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NOTA CIENTÍFICA
ON THE NATURE OF EVOLUTION: AN EXPLICATIVE MODEL
Sobre la naturaleza de la evolución: un modelo explicativo
Arcadio Monroy-Ata
Corresponding author
arcadiom@unam.mx

Corresponding author.
, Juan Carlos Peña-Becerril
Unidad de Investigación en Ecología Vegetal, Facultad de Estudios Superiores Zaragoza, Campus II, UNAM. Batalla del 5 de mayo esq. Fuerte de Loreto, Col. Ejército de Oriente, C.P. 09230, Ciudad de México, México
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    "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">INTRODUCTION</span><p id="par0005" class="elsevierStylePara elsevierViewall">What is life&#63; Technically&#44; it could be defined as cells with evolutionary potential&#44; make up by organic matter and getting on in an autopoyetic metabolism<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">&#91;1&#93;</span></a>&#46; Organisms use energy flow gradients at different organization levels in accord with physical laws&#46; The living systems have three principal functions as self-organizing units&#58; a&#41; compartmentalization&#44; b&#41; metabolism&#44; and c&#41; regulation of input and output information flux<a class="elsevierStyleCrossRef" href="#bib0010"><span class="elsevierStyleSup">&#91;2&#93;</span></a>&#46; The layer between internal and external environment of organisms controls matter&#44; energy and information flows&#59; metabolism regulates epigenetic and autopoyetic processes&#59; biological information is a program &#40;and a set of programs&#41; that operates both physiology and functionality&#44; codified in the DNA<a class="elsevierStyleCrossRef" href="#bib0015"><span class="elsevierStyleSup">&#91;3&#93;</span></a>&#46;</p><p id="par0010" class="elsevierStylePara elsevierViewall">Darwinian theory of evolution by means of variation&#44; natural selection and reproductive success of heritable variation in populations and organisms&#44; can be defined as an ecological process that change the covariance of phenotypic traits &#40;as expression of genetic&#44; epigenetic&#44; ontogenic and environmental factors&#41; in living organisms or biological systems grouped at different organization levels<a class="elsevierStyleCrossRef" href="#bib0020"><span class="elsevierStyleSup">&#91;4&#93;</span></a>&#46; Natural selection operates on biological systems that have three features&#58; a&#41; variability&#44; b&#41; reproductivity&#44; and c&#41; heritability&#59; one result of natural selection is a tendency toward to an increase in fitness and functionality of biological systems in an environmental stochasticity &#40;both biotic and abiotic&#41;&#46; Fitness is a measure of reproductive success of changes in allele frequency of organisms on a determinate ecological noise&#44; conditioned on the phenotype or genotype<a class="elsevierStyleCrossRef" href="#bib0025"><span class="elsevierStyleSup">&#91;5&#93;</span></a>&#46;</p><p id="par0015" class="elsevierStylePara elsevierViewall">In this paper&#44; an analogy between a biological system and a message was made&#59; it was also considered the environmental stochasticity as the noise when a message is transmitted&#46; Thus&#44; the biological system is analogous to the amount of information of a message &#40;for example&#58; genetic information&#41; that is transported to the next generation inside an ecological noise&#46; This favors the use of the Norbert Wiener model of message&#39;s transmission in a telephonic line with noise<a class="elsevierStyleCrossRef" href="#bib0030"><span class="elsevierStyleSup">&#91;6&#93;</span></a>&#46; In our model&#44; it has been considered that information could be as simple as a binary unit &#40;bit&#44; 0 and 1&#41;&#44; but it can grow by the additive property<a class="elsevierStyleCrossRefs" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#44;8&#93;</span></a>&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">The amount of information defined by Wiener<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 62&#41; is the negative of the quantity usually defined as statistical entropy&#46; This principle of the second law of thermodynamics can be understood for a closed system as the negative of its degree of restrictions<a class="elsevierStyleCrossRef" href="#bib0045"><span class="elsevierStyleSup">&#91;9&#93;</span></a> &#40;p&#46; 23&#41;&#44; i&#46;e&#46;&#44; its structuration level&#46; Also&#44; G&#46;N&#46; Lewis in 1930 &#40;cited by Ben-Naim<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">&#91;10&#93;</span></a> p&#46; 20&#41; quotes&#58; &#8220;Gain