SUMMARY OF THE THEORY OF Vincent Fleury

One may certainly debate all the points which I put forward here, I have hardly the time to discuss more deeply each and every detail.

What I summarize here below gives a perfectly physical scheme of what an animal is. With these concepts, one truly understands what is an animal, and why there should exist humans eventually.

First of all, let us note that Darwin’s theory is really incomplete. Nowhere does Darwin explain by what mechanism animals are formed. This is quite troublesome, since natural selection should apply to any morphogenetic process. It cannot in itself predict the outcome of any particular animal. Natural selection ignores the very mechanisms which provoke the growth and development of a little piece of living stuff.

More precisely, Darwin himself acknowledges that there exist at most 4 archetypes of animals (archetypes is even en entry in the glossary of his book). All tetrapods seem to be obtained, one from each other by simple extensions of the parts “by conserving the scaffold”). In Darwin’s book, the parts of the bodies seem to be obtained by affine transformations from an archetype. For example, Darwin explains explicitly that the limb of the ancestral vertebrate might have been dedicated to whatever purpose, it fitted all the other purposes ascribed to it since then by evolution.

This idea is very odd : in effect Darwin states that there might have been some purpose to the initial plan of the tetrapod limb, but this plan was passed to all the other tetrapods, which made so many other uses of the same scaffold of bones. This bizarre idea would mean that zillions of purposes were found to the limb, after the limb was selected for one determined purpose in an ancestral animal. It does not make sense. It makes more sense to believe that the limb shape has some deep physical , deterministic, origin, and that, after some minor adaptations, it can serve roughly all the observed purposes, even if not optimized in any way. It serves the purpose of the first animal which happened to have limbs, as well as it serves any other purpose. This is to say that the true origin of the limb is in fact independent of its purpose, which is completely opportunistic, if not anecdotal. The “origin” or the “cause”, is to be found in the actual physical process of animal formation : they have limbs, because something that we call a limb, protrudes outwards during development.

I think that Darwin does two errors with the limb “scaffold” idea. All transformations invoked by Darwin are affine, as for example between the mouse and the bat. But there does not exist any particular reason for that, unless there is some deep physical constraint (and there is one, in the nematoid structure of cartilages). Darwin is certainly right in claiming that there exist simple extensions of limbs, “without changing the scaffold”, but one needs a global model of morphogenesis in order to understand why some areas transform affinely, and others not. (There is no way nature can transform a round ovocyte into a fish, by an affine transformation). Darwin states that this “conservation of the scaffold” is related to the fact that the evolution is incremental, which is certainly wrong : in any physical system, any progressive systematic increment of variables will eventually lead the system to all sorts of bifurcations. There must be some deep constraint to this observation, or otherwise, the animals are truly quite close to each other. I believe that the affine aspect of progressive transformation has nothing to do with the fact that the transformations are progressive, but it is linked to the bi-axial, or even uni-axial character of the biopolymers in the cartilages, and more generally, to the orientational texture of the living tissues during development.

In order to understand the formation of an animal, one needs to run and analyze properly the entire “film” of its formation.

*The early ovocyte is formless. By this it is meant that it is round. However the ovocyte has inherited from fertilization, and from the cortical rotation, two major preferred axis of cleavage. The first cleavage occurs across the gray crescent, and the second in the plane perpendicular, oriented towards the point of entry of the spermatozoid. The next rounds of cell divisions transform progressively the ovocyte into a morula which has conserved a crescent or sickle area, related to the successive accumulation of small cellular wall deformations at each division (which are systematically biased). As a consequence, prior to gastrulation, the blastula is round, but the texture contains a symmetry breaking with a specific sickle located caudally.

*All these cells start to move. I do not know whether cellular motion is trigerred by some specific molecular event, or whether it occurs only above a certain threshold of cell drag (shear-thinning effect). During the early phase of cell motion, the movements are slow, so a linear Stokes flow approximation can be made. In thin shells, with cells crawling on an extra-cellular matrix, taking into account friction leads to a Poiseuille profile for the cell flow. I insist that, to my knowledge, there is no reason that the displacement of cells should have a direct deterministic cause. All chemicals undergo the same mismatch during cortical rotation (which is a physical process), therefore there is no point in looking for a spot of one peculiar chemical, and ascribe to it the important role of launching the gastrulation. The rationale is otherwise : there is an initial symmetry breaking around the sickle, the sickle “in toto” is attracting, repulsive, or has nihil effect, but it is a property of the entire thing, not a particular chemical.

