suggested that Gould, Raup and Eldredge got Darwin wrong by thinking of him as one of us today rather than as a man trying just to convince others ("old doubters") that descent with modification (big mammals to small mammals on SA) had happened (Owen's homology of Darwin's fossils).

I see this issue further exascerbated by Fisher when he takes Darwin to task on blending inheritanceart but only considers the forms of critters that were domesticated and/or artificially selected by man (it does not include South American mammals as largerly as Darwin did  and thus smooths over the continuous vs discontinuous changes in phenotypic form-making that Croizat understood).  Failure to realize that Darwin was simply thinking of blending all large mammals into smaller ones in  one place while horses die out was all that was behind his idea that we accept.  Natural selection may or may not work when it comes to every law of succession.  Orthogenesis may indeed function as a better biogeographic instructability without having to discount the importance of Darwin having argued for evolution in the first place (to vindicate his grandfather?).

It was clear to me that my Grandfather's parents were "new doubters" that still had to be convinced in the 1920s but never were so Darwin was well ahead of that time!!

Wright also wrote (Fisher appears to have objected over Wrigh's biophilosophy (not math) between homogeneity and heterogeneity of effects (attention to allopatric side isolation  (non-adaptive orthogenesis) and vicaraiance fracturing of the whole is important(possible adaptive radiation through parallelization))): "The most serious difficulties are perhaps in apparent cases of nonadaptive orthogensis on the one hand and extreme perfection of complicated adaptations on the other.  In so far as extreme degeneration of organs is concerned, there is little difficulty - this is to be expected as a by-product of other evolutionary changes.  Because of their multiple effects, there can be no really indifferent genes, whatever may be true of organs which have been reduced beyond a certain size.  Zero as the value of a selection coefficient is merely a mathematical point between positive and negative values.  It is common observation that mutation is more likely to reduce the development of an organ than to stimulate it.  It follows that evolutionary change in general will have as a by produce the gradual elimination of indifferent organs.  Nonadaptive orthogenesis of a positive sort, increase of size of organs to a point which threatens the species, constitutes a more difficult problem, if a real phenomenon.  Probably many of the cases cited are cases in which the line of evolution represents the most favorable immediately open to a species doomed by competition with a form of radically different type or else cases in which selection based on individual advantage leads the species into a cul-de-sac. The nonadaptive differentiation of small subgroups and the great effectiveness of subsequent selection between such groups as compared with that between individuals seem important factors in the origin of peculiar adaptations and the attainment of extreme perfection." -Wright page 154 op. cit.

The structurality thus depends on whether the cells involved are aggregating in larger or smaller piles and if hadicapping really has any downward affect.  Social evolution under social selection provides intricate enough cases to investigate this difference. Vicariant side-isolation followed by behavioral dynamics subject to social selection can provide a framework for stratagies that differentiate ideal (possibly man-made teleologically enforced) and more perfect (closer tolerance to physical force potentialities involved)  adaptations (through evolvability). This may not be the entire background Croizat afforded to the difference of orthoselection (to browsing quadruped) and orthogeny (STF pages 720s to end) but it can establish a rigorous empirical reality for Croizat's "orient" and Wright's comprehensible orthogensis. Explanation of Provine's and Gould's position can simply be chalked up to an atmosphere of elitism that supports books from Cornell trained-authors such as RobertFrank (Darwin Economy) and Greg Graffin (Anarchy Evolution) and support popularization through the likes of the work of Yale student CarlZimmer (Evolution) but yet does not permit tacts that searches for patterns and formulas and/or a plurality of kinds of equilibria. Frank's view, though supportive of Roughgarden's response to critics (Science) on individual ESS confuses the collective of social evolution with the distributive population genetics in its composition.

