At the end of our study, we can conclude that our model sees its credibility supported by a beam of evidence and solid factual arguments. The selective mass extinctions at the KT limit and the four other more significant, the acme and the Dinosaurs disappearance, the "cambrian explosion", constitute the probabilistic effect of the calcium stimulus most convincing arguments. The hominisation process and the ecoumene current settlement, with their paleontological and geographical correlations, validate the iodine stimulus probabilistic influence assumption. The parallelism between the increase in the PO2 P.A.L. rate and the biological and respiratory systems evolution also testifies, without any ambiguity, of the influence of the probabilistic oxygen stimulus. .

If, as we tried to show it, the chemical stimuli like calcium, iodine, oxygen, seem to play a major role in the biological evolution, it is probable that a great number of other chemical elements, or stimuli, like carbon, hydrogen, nitrogen and others less abundant exert a considerable or appreciable probabilistic influence. In the same way, many probabilistic couples, physical stimuli/physiological réactions, had to play a significant role in the evolution: électromagnetic waves/vision, sonorous waves/hearing, pheromones/sense of smell, etc... All these parameters are part of a probabilistic context more vast and complex, the general environmental conditions, where many factors intervene more or less, according to circumstances (climatic, courantologic, sedimentological factors, orogeny and volcanicity, transgressions and regressions, ecosystems, available niches, insulation, mechanical constraints on the anatomical characters, etc...).The environment/organisms interaction is total and is exerted simultaneously on distant sub-kingdoms (calcium on the Invertebrates and the Vertebrates, oxygen on the sub-kingdoms major part). We will examine in paragraph 9 the genome influence in this interaction.

A few words about chance. The probability concept is opposed to the determinism concept (Laplace 1814) which refers to a strict causality whereas, in the probability, the causal relation is looser and the foreseeability statistical. The statistical probability has, nevertheless, nothing in common run with the chance which is pure contingency, unpredictability and which one can define as the two independent causal series meeting (Cournot 1843). Thus, in the mass extinction at the KT limit, the meteoric shock assumption (Alvarez 1980) arises from the pure contingency and is the result, a priori unforeseeable, of two independent trajectories meeting, those of the earth and a meteorite. In the probabilistic model, the phenomenon is interpreted by the calcium stimulus probabilistic influence on the organisms (Vertebrates and Invertebrates), which appears at the same time by the organisms acme and disappearance with significant calcic metabolism, the extinctions selectivity, the Dinosaurs radiation and extinction (with its paleogeographic locations), etc... All these facts are unexplainable in the models based on chance, which take into account only the extinctions, without their selectivity, and ignore completely the former radiation phenomena. The same argumentation applies in the biological and respiratory systems chronological emergence phenomena, in many sub-kingdoms , in relation to the PO2 P.A.L. stimulus oxygen growth. It is the same, as we highlighted, in the correlation between the iodine stimulus and the volume Hominids brain evolution.

Biological evolution, from the eubacteria and archaebacteria (Woese 1977 - 1998) (Lake 1983), until the " higher " Primates, like the species Homo sapiens, cannot be described as progressive without being put forth a judgment of value. One can nevertheless observe, as well in the unicellular world as that of multicellular, a general tendency to complexification. This one is irregular, in mosaic, sometimes regressive, and appears by organism plans historically more and more complex, for example, at the metazoa, the triploblastic states after the diploblastic states, the coelomates after the acoelomates, the Mammals and the Birds endothermy after the Reptiles ectothermy. This historical evolution of the sub-kingdoms and classes, irregular but clear , towards an increasing complexification, is in phase with the probabilistic model where the events occur, statistically, according to the probabilities law, from most at least probable, proportionally with their chances. A simple organism (or an event) has more chance, or probability, to occur that a complex, or less probable event.

The mere fact of being alive implies, for an organism, to be adapted. Life is adaptation. One can define the adaptation as an organism adjustment in the medium constraints. This adjustment applies to the various biological levels, as well macroscopic as molecular: morphological (legs, wings, fins...), metabolic (breathing, nutrition, excretion...), histological (gills, lungs, tracheas, stomachs, kidneys...), genetic (genome and genetic code, enzymes etc...).