*Cells cannot fix arbitrarily their velocity, what they do fix is the force they exert. Each force is a little dipole, and all forces have to be integrated to calculate the global pattern of viscous flow. Writing the integral of these motions gives the deformation rate field of the entire blastula. This incorporates two fundamental laws and one not-fundamental. The two fundamnetal laws are mass conservation (div(V)=0, where V is the displacement rate), and Newton’s equilibrium (div(s)=f, where s is the stress, and f the volume force –here cell drag). The not fundamental law is the constitutive equation of the living stuff s=H(V) we assume a Newtonian fluid, at these early stages.

*When the motion starts, it is a bit blurred, or noisy, but it gets more and more stable under the self-organizing stabilizing effect of pressure forces. The initial symmetry breaking launches the cells in a quadrupolar distribution, which self-enhances during the flow, and stabilizes itself into the shape of a collision of vortex rings around a stagnation point (presumptive navel).

*All molecular fields are dynamically transported in the same flow, and exhibit a simple dynamic deformation consisting of an elongation into a hyperbolic flow. The flow is composed of two jets of cells, colliding at a stagnation point, which is the presumptive navel, actually.

*The flow compresses the animal, elongates it, transform it into a large 8, folds it, and this is how it starts to acquire the typical shape it has at that moment.

*During all this, segmentation starts. It is a different process, due to the fact that the tissues are dipoblastic,. Although it is a different process than in-plane flow or out-of-plane buckling, it is triggered by the compressive stress in the navel area. This is why the segmentation wave starts there, and propagates to the head and tail buds, and next to the limb buds.

*The limb buds are formed by the lifting up of the tissue in the low stress area which is winding.

*Due to the combination of in-plane flow, out-of-plane buckling and segmentation, some areas show skull bones (flat and round) some others phalanges, some other ribs, etc. But this has nothing to do with “a gene of rib” or “a gene of finger” etc. It is a matter of how the tissue is physically handled by the process. The very same genes give different outcomes, in this process.

*The entire animal body formation is a continuous flow, which has nothing to do with a series of discrete “stop-and-go” inductions.

*During this flow a texture appears in the embryo, due to alignment of cells in the stretch force.

The streamlines orient cells individually, and form a global pattern with typical strems-highways inside the embryo. The consequence is that all the animal parts are well organized, with what physicists call orientational texture.

This is why, further evolution of the animal have to comply with this orientational order.

*If nature changes randomly some factor in the genes of the offspring, that will change the parameters of the gel, but likely not the orientational character. If it does change the textural parameters, the pattern will be grossly aberrant. If it does not, the pattern elongates or shorten, along the paths formed by the streamlines. The tissue conserves “in the hardware”, the direction of the cellular flows, and hence of the possible evolutions.

*Animal evolution consists mostly (except in areas of strong vorticity, like the pelvis) to shortening or elongating the patterns affinely, in the directions of the existing pattern, as observed by Darwin, but interpreted wrongly.

*Therefore, the tendencies in animal evolution are not mere retrospective illusions. The set of possible animals is quite restricted, and obtained by elongating or shortening the animals, on the basis of an archetype, itself obtained from a sphere by letting a low-Reynolds hyperbolic flow carry away and deform the sphere.

Conclusion : the darwinism, fair enough, it works. But it is useless to calculate the actual shapes of animals. Natural selection works as well on planets where animals are bubbles of silane floating in oceans of liquid methane. This is to say, Darwinism cannot predict any specific shape.

To predict specific shapes, you need a model of morphogenesis, and this is almost completely absent from Darwin’s book. And when Darwin does write of morphogenesis, it is mostly rubbish, and theoretical nonsense.

*For the specific case of craniates, one can show that there exists a vortex ring structure (like a thermal plume) injecting the cephalic region above the AP axis, by rocking the neural crest above the eye horseshoe, and above the ear duct. This sets topologically a deterministic pattern, and the increase of skull size, is correlated to a decrease of jaw size. It has nothing to do with God (the useless hypothesis, as ever).