Now this notion of orthogeneis is possible for individual organisms that are subject to social selection that acquire random variation in behavioral-time-actions and if it is ESS. This is Frank's point but in actual organisms the unconditional behavioral choice has a stable (equilibrial outcome) provided the negotiation distribution amongst the traits individually sums or multiplies to a large enough magnitude. This is not group selection (and in the Frank case he makes this clear by asserting that moral actions of individuals if not harming others would be "darwinist" in his sense). Simple quality narratives are not able to capture the detail of the social selection relative to other population genetic pressures that affect the difference of collective and/or merely distributive effects, absolutely. Hence the need for a particular individual -species case.

Variations in behavior that lead to different dynamic behavorial equilibria occur during the times of "largely random" direction in the short run and the issue of which of different multiple Nash equilibria are sustained  ("which of the two NE will the behavioral dynamics result in"(page 2201))can depend on the a lessening of variations available to the behavioral differences (while some behavior is used for a season etc) and thus with an ESS may accomplish the adaptive orthogenesis Wright indicated between the two equilibria.

Here we suggest that this is happening in anurans and that panbiogeography enables biogeographic data to discriminate where the directions of orthogenesis (formerly "replacements" of Darlington)have occurred because vicariance can be coordinated with Wright's view of "parrallel" adaptive orthogenesis as species divide. 

 How are motions of creatures graphed to be visualized. Consider motion in outer space.  What would this be if it was a live?  How could we tell?

This background orthogeny is orthogonal to the geography of salamanders and caecilians.

This will give an example of what Croizat may have meant when he said that "orthogeny" provides the background on which adaptation operates in STF, for as Wright suggested that in diverse conditions an adaptive radiation can/may result.

Here we show that Darlington's localization of this background to Africa and Savage's view of "base stock"

 is wrong and that theories based on competetive origination also can not return the functional relationship between orthogeny and specific uses of tracks, nodes, masses and baselines in different orthoselectable directions. Savage notices that Darlington supposed a north-south bipolar vector for the Leptodactlyids ostensibly forcing out by extinction the A character state groups

Congruence is a fundamental concept in panbiogeography (used in algorithms of Martitracks) and there is a distinction between  geographic congruence which can be defined wholly geometrically and biogeographic congruence which depends on prior historical biogeographic congruence.  This difference is not attended to much in comparative biogeography but must intricate details of the relations of space, time and form.

The type of orders suggested here enable congruence to be developed for anurans in an orthogonal way to the geography of salamanders and caecilians.  This was not the case for Darlington as he had Lepodactlids being orthogonal in any kind of congruence to the tailed frogs with current distributions in New Zeland and Western US and  with this right split occurring purportedly in Africa. This current distribution is associated with a Pacific Baseline rather than a continent in panbiogeography.

Congruence as a concept , independent of its defintion and use is bounded by unity, plurality, and totality.  Martitracks confuses unity and plurality and comparative biogeography confounds totality and unity.

How to build up systems of congruence is what is the formation of individual tracks into generalized tracks.  Thus a generalized tack can be a pattern of a plurality of kinds of creatures of different taxanomic rank.  It is not the same as a biota since it can contain extinct forms as well. The names attempted in comparative biogeography are totalities that need not contain congruent unities (direct motions compounded mechanically) but for a lexicologically large enough denotation are sufficiently plural.

Micro and Macro evolution can be combined vicariantly in a two tier system that express irreversible change across a scale of this time.

as Wright suggested, if the isolation of small group vicariantly occurs (rather than a tetratable exit through the fracturing of a widspread species into large subspecies groups) then nonadpative radition will proceed nontheless. This would be the ESS for a behavior that can only lead to one possible NASH equilibrium under cooperative conditions. So if SPF is the only possible pheromone Nash equilibrium the speciation in Newts is nonadaptive and not an orthogenesis but if PMF and PRF can be alternative Nash equilibria sign vehicles then and adpative orthogeny can occurr from SPF to PMF to PRF..  Similarly the Tailed frogs have a nonadaptive radiation while those with a complexifyable innear ear form an orthogenetic series.

