10,556 research outputs found
Analysis of adaptive walks on NK fitness landscapes with different interaction schemes
Fitness landscapes are genotype to fitness mappings commonly used in
evolutionary biology and computer science which are closely related to spin
glass models. In this paper, we study the NK model for fitness landscapes where
the interaction scheme between genes can be explicitly defined. The focus is on
how this scheme influences the overall shape of the landscape. Our main tool
for the analysis are adaptive walks, an idealized dynamics by which the
population moves uphill in fitness and terminates at a local fitness maximum.
We use three different types of walks and investigate how their length (the
number of steps required to reach a local peak) and height (the fitness at the
endpoint of the walk) depend on the dimensionality and structure of the
landscape. We find that the distribution of local maxima over the landscape is
particularly sensitive to the choice of interaction pattern. Most quantities
that we measure are simply correlated to the rank of the scheme, which is equal
to the number of nonzero coefficients in the expansion of the fitness landscape
in terms of Walsh functions.Comment: 29 pages, 9 figure
Greedy adaptive walks on a correlated fitness landscape
We study adaptation of a haploid asexual population on a fitness landscape
defined over binary genotype sequences of length . We consider greedy
adaptive walks in which the population moves to the fittest among all single
mutant neighbors of the current genotype until a local fitness maximum is
reached. The landscape is of the rough mount Fuji type, which means that the
fitness value assigned to a sequence is the sum of a random and a deterministic
component. The random components are independent and identically distributed
random variables, and the deterministic component varies linearly with the
distance to a reference sequence. The deterministic fitness gradient is a
parameter that interpolates between the limits of an uncorrelated random
landscape () and an effectively additive landscape ().
When the random fitness component is chosen from the Gumbel distribution,
explicit expressions for the distribution of the number of steps taken by the
greedy walk are obtained, and it is shown that the walk length varies
non-monotonically with the strength of the fitness gradient when the starting
point is sufficiently close to the reference sequence. Asymptotic results for
general distributions of the random fitness component are obtained using
extreme value theory, and it is found that the walk length attains a
non-trivial limit for , different from its values for and
, if is scaled with in an appropriate combination.Comment: minor change
Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model
Much of the current theory of adaptation is based on Gillespie's mutational
landscape model (MLM), which assumes that the fitness values of genotypes
linked by single mutational steps are independent random variables. On the
other hand, a growing body of empirical evidence shows that real fitness
landscapes, while possessing a considerable amount of ruggedness, are smoother
than predicted by the MLM. In the present article we propose and analyse a
simple fitness landscape model with tunable ruggedness based on the Rough Mount
Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79
(2000)] in the context of protein evolution. We provide a comprehensive
collection of results pertaining to the topographical structure of RMF
landscapes, including explicit formulae for the expected number of local
fitness maxima, the location of the global peak, and the fitness correlation
function. The statistics of single and multiple adaptive steps on the RMF
landscape are explored mainly through simulations, and the results are compared
to the known behavior in the MLM model. Finally, we show that the RMF model can
explain the large number of second-step mutations observed on a highly-fit
first step backgound in a recent evolution experiment with a microvirid
bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number
of fitness maxim
Universality classes of interaction structures for NK fitness landscapes
Kauffman's NK-model is a paradigmatic example of a class of stochastic models
of genotypic fitness landscapes that aim to capture generic features of
epistatic interactions in multilocus systems. Genotypes are represented as
sequences of binary loci. The fitness assigned to a genotype is a sum of
contributions, each of which is a random function defined on a subset of loci. These subsets or neighborhoods determine the genetic interactions of
the model. Whereas earlier work on the NK model suggested that most of its
properties are robust with regard to the choice of neighborhoods, recent work
has revealed an important and sometimes counter-intuitive influence of the
interaction structure on the properties of NK fitness landscapes. Here we
review these developments and present new results concerning the number of
local fitness maxima and the statistics of selectively accessible (that is,
fitness-monotonic) mutational pathways. In particular, we develop a unified
framework for computing the exponential growth rate of the expected number of
local fitness maxima as a function of , and identify two different
universality classes of interaction structures that display different
asymptotics of this quantity for large . Moreover, we show that the
probability that the fitness landscape can be traversed along an accessible
path decreases exponentially in for a large class of interaction structures
that we characterize as locally bounded. Finally, we discuss the impact of the
NK interaction structures on the dynamics of evolution using adaptive walk
models.Comment: 61 pages, 9 figure
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
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
Fitness landscape of the cellular automata majority problem: View from the Olympus
In this paper we study cellular automata (CAs) that perform the computational
Majority task. This task is a good example of what the phenomenon of emergence
in complex systems is. We take an interest in the reasons that make this
particular fitness landscape a difficult one. The first goal is to study the
landscape as such, and thus it is ideally independent from the actual
heuristics used to search the space. However, a second goal is to understand
the features a good search technique for this particular problem space should
possess. We statistically quantify in various ways the degree of difficulty of
searching this landscape. Due to neutrality, investigations based on sampling
techniques on the whole landscape are difficult to conduct. So, we go exploring
the landscape from the top. Although it has been proved that no CA can perform
the task perfectly, several efficient CAs for this task have been found.
Exploiting similarities between these CAs and symmetries in the landscape, we
define the Olympus landscape which is regarded as the ''heavenly home'' of the
best local optima known (blok). Then we measure several properties of this
subspace. Although it is easier to find relevant CAs in this subspace than in
the overall landscape, there are structural reasons that prevent a searcher
from finding overfitted CAs in the Olympus. Finally, we study dynamics and
performance of genetic algorithms on the Olympus in order to confirm our
analysis and to find efficient CAs for the Majority problem with low
computational cost
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