95,683 research outputs found

    Exact scaling in the expansion-modification system

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    This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a \emph{mutation probability}. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a significant range of mutation probabilities, that the decay of correlations indeed follows a power-law with scaling exponent smoothly depending on the mutation probability. Finally we put forward an argument which allows us to give a closed expression for the corresponding scaling exponent for all the values of the mutation probability. Such a scaling exponent turns out to be a piecewise smooth function of the parameter.Comment: 22 pages, 2 figure

    Entropic Sampling and Natural Selection in Biological Evolution

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    With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this scheme the system evolves continuously into new configurations, yielding non-stationary behavior of the total fitness. Further, both the waiting time distribution of species and the avalanche size distribution display power-law behaviors with exponents close to two, which are consistent with the fossil data. These features are rather robust, indicating the key role of entropy

    Self-organized Criticality in Living Systems

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    We suggest that ensembles of self-replicating entities such as biological systems naturally evolve into a self-organized critical state in which fluctuations, as well as waiting-times between phase transitions are distributed according to a 1/f power law. We demonstrate these concepts by analyzing a population of self-replicating strings (segments of computer-code) subject to mutation and survival of the fittest.Comment: 8 p., tar-compressed uuencoded postscript incl. figures, submitted to Phys. Rev. Let

    The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

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    Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it

    Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection

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    The process of `Evolutionary Diffusion', i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of local peaks with a characteristic width that undergo drift, even in the infinite population limit. We analytically calculate the mean peak width and the effective random walk step size, and obtain the distribution of the peak width which has a power law tail. We find that independent local mutations act as a diffusion of interacting particles with increased stepsize.Comment: 4 pages, 2 figures. Paper now representative of published articl
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