Savage has suggested a non-Darlingtonian view of Anuran evolution based on biased orginiation (king of the hill phenomenon (once a kind originates in a place) others can not originate in the same place.  Thus Savage utilizes geographic congruence possiblities to build biogeographic influences. This leads to notions of centers not unlike those founder events in Darlingtion's view.

Vicariance provides an alternative view.
 What we develop here is the ability to use panbiogeography to discern the difference between Single Nash equilibiria social selection that offer biogeographic cul de sacs and social evolution of whole range vicariances where variances in gene frequencies my be behavirorally reduced and lead to adaptive orthogenesis.  Thus historical biogeography is able to sort distributions into adaptive and non-adaptive orthogenesises which all combine to functionally relate tracks, nodes, masses and baselines to systematic proposals for the group.

Thus is fused Wright,Croizat and Roughgarden.

Here we allow the data to back up the theory and thus offer a specific notion of "orthoselection" as those cases of adaptive orthogenesis which can be panbiogeographically differentiated from without of biogeographic patterns caused by direct selection on single nash equilbiria or isolated groups vicariances.

Provine seems to have been more interested in sorting out the difference between Wright and Fisher than understanding the intricacy of Wright's supposition. It was not really "unfair" to saddle Fisher with the idea where the number of alleomorph at each locus are limited (since random changes NOT part of what the organism already is or the organization evolutionarily was are not within his idea of evolution in mendenlian populations as a deterministic part) and a full equilibrium would have occurred (need these for Fisher's differential equation approach as opposed to discrete path analysis across generations). Constant degeneration of the enviornment only leads to differences between parallel adaptive orthogeneis IN SPACE (cul de sacs or no) without respect to form.  Different "laws of growth" or developmental affects (which may not be in behavioral ecology domain per say) can occur even with the degeneration.  Fisher does not enable one to determine what this "entropy" or any other measure of the degeneration could be but Wright's irreversibility which includes Fisher's perspective can make some measure of irreversibility that may be correlated with environmental degeneration.

Why Gould sought to agree with Provine can not be becuase of this position of provine but simply because of Dobshanshy on adaptive landscape usage.  Provine's reference to "previous wild-type" genes fails to belie the then current difference of mutant, wild-type and heterozygote and confounds Wright difference of organization, organism and organ where with Croizat noticed that (xxxx? is null without xxxx?(was found by seraching orthogeny)) and that evolutionary change in general can elimiate zero functioning organs while genes just change across 0 from positigve to negative. Provine confuses orhogenesis with the differenent environments in which it can exist or extinct.Gould confuses it with what can extinct. Only a panbiogeography which displays orthogenies based on relations to tracks, nodes, masses and baselines can clear this discrepncy in interpreation up. Provine and Gould fail to recognize Wright precisely for the same reason that Croizat accuses Fisher's mutation of failing to cognize the "directional factor of evolution" (focusing only on perfect adaptation instead roughly).  Wright understood it. Provine confused the wild type gene (which does not exist) and the wild -type organism that has genes. Social evolution of panbiogeographically recognizble differences in distributions can indentify the unity that elite 20th century evolutionary theory and biology missed.

The example even if not actually true demonstrates the concerns of David Williams and possibly others that Croizat's method be avoided because it seems to utilize a polytopy associated with Aggaisz's notion of orthogeny. What has been missing is the ability to distingish geographically parallels and cul de sacs (which is not clines and founder speciations). This however is not the case at all.  Croizat's reference to Bergson's elan vital was simply to direct people to the evidence of  macroevolution Over micro evolution (of a particular reading).  This example shows that David Jordan's use of orthogenesis which IS associated with Agassiz's understanding of types and not to Darwin's "browsing quadroped" is different than the orthogeny that is the background of adaptation.  It also shows that while Kellog's writing can be used to situtate the confusing arrary of ideas at that time it is of little use to inform current opinion (both Provine and Gould seemed to have done this).