The S.T.E. (Synthetic Theory of the Evolution), the current standard evolution model, founded on enrichment, by the populations genetics and the molecular biology, the darwinian diagram, explains the evolution by two factors: 1) genetic variation by randomly genome mutations 2) the favorable mutations natural selection which ensures the adaptation (Dozhbansky, Mayr 1993). A "supersynthesis", elaborate with the eucaryote organisms molecular genetics assets interprets the evolution by organic integration various levels (Armand de Ricqlès).

The probabilistic evolution model proposes a probabilistic interaction between the whole environment stimuli variations and the organisms reactions, among the possible choice (François Jacob 1981). This interaction was illustrated by the several chemical stimuli variation study (Ca, I, O) and its effects on that of the organisms. If the probabilistic model proposes a credible alternative to the organisms evolution based on the favorable random genetic mutations natural selection, this alternative seems insufficient to explain the organisms adaptation general phenomenon. The recourse to other concepts seems essential to us.

Physical sciences very whole are dominated by conservation principles. Movement is preserved: inertia law or first Newton's law, kinetic moment conservation, angular momentum, etc... Energy is preserved, with the quantum reserves near: electric, kinetic, chemical energy conservation or transformation, etc... Physical constants : c, G, h

Parallel to the conservation principles, the physical phenomena modelisation is interpreted in terms of principles of economy or optimization. In the einsteinian gravitation, the Newton's law, dynamic concept, is replaced by a kinematic concept, the space-time geodetic (the shortest trajectory traversed by a test particle in a four-dimensional space more or less curved by the masses and energy). Quantum physics uses the energy concept minimal fundamental level (nonexcited atom state). In quantum mechanics, the Planck quantum action h, minimal action, is all the physical phenomena cornerstone. In traditional mechanics, the less action Maupertuis Principle dominates. This Principle importance is found in the quantum electrodynamics where the movement equations, in the fields theories, rise from a less quantum action Principle (Hildebrandt 1998). In these various fields, movement, energy, action are minimal. What one can translates into an economy or optimization physical phenomena Principle.

We postulate the natural laws unicity. All the projections in knowledge indicate that there is not solution of continuity between the life field and that of the inanimate matter. The laws which govern physics or the inorganic and organic chemistry apply as well to molecular biology and, more largely, to biochemistry. There is no difference in nature between abiotic chemistry and life chemistry but a difference in degree, in complexity, because in particular of considerable difference of the number of molecules which intervene in the chemical reactions of both fields. If an economy, or optimization Principle, the physical phenomena dominates, it thus seems legitimate to extend it to the biological phenomena.

The biological processes interpretation is, historically, of finalist and utilitarian nature (organs and functions, i.e. organs activity for an end, rather than structures and their properties). This interpretation leads directly to the natural selection concept, i.e. with the primacy, in the alive evolution, of advantageous processes, morphologies or organisms (mutations, phenotypes, species). It constitutes a true value judgment and seems a concept with first degree of the alive. It is comparable to the concept, also with the first degree, of the gravitation by the Newton's attraction. With the second degree, the gravitation arises like a curve of four-dimensional space-time simple property. In parallel, interpretation, with the second degree, from the organisms evolution, arises with the probability concept.

In any event, the biological evolution leads to an adaptation of the organisms.

We thus propose an optimization Principle existence (or economy) specific to the biological phenomena complexity. This optimization Principle represents an economy or optimization various physical principles biological synthesis, and in particular of less action or minimal action. This optimization Principle relates to all the biological levels, molecular as cellular, macroscopic, metabolic, histological, morphological, physiological, or even behavioral. This total optimization resultant has as a consequence the biological processes major phenomenon: the adaptation.

According to our model, the adaptation, on all the biological processes levels , rises from the optimization Principle existence. Under this Principle terms, the organisms, as entities, just as their parts (anatomical, physiological, cellular, genetic...) function in an overall optimal way. It is clear that this optimization is a compromise, which has as limits the constraints, at the same time medium and organism itself. The mechanisms implemented in this biological processes optimization are multiple (enzymatic, molecular, histological actions and feedbacks...)..

