Scaling law of the biological evolution and the hypothesis of the self-consistent Galaxy origin of life

A. D. Panov

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Russia



It is shown that the sequence of the Earth's biospheric revolutions obeys the scaling law. An estimation of the duration of the prebiological chemical evolution as (5-7)×109 years is obtained by an extrapolation of the scaling law of the biospheric evolution. The expected scale of time of interstellar prebiological panspermia ( ~0.2×109 yr) is much shorter then the estimated duration of the prebiological chemical evolution. It implies that a) the prebiological chemical evolution and the origin of life may be a self-consistent Galaxy process and not a process localized on single planets and b) life in the Galaxy has the same chemical base and the same chirality in all places.


1  Scaling law of the Earth's biospheric evolution

Life must be originated in a process of a natural chemical prebiological evolution-maybe on the Earth, maybe in some other place, and then brought to the Earth by the panspermia process. Nobody can estimate now the duration of the prebiological evolution from the 'first principles' or from experiment. In the first part of the present paper we will show that it is possible to obtain an independent phenomenological estimation of the duration of the prebiological chemical evolution on the base of the phenomenon of scaling law of the Earth's biospheric evolution. This estimation should be considered as a hypothesis.

The history of life on the Earth was started with arising of the biosphere about 4×109 years ago [1] and was continued by the history of the intelligence after arising of Homo about 4.4×106 years ago [2]. We will speak about the evolution of biosphere in the generalized sense. We consider the evolution of the biosphere itself and then the history of humankind to be united continuous process. Similarly, the term 'biosphere' is understood in the generalized sense. Biosphere includes the civilization at the latest stages of its history.

The evolution of the Earth’s biosphere passed trough a sequence of phases with phase transitions between them-biospheric revolutions. The complete set of biospheric revolutions will be used in the following analysis. There is no exact method to select biospheric revolutions, therefore the following list of them should be considered as a proposal for farther discussion. To collect the events that may be qualified as biospheric revolutions we use a number of signs of them as proposed by A. Nazaretian [3,4] and estimations of some well-established biospheric or historical events that are presented in literature. The sequence of biospheric revolutions is listed below with numeration starting from zero. The dates of events in the list are presented very approximately, but high accuracy of dates is not needed in the following analysis. Each date may be safely moved to the past or future up to 30% relative to the present time.

0. The origin of life-4×109 years ago [1]. The biosphere after it's appearance was represented by nucleusless procaryotes and existed the first 2-2.5 billion years without any great shocks.

1. Neoproterozoic revolution (Oxygen crisis)-1.5×109 years ago [5,6]. Cyanobacteria had enriched the atmosphere by oxygen that was a strong poison for anaerobic procaryotes. Anaerobic procaryotes started to die out and anaerobic procaryote fauna was changed by an aerobic eucaryote and multicellular one.

2. Cambrian explosion (The beginning of Paleozoic era)-570×106 years ago [7,V1], [8]. All the modern phyla of metazoa (including vertebrates) appeared during a few of decades of million years. During the Paleozoic era the terra firma was populated by life.

3. Reptiles revolution (The beginning of Mesozoic era)-235×106 years ago [9,10], [7,V1,V2]. Almost all paleozoic Amphibia died out. Reptiles became the leader of the evolution on the terra firma.

4. Mammalia revolution (The beginning of the Cenozoic era)-66×106 years ago [10,11], [7,V2,V3]. Dinosaurs died out. Mammalia animals became the leader of the evolution on the terra firma.

5. Hominoid revolution (The beginning of the Neogene period)-24×106 years ago [11,12], [7,V3]. A big evolution explosion of Hominoidae (apes). There were 14 genera of hominoidae between 22 and 17 millions years ago-much more than now [12]. The flora and fauna became contemporary.

6. The beginning of Quaternary period (Anthropogene)-(4-5)×106 years ago [2,13]. The first primitive Homo genus (hominidae) separated from hominoidae.

7. Palaeolithic revolution-(2-1.5)×106 years ago [13]. Homo habilis, the first stone implements.

8. The beginning of Chelles period-0,7×106 years ago [13]. Fire, Homo erectus.

9. The beginning of Acheulean period-0,4×106 years ago [13]. Standardized symmetric stone implements.

10. The culture revolution of neanderthaler (Mustier culture)-(150-100)×103 years ago [13]. Homo sapiens neandertalensis. Fine stone implements, burial of deadmen (a sign of primitive religions).

11. The Upper Palaeolithic revolution-40×103 years ago [13]. Homo sapiens sapiens became the leader of the evolution. Development of a hunter automatic-spears, snares. Imitative art is widespread.