Formal orthogenseis that is geographically dividable needs to be canvased before actual cases of orthoselection (selection in the context of orthogeny) can be discarded within macro evolutionary suggestions of trends whether part of raditations or not.  Attention to the size of organs (under vs over sized relative to a zero evaluation) vs genes that may be expressed with negative or positive numbers analyze this division.  Social selection provides a means to directly apply orthogeny on the evolutionary (macro) tier given a supposition of microevolutioanry behaviroal kinematics within differenet classes of gene frequency varaiances around different norms/means.

Anuran Orthogenesis -

This example will suggest that Tailed frogs are not under different adaptive conditions and requirements that Ryan associates with neuroanatomy and that inadaptive conditions are  not in Africa as Darlington suggested for Lepotydalitds competatively extincting both north and south the tailed forms.  These tailed forms instead form a stable adapative zone of bradytelic populations survivng in New Zealand and Western US.

The current status of "orthogenesis" in Evoulutionary Theory seems misread to me.
I am starting to realize that Wright's use of statistical orthogenesis  (adaptive and nonadaptive) in 1931 (in contrast to Eimer and Cope) within a moving equilibrium later was transformed graphically into the topography of the adaptive landscape a few years later. This plays itself out in the two surfaces (of selective values and that on which populations move). 
 In fact his references to orthogenesis in 1982 seems occluded from continued discussion of his work. This kind of orthogeneis is fully comphrensbile within Croizat's difference of orthoselection and orthogenesis in SPACE,TIME and FORM and is beyond that view of orthogenesis as contemplated by David S. Jordan for instance. McFadden's understaind of Cope's law, aka horse "orthogenesis" of Marsh etc.  fails to work when thought across phyla non-mammilan. 
In the construction of the orthogonal as a function that maps between
two surfaces
it must be realized along with M. Heads on Mayr's view of the genetic program that there are NO end points. The structure being established already is so as quoted by Colocino and Grehan (below)
The selective pressures that are one to one and onto in this (Mayr's) case are completely contingent and teleological. Comparative biogeographer's have called for the discovery of biogeographic pattern which is not so. This difference is obviated by Kant in his Opus Postumum but needs to be reread in terms of current differences between molecular and organismal biology.
The orthogonal mould however is all structure.  This understanding of orthogenesis is more in line with Grehan and other panbiogeographers and is completely at odds with the construction constricted and restricted by Provine and Gould that relegate its understanding wholly from Kellog's position. There may be a possible explanation of this failure in that on a page of Darwin's handwriting where he was to speak of special creation he was writing instead formerly of two differnernt functions for the same organ. If this is true then Darwin may have used (time) of biogeographic space (accessible phoronomically in axiomatic panbiogeography but not in the differences of Simpson Gould relied on when thinking of Kelvin's notion of rates of evolution) where physiological function was and inverted function and structure such enabling Gray to comment that he had wedded teleology and morphology rather than had them seperate as Kant did with respect to design or contrivances in other works (Gould's notion of "reptile design" rather confusedly falls into this case).

Wright’s understanding of “orthogenesis” seems to have been summarily underestimated.

Wright distinguished a statistical perspective from De Vries’ abrupt mutational origin theory and from a direct developmental process out of the protoplasm. Direct protoplasmic evolution was a claim without accessible intuition while the mutational theory though relying on selection statistically focused on the physiology of the mutation process. Orthogenesis of Eimer and Cope was  considered “in opposition” the statistical viewpoint which included Wrights’ and De Vries’ views also counter to a special reading of "Darwin."

David Starr Jordan seems to have understood orthogenesis in line with Wright’s characterization.