in entropy always means loss of information&#8221;&#46;</p><p id="par0025" class="elsevierStylePara elsevierViewall">In relation to information theory&#44; L&#233;on Brillouin in his book &#8220;La informaci&#243;n y la incertidumbre en la ciencia&#8221;<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">&#91;11&#93;</span></a> &#40;p&#46; 22-25&#41; wrote that entropy is connected with probabilities as is expressed in equations by Ludwig Eduard Boltzmann and Max Planck&#44; and suggested that information is a negative entropy<a class="elsevierStyleCrossRefs" href="#bib0060"><span class="elsevierStyleSup">&#91;12&#44;13&#93;</span></a> or negentropy<a class="elsevierStyleCrossRef" href="#bib0060"><span class="elsevierStyleSup">&#91;12&#93;</span></a>&#46; But instead of using the term of entropy&#44; Arieh Ben-Naim<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">&#91;10&#93;</span></a> &#40;p&#46; 21&#41; proposes to replace it by &#8220;missing information&#8221;&#46;</p><p id="par0030" class="elsevierStylePara elsevierViewall">Nevertheless&#44; the second law of thermodynamics neither implies one-way time&#44; nor has a statistical probabilities model&#46; For this reason&#44; in this paper it was employed a time series tool and the Brownian motion as a model to simulate the dynamics of the amount of information of a message&#44; as an analogous of a biological system&#46; This approach shows that biological information could be carried by &#8220;some physical process&#44; say some form of radiation&#8221; as Wiener<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> wrote &#40;p&#46; 58&#41;&#46; What wavelength&#63; Brillouin<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">&#91;11&#93;</span></a> &#40;p&#46; 132&#41;&#44; in his scale mass-wavelength equals a mass of 10<span class="elsevierStyleSup">&#8722;17</span> g to a wavelength of 10<span class="elsevierStyleSup">&#8722;20</span> cm&#59; for this scales&#44; it could be important to consider <span class="elsevierStyleItalic">k</span>&#44; the Boltzmann constant&#44; because its value is 1&#46;38 x 10<span class="elsevierStyleSup">&#8722;16</span> erg&#47;&#176;K&#44; in unities of the system cm&#44; g&#44; second&#46; Likewise&#44; a quantum <span class="elsevierStyleItalic">h</span> can be expressed as <span class="elsevierStyleItalic">h</span> &#61; 10<span class="elsevierStyleSup">&#8722;33</span> cm&#59; this smaller length &#8220;plays a fundamental role in two interrelated aspects of fundamental research in particle physics and cosmology&#8221;<a class="elsevierStyleCrossRef" href="#bib0070"><span class="elsevierStyleSup">&#91;14&#93;</span></a> and &#8220;is approximately the length scale at wich all fundamental interactions become indistinguishable&#8221;<a class="elsevierStyleCrossRef" href="#bib0070"><span class="elsevierStyleSup">&#91;14&#93;</span></a>&#46; Moreover&#44; it is necessary to mention that Brownian motion is a thermic noise that implies energy of the level <span class="elsevierStyleItalic">k</span>T &#40;where T is temperature&#41; by degree of freedom<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">&#91;11&#93;</span></a> &#40;p&#46; 135&#41;&#46; It was hypothesized that this radiation could be the wavelength of photons incoming on Earth&#39;s surface&#44; irradiated by the photosphere of the Sun at a temperature of 5760 &#176;K&#59; after the dissipation of high energy photons to low energy ones&#44; through irreversible processes that maintain the biosphere&#44; the temperature of the outgoing photons that Earth radiates to space is 255 &#176;K<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">&#91;15&#93;</span></a>&#46; This incoming radiation support plant photosynthesis&#44; evapotranspiration flow&#44; plant water potential&#44; plant growth&#44; energy for carbon-carbon bonds &#40;or C-H&#44; C-O&#44; O&#61;O&#44; etc&#46;&#41;&#44; and food of the trophic chains in ecosystems&#44; among other energy supported processes&#46;</p><p id="par0035" class="elsevierStylePara elsevierViewall">The question to answer in this paper is&#58; What is the driven force of biological evolution&#63; The possible answer is that driven force is the dynamics of the amount of information in a biological system &#40;genetic and epigenetic messages&#41;&#46; Antoine Danchin<a class="elsevierStyleCrossRef" href="#bib0080"><span class="elsevierStyleSup">&#91;16&#93;</span></a>&#44; in a similar approach&#44; proposes that mechanical selection of novel information drives evolution&#46; In the next section&#44; it will be described the mathematical model of the dynamics