12. Neolithic revolution-(12-9)×103 years ago [14,3]. Appropriative economy had been replaced by productive economy.

13. Urban revolution (the beginning of the Ancient world)-4000-3000 B.C. [14,3]. Appearance of state formations, written language and the first legal documents.

14. Imperial antiquity, Iron age, the revolution of the Axial time-750 B.C. [14,3,15]. The appearance of a new type of state formations-empires, and a culture revolution. New kinds of thinkers such as Zaratushtra, Socrates, Budda, and others.

15. The beginning of the Middle ages-500 A.D. [14].

16. The beginning of the New Time, the first industrial revolution-1500 A.D. [14,3]. Appearing of manufacture, printing of books, the New time culture revolution etc.

17. The second industrial revolution (steam and electricity)-1830 [14]. Appearance of mechanized industry, the beginning of globalization in the information field (telegraph was invented in 1831), etc.

18. Information revolution, the beginning of the postindustrial epoch-1950 [14]. The main part of population of industrial countries work in the field of information production and utilization or in the service field, not in the material production.

It is easy to see that the duration of the phases of biospheric evolution reduces from the past to the present. It is a manifestation of the well known "acceleration of the evolution time" phenomenon. Moreover, the sequence of biospheric phase transitions in some approximation has a property of scale invariance [16]. It means that the sequence of corresponding time points is a simple geometrical progression and different parts of this sequence may be obtained from each other by scale transformation.

An ideal scale invariant sequence of points may be written as

tn = t* - T / an.



In Eq. (1) the coefficient a > 1 is a coefficient of reduction of the duration of each subsequent evolution phase comparing with the corresponding preceding one. T is a duration of the whole period of time under consideration, n is a number of phase transition, and t* is the limit of the geometrical progression {tn} and t* may be called as 'singularity of the evolution'.

There are three free parameters a,t*,T that can be obtained by the best fitting of scale invariant sequence Eq. (1) to the actual (experimental) sequence of the biosphere revolutions-it is a simple mathematical procedure. To understand what is the quality of the approximation it is suitable to rewrite Eq. (1) as

lg(t* - tn) = lgT - nlga.


It is seen that the dependence of the distance from the point of transition tn to the singular point t* in the logarithmic scale from the transition number n must be approximately a straight line.

The result of such kind of analysis is shown on Fig. 1. It is seen that the sequence of the biospheric revolutions satisfies the scaling law in a good approximation. It is possible to say that there exists an scale invariant attractor of the evolution (straight line on Fig. 1). The actual evolution follows this attractor only with relatively small fluctuations. Since the scale invariant attractor exists, the parameters a and t* become meaning. The analysis produces the values:

a = 2.67±0.15;    t* = (2004±15) year.



It is funny to note that a » e = 2.718... Note also that since t*=2004 year, one can conclude that we live near the final point of the cycle of the scale invariant evolution with duration four billion years. The phenomenon of the acceleration of the evolution time must stop in the nearest future and the evolution on the Earth must proceed in a completely new way.

2  Time scale of prebiological chemical evolution

E. M. Galimov [17,Chapter 3] argued that the prebiological chemical evolution, origin of life, and the subsequent evolution of a biosphere (on any planet) is a united process based on disproportioning of entropy, transferability and evolution conservatism in the stationary no-equilibrium systems. We see (Section 1) that the higher the organization of the biosphere, the higher the speed of its evolution. Since any prebiological system is organized lower than any biological system and since the prebiological chemical evolution and the biological evolution may be considered as a united process, then one can suppose that the speed of the prebiological evolution is to be lower than the speed of subsequent evolution of a biosphere. Moreover, being the united process with evolution of life, one can suppose that prebiological evolution lies in the same scale invariant attractor of evolution as evolution of a biosphere. Since we have one example of such scale of time, we can estimate the duration of the prebiological chemical evolution by extrapolation of this scale back in time. Using the estimated value of a as in Eq. (2) and the duration of the first step of the biological evolution 4.0×109-1.5×109=2.5×109 years (it is the distance between the origin of life and the Neoproterozoic revolution) one can obtain the estimation for the duration of the prebiological chemical evolution: tchem = 2.5×109×2.67 » 6.7×109 years. A more rigorous technique is to extrapolate directly the optimal scale invariant attractor. This method produces the value tchem » 5.5×109 years. One can conclude that the extrapolated value of the duration of the prebiological chemical evolution is tchem = (5-7)×109 years.