“Two generalizations in Ichthyology, both extremely obscure, have also (248) intrigued me.  There are “orthogenesis” on the one hand and, on the other, the relation of temperature to the number of vertebrae in individuals or species. According to Eimer, the German investigator who coined the word, orthogenesis may be defined as determinate evolution along definite lines as contrasted with the movement of divergence. Among fishes I notice that in certain groups some particular structure, having attained an extreme degree of development and specialization along a given line, next undergoes progressive degeneration, to be finally lost... My only explanation of these phenomena is that specialization was overdone and thus became a positive hindrance.  If this view be correct it certainly Is not a matter of orthogenesis as conceived by Eimer, for that he interprets as the result of an impulse from within.  Jordan has the idea of “surface” traits (556)and seems only to associate orthogenesis to the changes supposed in a continued degree across kinds but being IN either species or individuals is susceptible to Wright’s explanation for a failure of “orthogenesis” to realize the statistical viewpoint.


“The difficulty seems to be the tendency to overlook the fact that the evolutionary process is concerned, not with individuals , but with the species, an intricate network of living matter, physically continuous in space-time, and with modes of response to external conditions which it appears can be related to the genetics of individuals only as statistical consequences of the latter. From a still broader viewpoint (compare Lotka 1925) the species itself is merely an element in a much more extensive evolving pattern but this is a phase of the matter which need not concern us here.”


Gould’s attempts to hierarchicalize selection leads one into this phase but as we shall see orthogenesis formulated in the statistical viewpoint is necessary to discriminate change by direct imposition of force, should the directum be coming from surficial or bodily forces as defined by Kant. There was an overemphasis on effient vs final cause and not enough on just what the “lines” are that orthogenesis is orthogonal to.

Wright actually attempt to restructure the notion of orthogenesis from within his viewpoint. Important was his acquisition from Fisher that variance of characters be divided into three portions (that due to genetic segregation, that due to dominance (something which causes deviations of the phenotype from the closest linear relation with the genotype, and that due to environment). Non-statistical (acquired character) orthogenesis did not incorporate explicitly a notion of what was the “closest” linear relation between a given phenotype and the genotype from which an actual orthogonal may be constructed.  Thus Jordan had cognized orthogenesis simply as oppostional to divergent evolution. Attempts to define Baramin’s also fall into this lack of explicit need to define the closest linear relation possible.

Wright wrote, “The direction of evolution of the species as a whole will be closely responseive to the prevailing conditions, orthogenetic as long as these are constant, but changing with sufficiently long continued environmental change” and “A review of the data of evolution would go far beyond the scope of the present paper.  It may be suggested, however, that the type of moving equilibrium to be expected, according to the present analysis, in apopulation comparable to natural species in numbers, state of subdivision, conditions of selection, individual adaptability, etc. agrees well with the apparent course of evolution in the majority of cases, even though heredity depend wholly on genes with properties like those observed in the laboratory. Adaptive orthogenetic advances for moderate periods of geologic  time, a winding course in the long run, nonadaptive branching following isolation as the usual moder of origin of subspecies, species and perhaps even genera, adaptive branching giving rise occasionally to species which may originate new families, orders, etc.; apparent continuity as the rule, discontinuity the rare exception, are all in harmony with this interpretation.”(153)

Gould doubts that evolution by imposition of force will alter much of the new hierarchical view of evolution he attempts to stimulate and he argues that Tompson’s theory of form fails by giving in connection to phylogeny the ground it was supposed to hold for mathematics. This of course conflated algebraic and geometrical intuition and further falters if the imposition should be via surficial or body forces as phoronomically differentiated by Kant.  Thus the winding larger pattern that Wright orthogenetically imagined (within the domain Gould attempts to find inution for ) may be angled EITHER by surficial OR body forces and Gould’s argument about gravity and volume vs surface tension descent losses its bubble and pops. How these are to be defined interms of Fisher’s divisions of character variation remains to be explained and explored. Nonadaptive branching following  closet linear genotype-phenotype orthogeneis (statistically) can occur in the same orthogenetic class or Panbiogeographic track through similar divisions of surfical and body forces effects relative to surface and volume ratios discussed by Tompson and connected to transformed grids. This is one way to coordinate orthogeneis and panbiogeography. This analysis also shows that Gould has overemphasized anagenesis (adaptive branching giving rise to families, orders) by restricting orthogenesis to the earlier than Wright (1933) (Kellog) view.