of message transmission&#44; as a proposal to explain the nature of biological evolution&#46;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0030">THE MODEL</span><p id="par0040" class="elsevierStylePara elsevierViewall">Shannon entropy formula is<a class="elsevierStyleCrossRef" href="#bib0085"><span class="elsevierStyleSup">&#91;17&#93;</span></a> &#40;p&#46; 291&#41;&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia></p><p id="par0045" class="elsevierStylePara elsevierViewall">Where &#937; is the number of microstates or possible arrangements of a system&#44; for N particles that can occupy <span class="elsevierStyleItalic">m</span> states with occupations numbers &#40;<span class="elsevierStyleItalic">n</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#44; n</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span>&#44; &#8230;&#46;&#46;&#44; <span class="elsevierStyleItalic">n</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">m</span></span>&#41; and <span class="elsevierStyleItalic">k</span> is the Boltzmann constant&#44; that is R &#40;the ideal gas constant&#41; divided by the Avogadro&#8242;s number&#58;<elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0050" class="elsevierStylePara elsevierViewall">and Brillouin information &#40;I&#41; formula<a class="elsevierStyleCrossRef" href="#bib0090"><span class="elsevierStyleSup">&#91;18&#93;</span></a> &#40;p&#46; 1&#41; is&#58;<elsevierMultimedia ident="eq0015"></elsevierMultimedia></p><p id="par0055" class="elsevierStylePara elsevierViewall">Where K is a constant and P<span class="elsevierStyleInf">o</span> is the number of possible states of a system&#44; keeping in reserve that the states have <span class="elsevierStyleItalic">a priori</span> the same probability&#46; The logarithm means that information has the additive property&#46;</p><p id="par0060" class="elsevierStylePara elsevierViewall">For example&#44; if the configuration states of two independent systems are coupled in this way&#58; P<span class="elsevierStyleInf">0</span> &#61; P<span class="elsevierStyleInf">01</span> &#183; P<span class="elsevierStyleInf">02</span><elsevierMultimedia ident="eq0020"></elsevierMultimedia></p><p id="par0065" class="elsevierStylePara elsevierViewall">with<elsevierMultimedia ident="eq0025"></elsevierMultimedia></p><p id="par0070" class="elsevierStylePara elsevierViewall">The constant K can be equal to 1&#47;&#40;ln2&#41; if information is measured in binary units &#40;bits&#41; &#40;<span class="elsevierStyleItalic">op&#46; cit</span>&#46;&#44; p&#46; 2&#41;&#59; nevertheless&#44; if information of Brillouin&#39;s formula is compared with Shannon entropy formula&#44; and K is replaced by <span class="elsevierStyleItalic">k</span>&#44; the Boltzmann constant&#44; then information and entropy have the same unities&#58; energy divided by temperature<a class="elsevierStyleCrossRef" href="#bib0090"><span class="elsevierStyleSup">&#91;18&#93;</span></a> &#40;p&#46; 3&#41;&#46; The relationship&#44; between entropy and information&#44; if temperature -in centigrade scale- is measured in energy units is&#58;<elsevierMultimedia ident="eq0030"></elsevierMultimedia></p><p id="par0075" class="elsevierStylePara elsevierViewall">The problem to associate entropy and information as concepts and in unities is that information is not a change between an initial and a final state&#44; and it lacks of statistical treatment of possible configurations as in thermodynamical statistics&#46; Thus&#44; Norbert Wiener<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> developed the next model&#44; where information has a time series and their distribution follows the configuration of the Brownian motion &#40;chapter III&#41;&#46;</p><p id="par0080" class="elsevierStylePara elsevierViewall">For this&#44; Wiener<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 61&#41; established that the amount of information of a system&#44; where initially a variable <span class="elsevierStyleItalic">x</span> lies between 0 and 1&#44; and in a final state it lies on the interval &#40;<span class="elsevierStyleItalic">a&#44; b</span>&#41; inside &#40;0&#44; 1&#41;&#44; is&#58;<elsevierMultimedia ident="eq0035"></elsevierMultimedia></p><p id="par0085" class="elsevierStylePara elsevierViewall">The <span class="elsevierStyleItalic">a priori</span> knowledge is that the probability that a certain quantity lies between <span class="elsevierStyleItalic">x</span> and <span class="elsevierStyleItalic">x &#43; dx</span> is a function of <span class="elsevierStyleItalic">x</span> in two times&#58; initial and final or <span