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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 83 (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...
Fitness landscapes and evolvability
 Evolutionary Computation
, 2001
"... In this paper, we develop techniques based on evolvability statistics of the tness landscape surrounding sampled solutions. Averaging the measures over a sample of equal tness solutions allows us to build up tness evolvability portraits of the tness landscape, which we show can be used to compare ..."
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Cited by 52 (2 self)
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In this paper, we develop techniques based on evolvability statistics of the tness landscape surrounding sampled solutions. Averaging the measures over a sample of equal tness solutions allows us to build up tness evolvability portraits of the tness landscape, which we show can be used to compare both the ruggedness and neutrality in a set of tunably rugged and tunably neutral landscapes. We further show that the techniques can be used with solution samples collected through both random sampling of the landscapes and online sampling during optimization. Finally, we apply the techniques to two real evolutionary electronics search spaces and highlight differences between the two search spaces, comparing with the time taken to nd good solutions through search.
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 36 (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.
Optimizing Epochal Evolutionary Search: PopulationSize Dependent Theory
, 2001
"... Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a class of fitness functions that exhibit epochal behavior using ..."
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Cited by 30 (4 self)
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Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a class of fitness functions that exhibit epochal behavior using a mathematical framework developed recently, which incorporates techniques from the fields of mathematical population genetics, molecular evolution theory, and statistical mechanics. Our analysis predicts the total number of fitness function evaluations to reach the global optimum as a function of mutation rate, population size, and the parameters specifying the fitness function. This allows us to determine the optimal evolutionary parameter settings for this class of fitness functions. We identify a generalized error threshold that smoothly bounds the twodimensional regime of mutation rates and population sizes for which epochal evolutionary search operates most efficiently. Specifically, we analyze the dynamics of epoch destabilization under finitepopulation sampling fluctuations and show how the evolutionary parameters effectively introduce a coarse graining of the fitness function. More generally, we find that the optimal parameter settings for epochal evolutionary search correspond to behavioral regimes in which the consecutive epochs are marginally stable against the sampling fluctuations. Our results suggest that in order to achieve optimal search, one should set evolutionary parameters such that the coarse graining of the fitness function induced by the sampling fluctuations is just large enough to hide local optima.
Neutral Networks and Evolvability with Complex GenotypePhenotype Mapping
 EUROPEAN CONFERENCE ON ARTIFICIAL LIFE: ECAL2001
, 2001
"... In this paper, we investigate a neutral epoch during an optimisation run with complex genotypetofitness mapping. The behaviour of the search process during neutral epochs is of importance for evolutionary robotics and other artificiallife approaches that evolve problem solutions; recent work has ..."
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Cited by 28 (3 self)
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In this paper, we investigate a neutral epoch during an optimisation run with complex genotypetofitness mapping. The behaviour of the search process during neutral epochs is of importance for evolutionary robotics and other artificiallife approaches that evolve problem solutions; recent work has argued that evolvability may change during these epochs. We investigate the distribution of offspring fitnesses from the best individuals of each generation in a populationbased genetic algorithm, and see no trends towards higher probabilities of producing higher fitness offspring, and no trends towards higher probabilities of not producing lower fitness offspring. A second experiment in which populations from across the neutral epoch are used as initial populations for the genetic algorithm, shows no difference between the populations in the number of generations required to produce high fitness. We conclude that there is no evidence for change in evolvability during the neutral epoch in this optimisation run; the population is not doing anything “useful” during this period.
How Neutral Networks Influence Evolvability
, 2001
"... Evolutionary algorithms apply the process of variation, reproduction and selection to look for an individual capable of solving the task at hand. In order to improve the evolvability of a population we propose to copy important characteristics of nature's search space. Desired characteristic ..."