Since 4,6 billion years, age with which one credits the earth, the earth's crust is the various parameters, chemical ceaseless modifications theatre (Si, Ca, O, I, C, N, H, etc...), physics (volcanicity, tectonics, orogeny), ecological (transgressions and regressions, glaciations and warming up, ecosystems), etc... These environment parameters variations exerted a probabilistic action on the living organisms, as we endeavoured to show it. The organisms reactions appeared by multiple and complex answers (exoskeletons and endoskeletons, encephalisation, aerobiosis and respiratory systems). According to the optimization Principle, the organisms probabilistic reactions to the environmental variations are optimizing reactions, i.e. adaptive. .

One can note this biological processes optimization at the molecular level, since in last analysis, they are the biological molecules properties which determine those of the organisms. If oxygen is not essential to life (anaerobiose), " coupled with the respiratory chain, the cycle (of Krebs) thus has the maximum effectiveness met in biology as for the energy oxidation recuperation in the form of A.T.P. " (Schoffeniels 1984). By glycolysis and the fermentative way, the anaerobic cells manufacture, starting from glucose, 2 A.T.P. molecules, whereas the same reaction, continuing with breathing in the aerobic cells, produces 32 A.T.P. molecules (Krebs cycle oxydative phosphorylation) that is to say 16 times more energy (Mason 1992, Robert J.Huskey 1998).

After the oxygen rate reached, in the biosphere, towards 2 billion years, a 0,01 PO2 P.A.L. minimum rate, appeared the first eucaryote cells using the Krebs cycle. The procaryotic cells, whatever the eucaryote cells origin (Lynn Margulis endosymbiose assumption 1981), reacted to the increase in the PO2 P.A.L. rate by a metabolism optimizing evolution, the Krebs cycle, 16 times more effective than the fermentative way. At the biochemical level, the adaptation is thus basically an optimization process (Schoffeniels 1984). The abnormally high mutations experiments that we quoted at the colon bacilli (Cairns, Overbaugh and Miller 1988) and in the bacteria Escherichia coli (Barry Hall) (Allorge-Boiteau 1991) (Chapter I), just as the appearance, in protozoa or insects, resistance phenomena to chemicals (insecticides) or to antibiotics interprete themselves, in an identical way, like optimization biological processes compared to a modified environment.

All the evolution of the Metazoa respiratory systems carries the sign of the optimization of the biological processes. When an aquatic animal size is not compatible any more with the deep organs oxygen supply possibility (digestive tract, gonades...) by cutaneous respiration, devices improving transtegumentar breathing appear: external convection (lashes, whips, chooanocytes Sponges, endodermal cells at Hydrozoa, siphonoglyphes cells at Anthozoa), internal convection (circulatory apparatus with blood or hemolymph at Coelomates), respiratory pigments synthesis at advanced Metazoa (Vertebrates haemoglobins, Molluscs and Arthropoda haemocyanins). The branchial breathing, external or intern, which appears, historically, more tardily than the cutaneous respiration at watery Metazoa, constitutes the most powerful system to meet the requirements out of oxygen for the big size organisms. Among the animals with air breathing, the trachean apparatus represents, in the Arthropoda, the Invertebrates sub-kingdom adapted best to the terrestrial life, a particularly powerful respiratory system, carrying out an effective compromise between the tissues requirements cover out of oxygen and the risks for dehydration. The Amniotes breathing apparatus, except for that of the Birds, is characterized by improvements such as the pulmonary epithelium increasingly pushed alveolation, or the air conducting system individualization (trachea, bronchi, bronchioles). These improvements confer a great effectiveness, especially at the homeotherm species (Mammals), for which the requirements out of oxygen are considerable. The Birds lung does not have alveoli but its bronchial ways constitute a true tubular network. They have air bags which take part in the air circulation in the pulmonary apparatus. All these devices ensure, during the flight, the considerable supply oxygen required by an intense muscular activity and sometimes of long duration (migrations). (Turquier1994). It was shown that, for breathing at high altitude, the Birds breathing apparatus effectiveness is much higher than that of the mammalien lung (Tucker 1968).

