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Origins of life: first came evolutionary dynamics
- Charles Kocher, Ken A. Dill
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- Journal:
- QRB Discovery / Volume 4 / 2023
- Published online by Cambridge University Press:
- 22 March 2023, e4
- Print publication:
- 2023
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When life arose from prebiotic molecules 3.5 billion years ago, what came first? Informational molecules (RNA, DNA), functional ones (proteins), or something else? We argue here for a different logic: rather than seeking a molecule type, we seek a dynamical process. Biology required an ability to evolve before it could choose and optimise materials. We hypothesise that the evolution process was rooted in the peptide folding process. Modelling shows how short random peptides can collapse in water and catalyse the elongation of others, powering both increased folding stability and emergent autocatalysis through a disorder-to-order process.
New Evo-SETI results about civilizations and molecular clock
- Claudio Maccone
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- Journal:
- International Journal of Astrobiology / Volume 16 / Issue 1 / January 2017
- Published online by Cambridge University Press:
- 28 March 2016, pp. 40-59
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In two recent papers (Maccone 2013, 2014) as well as in the book (Maccone 2012), this author described the Evolution of life on Earth over the last 3.5 billion years as a lognormal stochastic process in the increasing number of living Species. In (Maccone 2012, 2013), the process used was ‘Geometric Brownian Motion’ (GBM), largely used in Financial Mathematics (Black-Sholes models). The GBM mean value, also called ‘the trend’, always is an exponential in time and this fact corresponds to the so-called ‘Malthusian growth’ typical of population genetics. In (Maccone 2014), the author made an important generalization of his theory by extending it to lognormal stochastic processes having an arbitrary trend mL(t), rather than just a simple exponential trend as the GBM have.
The author named ‘Evo-SETI’ (Evolution and SETI) his theory inasmuch as it may be used not only to describe the full evolution of life on Earth from RNA to modern human societies, but also the possible evolution of life on exoplanets, thus leading to SETI, the current Search for ExtraTerrestrial Intelligence. In the Evo-SETI Theory, the life of a living being (let it be a cell or an animal or a human or a Civilization of humans or even an ET Civilization) is represented by a b-lognormal, i.e. a lognormal probability density function starting at a precise instant b (‘birth’) then increasing up to a peak-time p, then decreasing to a senility-time s (the descending inflexion point) and then continuing as a straight line down to the death-time d (‘finite b-lognormal’).
(1) Having so said, the present paper describes the further mathematical advances made by this author in 2014–2015, and is divided in two halves: Part One, devoted to new mathematical results about the History of Civilizations as b-lognormals, and
(2) Part Two, about the applications of the Evo-SETI Theory to the Molecular Clock, well known to evolutionary geneticists since 50 years: the idea is that our EvoEntropy grows linearly in time just as the molecular clock.
(a) Summarizing the new results contained in this paper: In Part One, we start from the History Formulae already given in (Maccone 2012, 2013) and improve them by showing that it is possible to determine the b-lognormal not only by assigning its birth, senility and death, but rather by assigning birth, peak and death (BPD Theorem: no assigned senility). This is precisely what usually happens in History, when the life of a VIP is summarized by giving birth time, death time, and the date of the peak of activity in between them, from which the senility may then be calculated (approximately only, not exactly). One might even conceive a b-scalene (triangle) probability density just centred on these three points (b, p, d) and we derive the relevant equations. As for the uniform distribution between birth and death only, that is clearly the minimal description of someone's life, we compare it with both the b-lognormal and the b-scalene by comparing the Shannon Entropy of each, which is the measure of how much information each of them conveys. Finally we prove that the Central Limit Theorem (CLT) of Statistics becomes a new ‘E-Pluribus-Unum’ Theorem of the Evo-SETI Theory, giving formulae by which it is possible to find the b-lognormal of the History of a Civilization C if the lives of its Citizens Ci are known, even if only in the form of birth and death for the vast majority of the Citizens.
(b) In Part Two, we firstly prove the crucial Peak-Locus Theorem for any given trend mL(t) and not just for the GBM exponential. Then we show that the resulting Evo-Entropy grows exactly linearly in time if the trend is the exponential GMB trend.
(c) In addition, three Appendixes (online) with all the relevant mathematical proofs are attached to this paper. They are written in the Maxima language, and Maxima is a symbolic manipulator that may be downloaded for free from the web.
In conclusion, this paper further increases the huge mathematical spectrum of applications of the Evo-SETI Theory to prepare Humans for the first Contact with an Extra-Terrestrial Civilization.
Evolution and mass extinctions as lognormal stochastic processes
- Claudio Maccone
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- Journal:
- International Journal of Astrobiology / Volume 13 / Issue 4 / October 2014
- Published online by Cambridge University Press:
- 21 July 2014, pp. 290-309
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In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are:
(1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.
(2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics.
(3) The (Shannon) entropy of such b-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller ‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.
(4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics).
(5) But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the ‘constant rate of Evolution at the molecular level’ as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life.
(6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms.
(7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time.
SETI, Evolution and Human History Merged into a Mathematical Model
- Claudio Maccone
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- Journal:
- International Journal of Astrobiology / Volume 12 / Issue 3 / July 2013
- Published online by Cambridge University Press:
- 23 April 2013, pp. 218-245
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In this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:
(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.
(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.
(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.
(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.
(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.
(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.
On the applicability of Darwinian principles to chemical evolution that led to life
- Randall S. Perry, Vera M. Kolb
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- Journal:
- International Journal of Astrobiology / Volume 3 / Issue 1 / January 2004
- Published online by Cambridge University Press:
- 05 August 2004, pp. 45-53
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Chemical evolution at the primitive prebiotic level may have proceeded toward increased diversity and complexity by the adjacent possible process (originally proposed by Kauffman). Once primitive self-replicating systems evolved, they could continue evolution via Eigen's hypercycles, and by Prigogine's emergence of order at the far-from-the equilibrium, non-linear systems. We envisage a gradual transition from a complex pre-life system, which we call the transition zone. In this zone we find a mixture of complex chemical cycles that reproduce and secure energy. Small incremental changes in the structure and organization of the transition zone eventually lead to life. However, the chemical systems in this zone may or may not lead to life. It is possible that the transition to life might be the result of an algorithm. But, it is uncertain whether an algorithm could be applied to the systems in which chance plays a role.