class="elsevierStyleItalic">a priori</span> and <span class="elsevierStyleItalic">a posteriori</span>&#46; In this perspective&#44; the <span class="elsevierStyleItalic">a priori</span> probability is <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41; dx</span> and the <span class="elsevierStyleItalic">a posteriori</span> probability is <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span><span class="elsevierStyleItalic">&#40;x&#41; dx</span>&#46;</p><p id="par0090" class="elsevierStylePara elsevierViewall">Thus&#44; it is valid to ask&#58; &#8220;How much new information does our <span class="elsevierStyleItalic">a posteriori</span> probability give us&#63;&#8221;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 62&#41;&#46; Mathematically this means to bind a width to the regions under the curves <span class="elsevierStyleItalic">y&#61;f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span> and <span class="elsevierStyleItalic">y&#61;f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">2</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span>&#44; that is initial and final conditions of the system&#59; also&#44; it is assumed that the variable <span class="elsevierStyleItalic">x</span> have a fundamental equipartition in its distribution&#46; Since <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span> is a probability density&#44; it could be established<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 62&#41;&#58;<elsevierMultimedia ident="eq0040"></elsevierMultimedia></p><p id="par0095" class="elsevierStylePara elsevierViewall">and that the average logarithm of the breadth of the region under <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span> may be considered as an average of the height of the logarithm of the reciprocal of <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span>&#44; as Norbert Wiener<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> wrote using a personal communication of J&#46; von Neumann&#46; Thus&#44; an estimate measure of the amount of information associated with the curve <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#41;</span> is&#58;<elsevierMultimedia ident="eq0045"></elsevierMultimedia></p><p id="par0100" class="elsevierStylePara elsevierViewall">This quantity is the amount of information of the described system and it is the negative of the quantity usually defined as entropy in similar situations<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 62&#41;&#46; It could also be showed that the amount of information from independent sources is additive<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 63&#41;&#46; Besides&#58; &#8220;It is interesting to show that&#44; on the average&#44; it has the properties we associate with an entropy&#8221;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;p&#46; 64&#41;&#46; For example&#44; there are no operations on a message in communication engineering that can gain information&#44; because on the average&#44; there is a loss of information&#44; in an analogous manner to the loss of energy by a heat machine&#44; as predicted by the second law of thermodynamics&#46;</p><p id="par0105" class="elsevierStylePara elsevierViewall">In order to build up a time series as general as possible from the simple Brownian motion series&#44; it is necessary to use functions that could be expanded by Fourier series developments&#44; as it is showed by Norbert Wiener in his equation 3&#46;46&#44; and others&#44; in his book on cybernetics<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;pp&#58; 60-94&#41;&#46;</p><p id="par0110" class="elsevierStylePara elsevierViewall">It is possible to apply equation <a class="elsevierStyleCrossRef" href="#eq0045">&#40;5&#41;</a> to a particular case if the amount of information of the message is a constant over &#40;<span class="elsevierStyleItalic">a</span>&#44; <span class="elsevierStyleItalic">b</span>&#41; and is zero elsewhere&#44; then&#58;<elsevierMultimedia ident="eq0050"></elsevierMultimedia></p><p id="par0115" class="elsevierStylePara elsevierViewall">Using this equation to compare the amount of information of a point in the region &#40;0&#44; 1&#41;&#44; with the information that is the region &#40;<span class="elsevierStyleItalic">a</span>&#44; <span class="elsevierStyleItalic">b</span>&#41;&#44; it can be obtained for the measure of the difference&#58;<elsevierMultimedia ident="eq0055"></elsevierMultimedia></p><p id="par0120" class="elsevierStylePara elsevierViewall">It is important to say that this definition of the amount of information can be also applicable when the variable <span