Here are suggestions from fish distributions for the same.


There is no doubt that the issue of how ancestors have been cognized is dependent on this re-writing and righting of Wright since the lip-service given to Wright's two level theory (individual and deme-beyond), because an individual may be orthoselected but would not undergo orthogenesis itself, requires a complex plane notion of geometry to remain without the boundary crossed.  It seems that because Wright's balancing required subdivided populations (under both deterministic and random changability in form) the current renderings  (too dependent on external morphological phenomenology and phenetics)  isolate Wright's orthogenesis as not part of the the "two-level" theory and therefore put orthogenesis in the creation of different forms (hence while not a monomorphic ancestor) as not structurable ("incomprehensible" "does not even begin to work")in the abstract mathematical mentality of the likes of Gould and Provine.  I am also exploring the possibliity that macrothermodynamics provides a feedback that doesnt' just assume divided populations materially but actually causes the condition demanding orthoselection itself topographically. If this latter is a case then the criticism against Wright is not with much standing despite the authority of those marshalng such opinions. M. Heads and Gareth Nelson expressed differing views on ancestors on Panbiog-L.  I agree with Heads on this body but as to the place or position or locals of evolution itself (under spatial evolution NOT NEO-DARWINISM) it cannot be the "position" of Rhodes sincve the 60s as I have had many an opportunity to witness from Frank himself on the Cornell campus. This "perception" of Nelson and many others is correct.

 Spatial Evolution


It is the multiple senses of correlation (and Wright's use of a highly symmetrical format of analysis) that have confused the ability to recognize that Wright's orthogenesis of 1931 was a spatial construct later built into appreciable detail (and able to suppport vicariance I suspect) (but only really discussed in terms of "group" selection) within what even in 1982 he was still describing as a continuum. I have come to notice this in Wright because of a lack of detail in the discussion of the morphological forms themselves but find this lack can be contained within Wright's notion of ancestor and heredity when fully abstracted.  Instead of opening this place for theory Gould has sought to go beyond ("hierarchical selection theory") with little linguistic support and a failure to differentiate statistical orthogenesis from direct-effect orthogenesis the lexicological prerequiste of levels of organization.  I am fairly confident that octonions or a subset of quaternions may help to clarify this confusion.


I have chosen to think along with Pascal and Cantor here because what is happening is
"However, there is a constraint when using this method. As stated by Descartes' second principle, the analytical method uses an ascending reasoning, i.e. what is known about the whole (taxa or area) is nothing more than the combination, addition or congruence of the solutions to the partial problems."
"If Kant is talking about human intuition, then perhaps neither non-Euclidean geometry nor Einsteinean physics can refute him. (12)

12. Indeed, if Kant is talking about the nature of human intuition or its role in geometry, then he is saying nothing incompatible with non-Euclidean geometry. But he might in that case be falsified by Descartes' analytic geometry, first published (1637) about 150 years before Kant's Critique. By showing the intertranslatability of geometry and algebra, Descartes showed that, for most purposes, we can do geometry without diagrams, spatial intuition, or visualization. "

   I had proposed here that  immobilism was restricted spatially but this does not mean that it is not in operation (at a distance). Thus the map depicts mobilism and immobilism in an oppostie alternation than that suggested in the description to the right.


How mobilism and immobilism is related to population genetics remains to be developed.

Figuration in immoblism/mobilism has been described by Daniel Rafael Miranda-Esquivel and Sus Echeverria, authors of Martitracks (a means to conduct geometric track analysis) :


"Panbiogeography assumes that taxa distribution evolves through

two stages: mobilism and immobilism. The interaction of these two

states is called vicariant form-making model. Within the mobil-

ism stage, an ancestor taxon expands to establish on new territory

through its means of dispersal (”means of survival”) when the geographic and climatic factors are favorable. Later, when the range

geographic is established (immobilism) the appearance of barriers al-

lows the isolation and differentiation of taxa (vicariant form-making)"


From the Martitracks Manual


 So for instance with respect to speciation in Ambystoma one may try to speak of mobilism before the rise of the mountains and intracontinental seway or else dispersal depending on whether these are borders or barriers in history.

 or even whether the Pacific may have been closed and Plethodon in Korea and Laramardia are to be understood as immobilsm contrary to thoughts that US Crytobranchs dispersed across the Berring Landbridge as one example.