The optimization of the Metazoa respiratory systems, as well watery (cutaneous respiration and/or branchial, external or internal) as terrestrial (trachean and/or pulmonary systems), allowed them to conquer all the elements. If one excludes any finalist design from progress in the biological evolution, one can only note one complexification of the organisms and a frequent improvement (in a greater effectiveness direction) of the structures and operations (coelome, hemal system, homeothermy). In many fields, the biological evolution optimization allowed the transformation, towards more effectiveness, anatomical devices or existing physiological processes; thus the liquid circulating damming up in a closed circulatory apparatus (Nemertea, Annelids, Cephalocords, Vertebrates) (Turquier 1994). The blood circulation defect in the Amphibia, which appear in higher Devonian is the vitiated and oxygenated bloods mixture. This defect is corrected in the Reptiles, known starting from the superior Carboniferous, by a double circulation (pulmonary, of regeneration and aortic, of use), optimizing device which carries out a complete separation between vitiated and regenerated bloods (Bailenger 1989). Optimization can appear by an increased independence with respect to the medium (the endothermic homeothermy, Birds and Mammals) or simple correlations between environmental factors and morphological characteristics: the molars surface transformation, at the horse ancestor, and a feeding based on grass in the place of a feeding containing foliages (adaptive radiations according to G.G. Simpson). Also let us quote, among many remarkable adaptations the oxygen storage optimization by the Weddell seal, highly skilled plunger (Zapol 1988).

Like any Principle, the optimization Principle, like the natural selection Principle, is undemonstrable. It is a postulate. It is valuable only thanks to its fecondity and as long as it is not contradicted by the facts (Popper 1980). It is presented in an alternative the form to the natural selection Principle. This one is supposed to sort out, among the genetic variations, those which are favorable to the individual or the species, when they are not neutral (Kimura 1990). It is to give, in spite its partisans vigorous denials (Mayr 1993 - 2000), a finalist significance with the biological phenomena, directing them towards a panglossian end (Gould, Lewontin 1979).

The biological processes optimization is not registered like a isolated law from the alive world. It is only the synthetic expression, in the biological universe, of a general phenomenon, the physical phenomena optimization (movement, energy, action).

The optimization Principle, that we propose, is thus a synthetic principle of the economy of the means, ensuring the adaptation of organisms. What are its relationship with the probability concept ?

As we pointed out it (Chapter I), the probability theory is based on the great figures law or Bernoulli law (1680), than one can summarily translate as follows: the "events", of which the probability or the chances are very weak, do not occur and, vice versa, those of which the probability or the chances are high occur. The probability is a strong but nonabsolute causality factor, transcending the causes or conditions multiplicity, which seem secondary (object physical or chemical constitution, jet force, height, duration, etc... in a coin or a die examples, thrown in the air). The probability orders and simplifies the "events": the result of the throws, according to their mathematical chances, in fact 1/2 or 1/6.

Ultimately, the probability selects, among the many parameters which condition an "event" production (in the above mentioned examples, the object structure, chemical composition, kinetic energy, etc...), only one parameter, the faces object number (2 or 6), which simplifies the phenomenon and determines the mathematical chances to which the Bernoulli law applies. One notes thus that, in the probability theory, one finds the economy or optimization process, which we highlighted in the movement, energy and action physical phenomena. If such is the case, it is not surprising that, in the evolution biological processes, integrated in a probabilistic model, we note the existence of an economy or optimization specific biological process, that we indicated under the optimization Principle term and who ensures the organisms adaptation.

The optimization Principle globalise, by the great figures Bernoulli law means, in the biological field, the economy principles which govern the general physical phenomena (the shortest movement, minimal energy, less action). The optimization Principle thus appears, in last analysis, like the probability theory biological synthetic expression, applied to the biological processes.

Today, the S.T.E. (Synthetic Theory of the Evolution) constitutes, the standard model for the explanation of the evolution. The darwinian theory merit is to have proposed, in the nineteenth century, a credible theory of the vast evolution of organized beings. The natural selection is the result many centuries (if not millenia) where the biological concepts were based on anthropomorphic concepts (advantages), finalists (organs and functions) and, ultimately, value judgments. The S.T.E. reorientated towards rigorous and fertile disciplines, like the genetics of the populations, cellular biology or molecular biology but the original finalism sin persists. The adaptation, evolution engine, always arise, in the S.T.E., like a utility concept. The need for apprehending the biological phenomena without a priori finalist appears impossible to circumvent. To speak, for example, of the melanin "role", rather than of its properties, scientifically seems to us an unacceptable finalist drift. It is obvious that such a proposal cannot be accepted without a huge resistance. It runs up against centuries, if not millenia, of teleological attitude. One must however regard it as inescapable, if one wishes the neutral biological sciences existence, i.e. free from presupposed finalists.