class="elsevierStyleItalic">x</span> is replaced by a variable ranging over two or more dimensions&#46; In the two dimensional case&#44; <span class="elsevierStyleItalic">f&#40;x&#44; y&#41;</span> is a function such that&#58;<elsevierMultimedia ident="eq0060"></elsevierMultimedia></p><p id="par0125" class="elsevierStylePara elsevierViewall">and the amount of information is&#58;<elsevierMultimedia ident="eq0065"></elsevierMultimedia></p><p id="par0130" class="elsevierStylePara elsevierViewall">if <span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">1</span></span><span class="elsevierStyleItalic">&#40;x&#44; y&#41;</span> is the form <span class="elsevierStyleItalic">&#966;&#40;x&#41; &#968;&#40;y&#41;</span> and<elsevierMultimedia ident="eq0070"></elsevierMultimedia></p><p id="par0135" class="elsevierStylePara elsevierViewall">then<elsevierMultimedia ident="eq0075"></elsevierMultimedia></p><p id="par0140" class="elsevierStylePara elsevierViewall">and<elsevierMultimedia ident="eq0080"></elsevierMultimedia></p><p id="par0145" class="elsevierStylePara elsevierViewall">this shows that the amount of information from independent sources is additive<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">&#91;7&#93;</span></a> &#40;pp&#58; 62-63&#41;&#46;</p><p id="par0150" class="elsevierStylePara elsevierViewall">For this model&#44; it would be interesting to know the degrees of freedom of a message&#46; It would be convenient to take the proposal of L&#233;on Brillouin<a class="elsevierStyleCrossRef" href="#bib0090"><span class="elsevierStyleSup">&#91;18&#93;</span></a> &#40;pp&#58; 90-91&#41;&#44; who made the next development&#58;</p><p id="par0155" class="elsevierStylePara elsevierViewall">A certain function <span class="elsevierStyleItalic">f&#40;t&#41;</span> has a spectrum that does not include frequencies higher than a certain maximum limit&#58; &#957;<span class="elsevierStyleInf">M</span> and the function can be expanded over a time interval &#964;&#46; The outstanding question is&#58; How much parameters &#40;or degrees of freedom&#41; are necessary for to define the function&#63;</p><p id="par0160" class="elsevierStylePara elsevierViewall">If it is established that there is <span class="elsevierStyleItalic">N</span> degrees of freedom and<elsevierMultimedia ident="eq0085"></elsevierMultimedia></p><p id="par0165" class="elsevierStylePara elsevierViewall">To choose the independent parameters for the function&#44; it was considered the interval <span class="elsevierStyleItalic">0 &#60; t &#60; &#964;</span> and that it is suitable to know the function values before 0 and after <span class="elsevierStyleItalic">&#964;</span>&#44; without any addition of information to the message <span class="elsevierStyleItalic">f&#40;t&#41;</span>&#46; Thus&#44; it is chosen a periodic function that reproduces in an indefinite way the solution curve of the function <span class="elsevierStyleItalic">f&#40;t&#41;</span> between 0 and &#964; as&#58;<elsevierMultimedia ident="eq0090"></elsevierMultimedia></p><p id="par0170" class="elsevierStylePara elsevierViewall">and use a periodic function with a period &#964;&#59; thus&#44; applying a development of a Fourier series&#44; it is obtained&#58;<elsevierMultimedia ident="eq0095"></elsevierMultimedia></p><p id="par0175" class="elsevierStylePara elsevierViewall">with<elsevierMultimedia ident="eq0100"></elsevierMultimedia></p><p id="par0180" class="elsevierStylePara elsevierViewall">as was stated by Brillouin<a class="elsevierStyleCrossRef" href="#bib0090"><span class="elsevierStyleSup">&#91;18&#93;</span></a> &#40;pp&#58; 90-91&#41;&#46;</p><p id="par0185" class="elsevierStylePara elsevierViewall">This means that the degrees of freedom bound to a message could be a periodic function that is dependent on the amount of information and the time interval&#46;</p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">DISCUSSION</span><p id="par0190" class="elsevierStylePara elsevierViewall">It has been demonstrated a mathematical model that correlates the accumulation of information with biological evolution&#44; by means of additive information &#40;it could be genetic and epigenetic&#41;&#46; Biological systems can be assimilated as messages transmitted to the next generation in the middle of an environmental noise&#44; biotic and abiotic&#46; What kind of information&#63; It could be as simple as binary units &#40;bits&#44; 0 and 1&#41;&#44; which can be a set in a wavelength of a photon and that can be assembled into integrative structures&#46; For example&#44; in computer technology the hardware is the physical support of an ensemble of structured