14,042 research outputs found
An Analysis of Phase Transition in NK Landscapes
In this paper, we analyze the decision version of the NK landscape model from
the perspective of threshold phenomena and phase transitions under two random
distributions, the uniform probability model and the fixed ratio model. For the
uniform probability model, we prove that the phase transition is easy in the
sense that there is a polynomial algorithm that can solve a random instance of
the problem with the probability asymptotic to 1 as the problem size tends to
infinity. For the fixed ratio model, we establish several upper bounds for the
solubility threshold, and prove that random instances with parameters above
these upper bounds can be solved polynomially. This, together with our
empirical study for random instances generated below and in the phase
transition region, suggests that the phase transition of the fixed ratio model
is also easy
Critical properties of complex fitness landscapes
Evolutionary adaptation is the process that increases the fit of a population
to the fitness landscape it inhabits. As a consequence, evolutionary dynamics
is shaped, constrained, and channeled, by that fitness landscape. Much work has
been expended to understand the evolutionary dynamics of adapting populations,
but much less is known about the structure of the landscapes. Here, we study
the global and local structure of complex fitness landscapes of interacting
loci that describe protein folds or sets of interacting genes forming pathways
or modules. We find that in these landscapes, high peaks are more likely to be
found near other high peaks, corroborating Kauffman's "Massif Central"
hypothesis. We study the clusters of peaks as a function of the ruggedness of
the landscape and find that this clustering allows peaks to form interconnected
networks. These networks undergo a percolation phase transition as a function
of minimum peak height, which indicates that evolutionary trajectories that
take no more than two mutations to shift from peak to peak can span the entire
genetic space. These networks have implications for evolution in rugged
landscapes, allowing adaptation to proceed after a local fitness peak has been
ascended.Comment: 7 pages, 6 figures, requires alifex11.sty. To appear in Proceedings
of 12th International Conference on Artificial Lif
Adaptive walks on time-dependent fitness landscapes
The idea of adaptive walks on fitness landscapes as a means of studying
evolutionary processes on large time scales is extended to fitness landscapes
that are slowly changing over time. The influence of ruggedness and of the
amount of static fitness contributions are investigated for model landscapes
derived from Kauffman's landscapes. Depending on the amount of static
fitness contributions in the landscape, the evolutionary dynamics can be
divided into a percolating and a non-percolating phase. In the percolating
phase, the walker performs a random walk over the regions of the landscape with
high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.
Broken ergodicity in driven one-dimensional particle systems with short-range interaction
We present a one-dimensional nonequilibrium model for a driven
di�usive system which has local interactions and slow nonconservative reaction
kinetics. Monte-Carlo simulations suggest that in the thermodynamic limit
the steady state exhibits a phase with broken ergodicity. We propose a hydrodynamic
equation for the coarse-grained density (under Eulerian scaling),
augmented by a prescription how to treat shock and boundary discontinuities,
respectively. This conjecture can be readily generalized to other weakly nonconservative
driven di�usive systems and is supported by a heuristic identi�cation
of the main dynamical mode that governs the microscopic dynamics, viz. the
random motion of a shock in an self-organized e�ective potential. This picture
leads to the exact phase diagram of the system and suggests a novel and
mathematically tractable mechanism for \freezing by heating"
Statistical Physics of Evolutionary Trajectories on Fitness Landscapes
Random walks on multidimensional nonlinear landscapes are of interest in many
areas of science and engineering. In particular, properties of adaptive
trajectories on fitness landscapes determine population fates and thus play a
central role in evolutionary theory. The topography of fitness landscapes and
its effect on evolutionary dynamics have been extensively studied in the
literature. We will survey the current research knowledge in this field,
focusing on a recently developed systematic approach to characterizing path
lengths, mean first-passage times, and other statistics of the path ensemble.
This approach, based on general techniques from statistical physics, is
applicable to landscapes of arbitrary complexity and structure. It is
especially well-suited to quantifying the diversity of stochastic trajectories
and repeatability of evolutionary events. We demonstrate this methodology using
a biophysical model of protein evolution that describes how proteins maintain
stability while evolving new functions
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