On the explanatory level, the reproach which is generally made with the S.T.E., is its insufficiency to account for macro and the megaevolution. Anagenese, according to the adaptive zone changes, cladogenese according to the new ecological niches occupation, gradualism or punctuated balances find their origin in the genome random mutations (Tintant 1983). Those, which intervene in the speciation processes, have a very insufficient explanatory capacity with regard to the classes and the sub-kingdoms chronology appearance. The most current phyla origin in basal and middle Cambrian, with or without skeleton (certain authors consider the appearance at that time from 60 to 100 Baupläne, Valentine 1986), does not find its place in the S.T.E. It is the same for the mass extinctions, the evolution general tendency towards more complexity, effectiveness and independence with respect to the medium (diploblastic, triploblastic organisms, amniotes, homeotherms). All these major phenomena escape the standard model from the S.T.E. The correlations which we established between certain environment parameters (Ca, I, O) and the induced biodiversity evolution do not find either an explanation within the S.T.E. framework.

We thus propose, as an alternative to the S.T.E., a probabilistic interaction model between the environmental evolution and the evolution of the organisms. It is clear that the environment parameters are not reduced to the only chemical stimuli which we studied but extend to all those which are significant (C, N, H, P, S... to quote only some of them), with the physical stimuli (electromagnetic waves, sound waves and vibrations, pheromones, temperatures, etc...), with the varied ecological situations, the beasts of preys/preys relations, etc...

The biosphere environment is infinitely complex and is at all the levels, as well macroscopic as molecular. The organisms reaction to the environmental factors influence is multiple and varied (radiation and disappearance significant calcic metabolism organisms, encephalisation, watery or air respiratory systems, etc...). It is located as well at the genome level as behavior, with that of molecular biology, embryogenesis and anatomical structures.

The relation between the environmental parameters and the organisms, such as we propose it, is of probabilistic nature. The probabilistic model interprets the evolution major events (i.e. the macro one and the megaevolution), but also speciations, like the couple environment/organisms interactions resultant of the probabilistic influence, in an environment in perpetual modification: "cambrian explosion", radiations and mass extinctions, respiratory systems anatomical and physiological transformations...

Contrary to the S.T.E., where the genetic variations interest only populations or species, the probabilistic model integrate collective phenomena affecting simultaneously distant classes and phyla (Invertebrates and Vertebrates). In the S.T.E., the natural selection sorts, among the random genetic mutations, those which are favorable to the individual or the species (the Dawkins egoistic gene 1990). The result of this choice is adaptation. In the probabilistic model, the evolution of the organisms is a reaction to the environmental evolution. This reaction is probabilist and optimal. It is necessarily located at the genome level, organism memory and engine, by environmental directed mutations, chemical, physical, or other parameters. We saw (paragraph 6, Allorge-Boiteau 1991) the observation of colon bacilli and bacteria Escherichia coli optimizing mutations caused by a modified environment. The probabilistic model escapes the finalist critic from the S.T.E. The probability and optimization (or economy) concepts are neutral, objective and constant concepts in sciences of nature. As we tried to show it in three chemical examples (Ca, I and O), they offer a remarkable explanatory capacity.

The biological evolution probabilistic model stresses the environment influence and its variations. The S.T.E. is primarily based on the genome random mutations and the favorable mutations perennisation by the natural selection to ensure the adaptation of the organisms to a changing environment.

The darwinian model is a model where the organism internal factors, the random genetic mutations, are at the origin of the evolution directed by the natural selection. Among these random mutations, some are neutral, others are lethal, others are regarded as advantageous and thus retained by the natural selection which ensures the organisms adaptation. We will not extend on this point which caused violent controversies. One can simply point out that mutations, of strictly internal origin, which converge opportunely with environment modifications (increase in the calcium, iodine or oxygen rate) approach strangely miraculous coincidences. Whereas, in the probabilistic model, this convergence is directly induced by the organisms reaction to the influence of the environment stimuli.