The value tchem » 6×109 years is very long. At the same time it is argued that the duration of the prebiological chemical evolution on the Earth actually was very short: shorter than 0.2×109 years [1] (from 4.1 to 3.9 billion years ago). The actual duration of the prebiological evolution on the Earth is not only unexpectedly short. Moreover, it is in a deep contradiction with subsequent scale invariance of the biological evolution. It is seen a sharp anomaly if one draws the point of the beginning of the prebiological evolution on the Earth together with the biological phase transitions ("hockey stick", see Fig. 2). A resolution of this contradiction may be the following. The duration of the prebiological evolution is in fact about 6 billion years, but it took place not on the Earth but on the other Earth-like planets near the stars much older then the Sun. And life could be brought to the Earth by the panspermia process [18]. The idea of panspermia was supported by discovering the meteorites from the surface of Mars and other planets [19].

It is interesting that the extrapolated beginning of the prebiological evolution 4×109 + 6×109 = 10×109 years ago almost coincides with the time of the formation of the Galaxy disk [20]. The Galaxy disk is the subsystem of our Galaxy that contains the stars with a high fraction of heavy chemical elements. Just such stars are needed to produce Earthlike planets. Therefore to have time for the origin of life on the Earth the prebiological evolution must have started on the very first Earthlike planets in the Galaxy simultaneously with the Galaxy disk formation. This implies that the evolution on the Earth may be near to the front of the total evolution in the Galaxy.

3  Self-consistent Galaxy origin of life

In Section 2 it was argued that the short prebiological chemical evolution on the Earth may actually mean the possibility of the panspermia process and a long prebiological evolution on other Earth-like planets (but not on the Earth). But if we suppose the possibility of the biological panspermia, then we should suppose the possibility of prebiological panspermia as well, because the products of a prebiological evolution must be less sensitive to the difficulties of a cosmic travel than any biological systems. One can expect the time scale of the Galaxy panspermia process to be about 200 million years-the scale of one Galaxy year. Any matter (prebiological or biological systems and other) emitted from the surface of any planet will be spread upon the volume of almost the whole Galaxy disk for about one Galaxy year due to the differential rotation of the Galaxy disk. Therefore we have two time scales: one is a long scale, tchem » 6×109 years, this is the scale of the natural prebiological chemical evolution; and one is a short scale, tpan ~ 0.2×109 years-the scale of the panspermia process. The existence of these two scales of time implies that the prebiological chemical evolution on different Earthlike planets could not be independent from each other.

Let suppose, some good (in some sense) prebiological system (for example, a stable autocatalytic chain) appears on some Earthlike planet at the stage of the prebiological evolution of the Galaxy (before life originates in the Galaxy for the first time). This is quite a random event. Then during a short time of order tpan this good prebiological system will be spread by the panspermia process on all Earthlike planets which are also at the stage of chemical evolution. This progressive system must dislodge less fortunate prebiological systems of the host planet and move the evolution forward with the new chemical base. This is a selection process in the scale of the whole Galaxy. Due to the condition tpan << tchem this process must synchronize prebiological chemical evolution in the volume of the whole Galaxy and implicates the appearance of life almost simultaneously in all the planets that have suitable conditions for life hosting, and on the same chemical base and with the same chirality. This event is like a no-equilibrium phase transition of the Galaxy. The prebiological chemical evolution and the origin of life may be a self-consistent Galaxy process and not a process localized on single planets as is usually supposed-this is the formulation of the hypothesis of self-consistent Galaxy origin of life. This hypothesis is the implication of the supposition that the natural prebiological chemical evolution belongs to the same automodel scale of time as the evolution of the life on the Earth. If the hypothesis of self-consistent Galaxy life origin is valid, then after the transition of the Galaxy to the era of life, the life does not originate by a process of 'natural' chemical evolution. Natural evolution can not concurrent with the much faster process of biological panspermia.

Note, that if life may exist on planets with conditions which are sharply different from the Earth's, then life in the Galaxy may exist in a number of different phases corresponding the classification of the conditions on planets-without any competition between different phases. But in the present stage of the study of the problem this note may be considered as unimportant. The existence of the common chemical base and chirality of life in the Galaxy is an experimental critical test of the hypothesis of self-consistent Galaxy origin of life.

4  Conclusions

If the duration of the prebiological chemical evolution is very long (billion years) then the chemical evolution can not be localized on different single planets due to the prebiological panspermia and the origin of life is expected to be a self-consistent Galaxy process. The scale invariant attractor of the biospheric evolution on the Earth hints that the duration of the prebiological chemical evolution actually may be very long.


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Figure 1: The automodelity of the distribution of the biospheric phase transitions in time. Triangles-pure biospheric transitions, squares-transitions of the social history. Straight line-automodel attractor of the evolution on the Earth.


Figure 2: Extremely short time of the prebiological chemical evolution on the Earth produces an anomaly 'hockey stick' in the automodel scale of time of the evolution.