95,683 research outputs found
Exact scaling in the expansion-modification system
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
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
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
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
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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