I have chosen to think along with Pascal and Cantor here because what is happening is
"However, there is a constraint when using this method. As stated by Descartes' second principle, the analytical method uses an ascending reasoning, i.e. what is known about the whole (taxa or area) is nothing more than the combination, addition or congruence of the solutions to the partial problems."
"If Kant is talking about human intuition, then perhaps neither non-Euclidean geometry nor Einsteinean physics can refute him. (12)

12. Indeed, if Kant is talking about the nature of human intuition or its role in geometry, then he is saying nothing incompatible with non-Euclidean geometry. But he might in that case be falsified by Descartes' analytic geometry, first published (1637) about 150 years before Kant's Critique. By showing the intertranslatability of geometry and algebra, Descartes showed that, for most purposes, we can do geometry without diagrams, spatial intuition, or visualization. "

Here I explore an explanation of this middle return parallel in terms of cooperative orthogenetic vicariance rather than competitive extinction or origination.


In the preface to volume four  of Evolution and the Genetics of Populations Wright wrote “ the theory has attracted the attention of professional mathematicians to a greatly increased extent.  This will, no doubt, lead ultimately to a synthetic theory at a higher level of mathematical sophistication, but, as a zoologist, I am not the one to attempt it.  The present theory still seems adequate in most cases for such interpretation of the present data as is warranted in view of the extreme complexity of the array of factors acting upon organisms and the essential unpredictability of the consequences of mutation and of variations among local systems of gene frequencies. Where every individual has a unique genotype, the phenotypes are the results of unique systems of interactions, and the interactions of arrays of such individuals to each other and to the complex, everchanging environmental conditions are at each moment unique. The relation of theory to observation will always be much looser than in the physical sciences. We may gain a much greater understanding  of evolution than at present, but we will never predict its course in detail.”


In the process of make coarse this rough knowledge exact mathematics still will have to rely on the individual class distinction that Russell always had. Even with less subtleties  in a supposed new physical input into the difference of the real and apparent variables in the current array no matter the symbology in the description there needs be the individuality in the space and time of the variance no matter the relation of the genotype to phenotype. Incidence geometry in a chaotic approach to larger population numbers may be coordinated with some expression of the biogeographic space as defined by points, lines, nodes, masses, and baselines.

Quaternions and Cantor’s real number classes as a basis beyond Woodger in biology.

Leaders of 20th century biology eventually came to fear reductionism to such an extent that they facilitated a social perception of greater difference in opinion between religion and science. There was a duplicity in thoughts about how to relate relative frequency to the scale of the phenomenon under consideration. Thus, threaded discussions emerged from a false difference of perspective on whether cross-level observations were inherent or derivative. Lewontin and Gould expressed this condition differently. Richard said, “Unfortunately, both population biologists and cellular and molecular biologists have become confused about the differences between their modes of thought. It is not ((page 2-3) Population Biology and Evolution). Stephen said, “The ‘synthetic theory,’ or the ‘modern synthetic theory’ – in many was an oddly uninformative and overly broad name – derives from the title of abook written by the grandson of Darwn’s ,ost effective defender…(Historian of science B. Smocoviis (1996) points out that, as a general goal of among scholars, synthesis enjoyed great vogue during these years, especially as a central theme for measuring intellectual maturity, as expressed in the “unity of science” movement expounded by positivist philosophers of the Vienna Circle and supported by biological pundits like J. H. Woodger. Ernst Mayr, for example, strongly supported the unity of science movement early in his career, but changed his mind when he began to feat that misplaced claims for grander synthesis would bury natural history in a reductionist scheme to uphold the primacy of physics and chemistry.”(SETH page 503).

