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47
Combinatorial Landscapes
 SIAM REVIEW
, 2002
"... Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, ne ..."
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Cited by 33 (2 self)
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Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance or accessibility. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the "static" properties of landscapes as well as their influence on the dynamics of adaptation. In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.
Genetic Drift in Genetic Algorithm Selection Schemes
, 1999
"... A method for calculating genetic drift in terms of changing population fitness variance is presented. The method allows for an easy comparison of different selection schemes and exact analytical results are derived for traditional generational selection, steadystate selection with varying generatio ..."
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Cited by 22 (8 self)
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A method for calculating genetic drift in terms of changing population fitness variance is presented. The method allows for an easy comparison of different selection schemes and exact analytical results are derived for traditional generational selection, steadystate selection with varying generation gap, a simple model of Eshelman's CHC algorithm, and ( + ) evolution strategies. The effects of changing genetic drift on the convergence of a GA are demonstrated empirically. Keywords Genetic Drift, Selection Operator, Genetic Algorithm, Evolution Strategy I. Introduction Genetic drift is a term borrowed from population genetics where it is used to explain changes in gene frequency through random sampling of the population. It is a phenomenon observed in genetic algorithms (GA) due to the stochastic nature of the selection operator, and is one of the mechanisms by which the population converges to a single member. Analysis of genetic drift is often performed by calculating the Markov ...
Random partitions approximating the coalescence of lineages during a selective sweep
, 2005
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A coalescent model for the effect of advantageous mutations on the genealogy of a population
, 2008
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Exchangeable partitions derived from Markovian coalescents
 Adv. Appl. Probab
, 2006
"... Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. Möhle described the recursion which determines the generalization of the Ewens sampling formula when the ..."
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Cited by 11 (2 self)
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Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. Möhle described the recursion which determines the generalization of the Ewens sampling formula when the lines of descent are governed by a coalescent with multiple collisions. In [7] authors exploit an analogy with the theory of regenerative composition and partition structures, and provide various characterizations of the associated exchangeable random partitions. This paper gives parallel results for the further generalized model with lines of descent following a coalescent with simultaneous multiple collisions. 1
A waiting time problem arising from the study of multistage carcinogenesis
"... We consider the population genetics problem: how long does it take before some member of the population has m specified mutations? The case m = 2 is relevant to onset of cancer due to the inactivation of both copies of a tumor suppressor gene. Models for larger m are needed for colon cancer and othe ..."
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Cited by 11 (2 self)
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We consider the population genetics problem: how long does it take before some member of the population has m specified mutations? The case m = 2 is relevant to onset of cancer due to the inactivation of both copies of a tumor suppressor gene. Models for larger m are needed for colon cancer and other diseases where a sequence of mutations leads to cells with uncontrolled growth. 1. Introduction. It
A new model for evolution in a spatial continuum
"... o b a b i l i t y Vol. 15 (2010), Paper no. 7, pages 162–216. Journal URL ..."
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Cited by 9 (1 self)
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o b a b i l i t y Vol. 15 (2010), Paper no. 7, pages 162–216. Journal URL
B.: Evolutionary dynamics on smallworld networks
 International Journal of Computational and Mathematical Sciences
, 2008
"... Abstract—We study how the outcome of evolutionary dynamics on graphs depends on a randomness on the graph structure. We gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increa ..."
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Cited by 6 (0 self)
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Abstract—We study how the outcome of evolutionary dynamics on graphs depends on a randomness on the graph structure. We gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increases; nevertheless, the increase is not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs. Keywords—evolutionary dynamics, smallworld networks. I.
Sequence Redundancy in Biopolymers  A Study on RNA and Protein Structures
, 1997
"... Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of structure. Two classes of biopolymers, RNA molecules and proteins are considered in detail. A general feature ..."
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Cited by 5 (3 self)
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Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of structure. Two classes of biopolymers, RNA molecules and proteins are considered in detail. A general feature of sequence to structure mappings is the existence of a few common and many rare structures. Consequences of redundancy and frequency distribution of RNA structures are shape space covering and the existence of extended neutral networks. Populations migrate on neutral networks by a diffusionlike mechanism. Neutral networks are of fundamental importance for evolutionary optimization since they enable populations to escape from local optima of fitness landscapes.
Modeling Genetic Algorithms with Interacting Particle Systems
 In Theoretical Aspects of Evolutionary Computing
, 2001
"... We present in this work a natural Interacting Particle System (IPS) approach for modeling and studying the asymptotic behavior of Genetic Algorithms (GAs). In this model, a population is seen as a distribution (or measure) on the search space, and the Genetic Algorithm as a measure valued dynamical ..."
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Cited by 5 (0 self)
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We present in this work a natural Interacting Particle System (IPS) approach for modeling and studying the asymptotic behavior of Genetic Algorithms (GAs). In this model, a population is seen as a distribution (or measure) on the search space, and the Genetic Algorithm as a measure valued dynamical system. This model allows one to apply recent convergence results from the IPS literature for studying the convergence of genetic algorithms when the size of the population tends to infinity. We first review a number of approaches to Genetic Algorithms modeling and related convergence results. We then describe a general and abstract discrete time Interacting Particle System model for GAs, an we propose a brief review of some recent asymptotic results about the convergence of the NIPS approximating model (of finite Nsizedpopulation GAs) towards the IPS model (of infinite population GAs), including law of large number theorems, IL p mean and exponential bounds as well as large deviations...