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Cited by 24 (0 self)
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Evolutionary algorithms apply the process of variation, reproduction and selection to look for an individual capable of solving the task at hand. In order to improve the evolvability of a population we propose to copy important characteristics of nature's search space. Desired characteristics for a genotypephenotype mapping are described and several highly redundant genotypephenotype mappings are analyzed in the context of a population based search. We show that evolvability, de ned as the ability of random variations to sometimes produce improvement, is inuenced by the existence of neutral networks in genotype space. Redundant mappings allow the population to spread along the network of neutral mutations and the population is quickly able to recover after a change has occurred. The extent of the neutral networks aects the interconnectivity of the search space and thereby aects evolvability.
Modelling ’evodevo’ with RNA
 Bioessays
, 2002
"... Introduction Phenotype refers to the physica , organizationa and behaviora expression of an organismduani its ifetime. Genotype refers to a heritab e repository of information that instruYl the produlTj" of moecu es whose interactions, in conjujlzTE with the environment, generate and maintain t ..."
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Cited by 24 (0 self)
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Introduction Phenotype refers to the physica , organizationa and behaviora expression of an organismduani its ifetime. Genotype refers to a heritab e repository of information that instruYl the produlTj" of moecu es whose interactions, in conjujlzTE with the environment, generate and maintain the phenotype. The processes inking genotype to phenotype are known as deve opment. They intervene in the genesis of phenotypic nove ty from genetic mu tation. EvouGYYYxl trajectories therefore depend on deve opment. In tu(( evouG""""l processes shape deve opment, creating a feedback known as "evodevo" 1,2 . The main thruj of this review is to show that some key aspects of this feedback are present even in the microcosm of RNA fo ding. In a narrow sense, the re ation between RNA sequY"jl and their shapes is treated as a prob em in biophysics. Yet, in a wider sense, RNA fo ding can be regarded as a minima mode of a genotypephenotype re ation . The RNA mode is not a representation of organis
Evolving Genetic Regulatory Networks Using an Artificial Genome
 SECOND ASIAPACIFIC BIOINFORMATICS CONFERENCE (APBC2004). VOLUME 29 OF CRPIT., DUNEDIN, NEW ZEALAND, ACS (2004) 291
, 2004
"... Boolean models of genetic regulatory networks (GRNs) have been shown to exhibit many of the characteristic dynamics of real GRNs, with gene expression patterns settling to point attractors or limit cycles, or displaying chaotic behaviour, depending upon the connectivity of the network and the relati ..."
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Cited by 13 (5 self)
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Boolean models of genetic regulatory networks (GRNs) have been shown to exhibit many of the characteristic dynamics of real GRNs, with gene expression patterns settling to point attractors or limit cycles, or displaying chaotic behaviour, depending upon the connectivity of the network and the relative proportions of excitatory and inhibitory interactions. This range of behaviours is only apparent, however, when the nodes of the GRN are updated synchronously, a biologically implausible state of affairs. In this paper we demonstrate that evolution can produce GRNs with interesting dynamics under an asynchronous update scheme. We use an Artificial Genome to generate networks which exhibit limit cycle dynamics when updated synchronously, but collapse to a point attractor when updated asynchronously. Using a hill climbing algorithm the networks are then evolved using a fitness function which rewards patterns of gene expression which revisit as many previously seen states as possible. The final networks exhibit "fuzzy limit cycle" dynamics when updated asynchronously.
Evolution and Speciation in a Hyperspace: The Roles of Neutrality, Selection, Mutation and Random Drift
, 1999
"... 2 The problem of speciation 2 Rugged adaptive landscapes 3 Nearly neutral networks and holey adaptive landscapes 6 The origin of the idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Simple models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..."
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Cited by 11 (3 self)
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2 The problem of speciation 2 Rugged adaptive landscapes 3 Nearly neutral networks and holey adaptive landscapes 6 The origin of the idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Simple models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Russian roulette model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Uniformly rugged landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Multiplicative fitnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Stabilizing selection on an additive trait . . . . . . . . . . . . . . . . . . . . . . . . 10 NK model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Conclusions from models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Experimental evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 A metaphor of holey adapt...
Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities
 J Theor
, 2007
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