information &#40;algorithms hierarchically organized&#41;&#59; this informatics programs run on a binary system where an alpha-numeric character is formed with a set of binary units&#44; <span class="elsevierStyleItalic">i&#46; e&#46;</span>&#44; a byte &#40;byte is equals to 8 bit series&#41;&#44; and then&#44; they can form data &#40;words&#41;&#44; concepts&#44; sentences&#44; routines&#44; algorithms&#44; programs and sets of programs as in computers software&#46; The DNA is a genetic information code and it must have epigenetic&#44; ontogenic and autopoyetic programs that regulate &#40;by expression or restriction&#41; its development&#46; The genetic pleiotropy in organisms is when a gene affects more than one phenotypic trait&#44; and it exhibits the gene modulation by an epigenetic process&#46;</p><p id="par0195" class="elsevierStylePara elsevierViewall">The mathematical model also shows that changes in information and entropy could be the same process&#58; an increase in entropy normally means a loss of structure or restrictions of a system&#46; On the contrary&#44; the evolution of a biological system usually means an enlargement in its amount of information and complexity that drives to an increase in its fitness and functionality&#46; Biological systems are information building systems<a class="elsevierStyleCrossRefs" href="#bib0095"><span class="elsevierStyleSup">&#91;19&#8211;21&#93;</span></a>&#44; i&#46;e&#46;&#44; genetic and epigenetic capacity to generate developmental functional complexity &#40;phenotype&#41;&#44; as is quoted by Elsheikh<a class="elsevierStyleCrossRef" href="#bib0110"><span class="elsevierStyleSup">&#91;22&#93;</span></a> in his abstract&#44; but organisms also face to environmental networks&#44; where there are stochasticity&#44; random processes &#40;positive or negative&#41; and&#44; sometimes&#44; chaos<a class="elsevierStyleCrossRefs" href="#bib0115"><span class="elsevierStyleSup">&#91;23&#44;24&#93;</span></a>&#46;</p><p id="par0200" class="elsevierStylePara elsevierViewall">Two emergent attributes of biological organisms are phenotype and behavior&#46; Phenotype is a synthesis of equilibrium between internal and external environments&#44; and behavior is a driven force in individual evolution<a class="elsevierStyleCrossRefs" href="#bib0125"><span class="elsevierStyleSup">&#91;25&#8211;27&#93;</span></a>&#46; A path frequently transited by evolutionary changes is the mutualistic symbiosis<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">&#91;1&#93;</span></a>&#46; In this sense&#44; the transmission of biological messages &#40;organisms&#41; to the next generation increases its possibilities to improve the amount of information&#44; if the message is redundant and symbiosis is a way to form additive messages&#46; For example&#44; if the organism A has three traits and become a functional unity with the organism B&#44; which has other three different traits and both can share all traits&#59; then&#44; they have 9 binomial sets of traits&#46;</p><p id="par0205" class="elsevierStylePara elsevierViewall">Finally&#44; it is necessary to point out that information create programs and a set of programs that drive toward power-law behavior of organisms&#46; Behavior also has two sources&#58; a&#41; phylogenetic memory &#40;i&#46;e&#46;&#44; genetically codified routines and conducts&#41;&#44; and b&#41; algorithms induced by epigenetic modulation and environmental noise or stochasticity&#46; It is already known that ecological behavior of organisms is the driven force to its evolution &#40;accumulation of information&#41; or its degradation &#40;loss of structures and information&#41;&#46;</p></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">CONCLUDING REMARKS</span><p id="par0210" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#fig0005">Figure 1</a> makes a synthesis of the role of information on the evolution of biological systems and on changes in entropy&#46; Mathematically&#44; the origin of matter in the universe could have begun above zero entropy<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">&#91;15&#93;</span></a>&#44; and matter evolution drives to form organization levels with increasing complexity and information&#46; The transition between both is called abiotic matter&#44; and living systems must be carried by the degrees of freedom due to the product of the Boltzmann constant by temperature &#40;<span class="elsevierStyleItalic">k</span>T&#41;&#46; The big source of heat on the Earth is the Sun that is at 5760 Kelvin degrees at the photosphere and the Earth average temperature in the biosphere