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536
Smoothness Within Ruggedness: The Role of Neutrality in Adaptation
, 1996
"... RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical structure. On such networks evolving populations split into subpopulations which diffuse independently in sequence space. This demands a distinction between two mutation thresholds: ..."
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Cited by 155 (40 self)
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RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical structure. On such networks evolving populations split into subpopulations which diffuse independently in sequence space. This demands a distinction between two mutation thresholds: one at which genotypic information is lost and one at which phenotypic information is lost. In between diffusion enables the search of vast areas in genotype space, while still preserving the dominant phenotype. By this dynamics the success of phenotypic adaptation becomes much less sensitive to the initial conditions in genotype space. Introduction To explain the high fixation rate of nucleotide substitutions in a population, Motoo Kimura argued that the vast majority of genetic change at the level of a population must be neutral, rather than adaptive [1]. Sewall Wright's reaction to Kimura's point was politely neutral [2, page 474]: "Changes in wholly nonfunctional parts of the molecul...
Cartesian Genetic Programming
, 2000
"... . This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node func ..."
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Cited by 135 (24 self)
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. This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node functions are also separately numbered. The genotype is just a list of node connections and functions. The genotype is then mapped to an indexed graph that can be executed as a program. Evolutionary algorithms are used to evolve the genotype in a symbolic regression problem (sixth order polynomial) and the Santa Fe Ant Trail. The computational effort is calculated for both cases. It is suggested that hit effort is a more reliable measure of computational efficiency. A neutral search strategy that allows the fittest genotype to be replaced by another equally fit genotype (a neutral genotype) is examined and compared with nonneutral search for the Santa Fe ant problem. The neutral search...
The Science of Breeding and its Application to the Breeder Genetic Algorithm BGA
 EVOLUTIONARY COMPUTATION
, 1994
"... The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection eq ..."
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Cited by 100 (23 self)
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The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection equation and the concept of heritability can be applied to predict the behavior of the BGA. Selection, recombination and mutation are analyzed within this framework. It is shown that recombination and mutation are complementary search operators. The theoretical results are obtained under the assumption of additive gene effects. For general fitness landscapes regression techniques for estimating the heritability are used to analyze and control the BGA. The method of decomposing the genetic variance into an additive and a nonadditive part connects the case of additive fitness functions with the general case.
Exploring Phenotype Space Through Neutral Evolution
, 1996
"... RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical secondary structures. Fitness landscapes that are based on the mapping between RNA sequence and RNA secondary structure hence have many neutral paths. A neutral walk on these fitnes ..."
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Cited by 81 (0 self)
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RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical secondary structures. Fitness landscapes that are based on the mapping between RNA sequence and RNA secondary structure hence have many neutral paths. A neutral walk on these fitness landscapes gives access to a virtually unlimited number of secondary structures that are a single point mutation from the neutral path. This shows that neutral evolution explores phenotype space and can play a role in adaptation. Introduction Ever since Sewall Wright introduced the metaphor of an "adaptive landscape" (Wright, 1932) the view on adaptive evolution has been dominated by that of an uphill walk of a population on a mountainous fitness landscape in which it can get stuck on suboptimal peaks. The neutralist perspective that evolution at the molecular level is dominated by nonadaptive, neutral changes (Kimura, 1983) has hardly changed this picture. A notable exception is Maynard...
Generic Properties of Combinatory Maps  Neutral Networks of RNA Secondary Structures
, 1995
"... Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any ..."
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Cited by 80 (36 self)
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Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any two different structures almost touch each other, and sequences folding into almost all "common" structures can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared with data obtained by folding large samples of RNA sequences. Differences are explained in terms of RNA molecular structures. 1.
Fitness Landscapes
 Appl. Math. & Comput
, 2002
"... . Fitness landscapes are a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space that is equipped with some notion of adjacency, nearness, distance or accessibility, into the real numbe ..."
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Cited by 64 (14 self)
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. Fitness landscapes are a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space that is equipped with some notion of adjacency, nearness, distance or accessibility, into the real numbers. 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. This chapter gives a brief overview on recent developments in this area, focusing on "geometrical" properties of landscapes. 1 Introduction The concept of a fitness landscape originated in theoretical biology more than seventy years ago [1]. It can be thought of as a kind of "potential function" underlying the dynamics of evolutionary optimization. Implicit in this idea is both a fitness function f that assigns a fitness value to every possible genotype (or organism), and the arrangement of t...
Shaping Space: The Possible and the Attainable in RNA GenotypePhenotype Mapping
 J. THEOR. BIOL
, 1998
"... Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equiva ..."
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Cited by 58 (13 self)
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Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equivalence classes of genotypes. The definition of neighborhood relations among phenotypes relies, therefore, on the statistics of neighborhood relations among equivalence classes of genotypes in genotype space. The folding of RNA sequences (genotypes) into secondary structures (phenotypes) is an ideal case to implement these concepts. We study the extent to which the folding of RNA sequences induces a "statistical topology" on the set of minimum free energy secondary structures. The resulting nearness relation suggests a notion of "continuous" structure transformation. We can, then, rationalize major transitions in evolutionary trajectories at the level of RNA structures by identifying those tra...
Statistical dynamics of the Royal Road genetic algorithm
 Theoretical Computer Science
, 1999
"... Metastability is a common phenomenon. Many evolutionary processes, both natural and artificial, alternate between periods of stasis and brief periods of rapid change in their behavior. In this paper an analytical model for the dynamics of a mutationonly genetic algorithm (GA) is introduced that iden ..."
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Cited by 58 (5 self)
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Metastability is a common phenomenon. Many evolutionary processes, both natural and artificial, alternate between periods of stasis and brief periods of rapid change in their behavior. In this paper an analytical model for the dynamics of a mutationonly genetic algorithm (GA) is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics. The GA’s population dynamics is described in terms of flows in the space of fitness distributions. The trajectories through fitness distribution space are derived in closed form in the limit of infinite populations. We then show how finite populations induce metastability, even in regions where fitness does not exhibit a local optimum. In particular, the model predicts the occurrence of “fitness epochs”—periods of stasis in population fitness distributions—at finite population size and identifies the locations of these fitness epochs with the flow’s hyperbolic fixed points. This enables exact predictions of the metastable fitness distributions during the fitness epochs, as well as giving insight into the nature of the periods of stasis and the innovations between them. All these results are obtained as closedform expressions in terms of the GA’s parameters.
Protein phylogenies and signature sequences: evolutionary relationships within prokaryotes and between prokaryotes and eukaryotes. Antonie Leeuwenhoek 72:49–61
, 1997
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EVOLUTIONARY DRIFT AND EQUILIBRIUM SELECTION
, 1996
"... This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equ ..."
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Cited by 54 (3 self)
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This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify the same behavior on the equilibrium path, but different outofequilibrium behavior, appear in connected components of stationary states. The stability properties of these components often depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A su±cient condition is provided for drift to create stationary states with strong stability properties near a component of equilibria. This result is used to derive comparative static predictions concerning common questions raised in the literature on refinements of Nash equilibrium