The probabilistic model is a model where the evolution engines are primarily external. The environment parameters influence passes nevertheless, necessarily, by the genome modification and thus of the genetic mutations. Whereas in the S.T.E., those are strictly random, in the probabilistic model, they represent the reaction of the organisms, via the genotype and the phenotype, with the variations of environment parameters. We saw higher than genetic mutations can be induced by environment modifications. Contrary to the S.T.E. model, in the probabilistic model, the evolutionary genetic mutations are not at random but are directed, in a probabilistic way. As we showed it, the phenotypical evolutions can be dated, chronologically, by the environmental parameters variations (PO2 P.A.L. rate growth, calcium stimulus influence in radiations and mass extinctions, "cambrian explosion", etc...) and thus, a posteriori, the genetic corresponding mutations.

The probabilistic model is not opposed to the S.T.E. and with its assets: genetic mutations, mutations rate, the populations genetics, population cages experiments (Dobzhansky), etc... It integrates the S.T.E. while interpreting, in a different way, the relations between organisms and environment. According to the S.T.E., the permanent interaction between the random genetic variations and the natural selection, which sorts the favorable variations, ensures the organisms adaptation to the medium. According to the probabilistic model, the permanent interaction between the organisms and a fluctuating environment, direct the genetic mutations. This interaction, not finalist, of probabilistic and optimal nature, ensure the organisms adaptation to their environment. The S.T.E. thus interprets the population cages experiments results like the most suited survival (value judgment). The probabilistic model integrates these facts, by interpreting them in a different way, objectifies, like the probability theory resultant. Individuals, or species, whose mathematical survival chances are largest, by their robustness, or all other factors, is those which survive. Thus, fecondity, as many other favours, is not interpreted anymore, in the probabilistic model, as an advantage which perrenializes the individual or the species, but like an increase in the mathematical chances of survival. Individuals, or the species, whose mathematical survival chances are weaker (more fragile, more vulnerable, less fertile, etc...), are eliminated. It is the simple application of the great figures law, in these experiments.

Like einsteinian relativity absorbed the newtonian gravitation, the probabilistic model integrates the S.T.E. genetic variations and their prolongations, mutations rate, populations genetics... by directing them and in substituing to a finalist logic, natural selection, a neutral logic, probabilistic and optimizing. This probabilistic logic is found in the Biston betuleria traditional example which we evoked in chapter IV. What the S.T.E. interprets as a selective advantage, the probabilistic model interprets like a mathematical survival chance. On a side, a utility concept, finalist, other, a probabilistic concept. In the probabilistic model, the darwinian "advantage" is preserved but is interpreted in "mathematical chance" term, within the probability theory framework. In a parallel way, all genetic favorable variations darwinian interpretations perennialized by the natural selection pressure can and must be interpreted in mathematical chances terms and probabilistic variations. The same facts thus concern two different interpretations, one finalist, the other strictly neutral and probabilistic.

In addition, the probabilistic model exceeds speciation, privileged S.T.E field. It includes the major biological macro and megaevolution phenomena, mass extinctions, "cambrian explosion", environment stimuli evolution (Ca, I and O) and organisms collective reactions chronological concomitance, of which the S.T.E. cannot explain.

If the probability factors have a considerable influence in the evolution, it would seem abusive to allot to them an exhaustive role in all structures and biological properties explanation. certain biological phenomena neutrality and specificity cannot be neglected (neutral mutations, genetic drift, genes connection, tissues differential growth, etc...).

Far from allotting a panglossian orientation (Gould, Lewontin 1979) to the biological phenomena, the probabilistic model interprets the biodiversity like the possible worlds most probable, in a given environment. It is probable that, just like the living matter evolution, the probability factors had to play a decisive role in the living matter origin on the earth. A certain number of chemical molecules availability (C, H, O, N, P), adequate physical conditions (temperature, pressure, etc...) and other essential parameters (solar energy, earth's crust cooling, etc...) created the conditions where the possibility of the emergence biotic chemistry were joined together. One can thus consider that the live emergence on the earth is not a random fact or a miracle but rather the most probable consequence, induced by the sufficient mathematical chances of a possible biotic chemistry, of an idoine environment.

Thus interpreted, the living matter existence on other planets does not seems exceptionnal but rather highly probable and banal, as soon as sufficient conditions of probability are present.

To conclude, it is significant to recall that the probability theory use is a constant in the study and the modelisation of many natural phenomena. Let us quote, out of memory, statistical mechanics, thermodynamics (in particular its second law), the kinetic gases theory, quantum physics, the Mendel's laws in genetics, etc...