actually is <span class="elsevierStyleItalic">ca&#46;</span> 288 &#176;K&#46; Then&#44; organisms absorb high energy solar photons and they use that energy for photosynthesis or as food in the trophic chain by means of dissipative processes&#46; Living organism &#8220;eat&#8221; high energy photons and they distribute them among photons with low energy&#46; The entropy of photons is proportional to the number of photons<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">&#91;15&#93;</span></a> in a system and on the Earth&#39;s energy balance&#44; Lineweaver and Egan<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">&#91;15&#93;</span></a> &#40;p&#46; 231&#41; say&#58; &#8220;when the Earth absorbs one solar photon&#44; the Earth emits 20 photons with wavelengths 20 times longer&#8221;&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0215" class="elsevierStylePara elsevierViewall">Likewise&#44; Karo Michaelian<a class="elsevierStyleCrossRef" href="#bib0140"><span class="elsevierStyleSup">&#91;28&#93;</span></a> &#40;p&#46; 43&#41; wrote&#58; &#8220;Direct absorption of a UV photon of 260<span class="elsevierStyleHsp" style=""></span>nm on RNA&#47;DNA would leave 4&#46;8<span class="elsevierStyleHsp" style=""></span>eV of energy locally which&#44; given the heat capacity of water&#44; would be sufficient energy to raise the temperature by an additional 3 Kelvin degrees of a local volume of water that could contain up to 50 base pairs&#8221;&#46; In this discerment&#44; solar photons increase the degrees of freedom&#44; in structure and functionality&#44; of living organisms&#46; One degree of freedom is an independent parameter of a system and it could be considered as novel information of it&#46;</p><p id="par0220" class="elsevierStylePara elsevierViewall">Finally&#44; it is important to say that information can be the driven force of biological evolution&#46; Life&#44; as a state&#44; can be defined as a dissipative system that has a structural biomass or <span class="elsevierStyleItalic">hardware</span>&#44; genetic and epigenetic programs or <span class="elsevierStyleItalic">software</span> and metabolic-ontogenic interface that regulates flows of matter&#44; energy and information&#44; in order to have an autopoyetic homeostasis&#44; behavior and increases in its fitness and functionality&#46; Furthermore&#44; a living system is an unique set of programs reservoir that evolves in face to ecological noise&#44; stochasticity and&#44; sometimes&#44; chaos&#46;</p></span></span>"
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        "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">For years&#44; links between entropy and information of a system have been proposed&#44; but their changes in time and in their probabilistic structural states have not been proved in a robust model as a unique process&#46; This document demonstrates that increasement in entropy and information of a system are the two paths for changes in its configuration status&#46; Biological evolution also has a trend toward information accumulation and complexity&#46; In this approach&#44; the aim of this article is to answer the question&#58; What is the driven force of biological evolution&#63; For this&#44; an analogy between the evolution of a living system and the transmission of a message in time was made&#44; both in the middle of environmental noise and stochasticity&#46; A mathematical model&#44; initially developed by Norbert Wiener&#44; was employed to show the dynamics of the amount of information in a message&#44; using a time series and the Brownian motion as statistical frame&#46; L&#233;on Brillouin&#39;s mathematical definition of information and Claude Shannon&#39;s entropy equation were employed&#44; both are similar&#44; in order to know changes in the two physical properties&#46; The proposed model includes time and configurational probabilities of the system and it is suggested that entropy can be considered as missing information&#44; according to Arieh Ben&#8211;Naim&#46; In addition&#44; a graphic shows that information accumulation can be the driven force of both processes&#58; evolution &#40;gain in information and complexity&#41;&#44; and increase in entropy &#40;missing information and restrictions loss&#41;&#46; Finally&#44; a living system can be defined as a dynamic set of information coded in a reservoir of genetic&#44; epigenetic and ontogenic programs&#44; in the middle of environmental noise and stochasticity&#44; which points toward an increase in fitness and functionality&#46;</p></span>"
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