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186
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 funct ..."
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Cited by 230 (59 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...
Plasticity, evolvability, and modularity in RNA
 J EXP ZOOL
, 2000
"... RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneou ..."
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Cited by 102 (3 self)
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RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly nonindependent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slowdown and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lockin. The causal bridge between environmental canalization and genetic canalization
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 90 (42 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.
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 88 (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...
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 78 (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 78 (14 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...
Neutrality and the Evolvability of Boolean Function Landscape
 Genetic Programming, Proceedings of EuroGP’2001, volume 2038 of LNCS
, 2001
"... This work is a study of neutrality in the context of Evolutionary Computation systems. In particular, we introduce the use of explicit neutrality with an integer string coding scheme to allow neutrality to be measured during evolution. We tested this method on a Boolean benchmark problem. ..."
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Cited by 74 (27 self)
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This work is a study of neutrality in the context of Evolutionary Computation systems. In particular, we introduce the use of explicit neutrality with an integer string coding scheme to allow neutrality to be measured during evolution. We tested this method on a Boolean benchmark problem.
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 73 (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.
The topology of the possible: Formal spaces underlying patterns of evolutionary change
, 2000
"... The current implementation of the NeoDarwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genoty ..."
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Cited by 73 (25 self)
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The current implementation of the NeoDarwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotypephenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pretopology. Patterns of phenotypic evolution  such as punctuation, irreversibility, modularity  result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological st...
Automatic detection of conserved RNA structure elements in complete RNA virus genomes
 Nucleic Acids Res
, 1998
"... We propose a new method for detecting conserved RNA secondary structures in a family of related RNA sequences. Our method is based on a combination of thermodynamic structure prediction and phylogenetic comparison. In contrast to purely phylogenetic methods, our algorithm can be used for small data ..."
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Cited by 72 (23 self)
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We propose a new method for detecting conserved RNA secondary structures in a family of related RNA sequences. Our method is based on a combination of thermodynamic structure prediction and phylogenetic comparison. In contrast to purely phylogenetic methods, our algorithm can be used for small data sets of ∼10 sequences, efficiently exploiting the information contained in the sequence variability. The procedure constructs a prediction only for those parts of sequences that are consistent with a single conserved structure. Our implementation produces reasonable consensus structures without user interference. As an example we have analysed the complete HIV1 and hepatitis C virus (HCV) genomes as well as the small segment of hantavirus. Our method confirms the known structures in HIV1 and predicts previously unknown conserved RNA secondary structures in HCV.