The confusion when not obscured by fear or less than rational intentions resulted in a philosophical discussion of levels of selection rather than a metric sieve for objectively dissociating levels of organization. As a result and due to inordinate attention to the creation/evolution discussion than the meaning of downward and upwarad causation replicators and interactors came to replace delimitation of causal unities. During this period Georgi Gladyshev suggested a means of cutting the difference of holism and reductionism into a common continuum but because it was only qualitatively extended to higher levels other forms of nonstandard evolution theory were discussed instead. Niche construction kinematics and upward causation variation can be reduced to experimental evidence of Maxwell’s equations in a quaternion structure and this is within Darwin’s notion of diversity. Roger Penrose has decided that quaterinons can not be used as the structure of physical space (with the scalar as time) because it/they does not have the “right” signature but I shall demonstrated the a posteriori utility in clearing up the confusion without the bias that currently dominates the spectrum of views on biological causality.

I will show that the temporal field, T, created by Peter Jack writing Maxwell’s equations in Hamilton’s Quaternions combined with the general Gladyshev law series temporality eliminates the need of Maxwell’s Demon in niche construction and effectively resolves enabling the expermintal biologist to asses the intersection geometry of the niche and non niche environmental variables despite the reservations echoed by MacArthur: “1. The niche space is infinite dimensional, and we do not know how the addition of dimensions might srink the niche intersection.
2. The niche coordinates are ambiguous, and we do not know how their alteration might change the niche intersection.
3. Where a variety of mobile resources (large and small, for example) are found in the same area, it is not clear whether that area lies in the niche intersection of a species which is efficient on large foods but able to eat small, and a second species which is efficient on small foods but able to eat large. If the area is in the intersection, then the conjecture appears false; if the area is not in the intersection, the conjecture appears untestable.” …(MacArthur page 160 ed. Lewontin Population Biology and Evolution)

Gould’s invocation of Buss must be synthesized with Gladsyhev’s generalization of substance stability and this will be mediated by the temporal field in quaternionic space of Maxwell’s thermoelectricity. This will also produce designs to extract energy from biological form and permit response to Nat Coa on hierarchical hypothesis constructs in the long-run.

What Gould suggested and Gladsyhev proposed are not prima facie compatible.

Gould said-“the first steps in adding a new level atop a preexisting hierarchy(page 679SETH) (for initial negativity against the previous highest level would preclude the origin of a new level). But, having once achieved a tentative foothold, the new level will tend to check any dysfunctional imbalance …-for these individuals have no become ..caused by differential proliferation from below.”

But Gladyshev generalized “The essence of the principle is as follows: when more stable structures of the highest hierarchic level (j), for example, the supramolecular structure of the membrane, are formed, nature uses lower stable structures at a lower hierarchic level, for example, the molecular level (j-1)

Gladsyhev’s process has more continuity or is more dense itself and works via amalgamation rather than branching but Gould’s suggests something more discrete as Gladyshevs’ is already at work correcting any possible dysfunctional imbalance by upward causation that Lloyd failed to conceptualize in her book, “The Structure and Confirmation of Evolutionary Theory”. The distinction tends to vanish for Gould but become more pronounced for Gladyshev. Gould merely showed his own preference for his own view. It is as if equation 25 of Jack spells out Gould’s effect while equation 26 Gladyshev except that neither is exclusively a true physical law or a consequence of the defining rules of quaternion algebra rather both devolve to cause and correlation.

An example where energy is temporally absorbed and stored heritably as artifacts in niche construction provides a case law. The spin off is the ability to design products able to extract energy and work from living creatures. Incidentally, this provides for the origin of genetic information often asked for by creationists and it shows how hierarchic information is to be combined from logical atoms within nature’s diversity.

This is the latent individual heterogenity to populational homogeneity that gives rise through orthoselection to orthogenesis.