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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...
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 71 (24 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...
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.
Information characteristics and the structure of landscapes
 Evolutionary Computation
, 2000
"... Various techniques for statistical analysis of the structure of tness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of tness lands ..."
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Cited by 34 (3 self)
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Various techniques for statistical analysis of the structure of tness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of tness landscapes. The underlying idea is to consider a tness landscape as an ensemble of objects that are related to the tness of neighboring points. Three information characteristics of the ensemble are dened and studied. They are termed: information content, partial information content, and information stability. The information characteristics of a range of landscapes with known correlation features are analyzed in an attempt to reveal the advantages of the information analysis. We show that the proposed analysis is an appropriate tool for investigating the structure of tness landscapes.
Amplitude spectra of fitness landscapes
 J. COMPLEX SYSTEMS
, 1998
"... Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying con guration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used f ..."
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Cited by 23 (9 self)
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Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying con guration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used for classi cation and comparison purposes. We consider here three very di erent types of landscapes using both mutation and recombination to de ne the topological structure of the con guration spaces. A reliable procedure for estimating the amplitude spectra is presented. The method is based on certain correlation functions that are easily obtained from empirical studies of the landscapes.
RNA Shape Space Topology
, 1999
"... The distinction between continuous and discontinuous transitions is a longstanding problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabi ..."
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Cited by 17 (7 self)
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The distinction between continuous and discontinuous transitions is a longstanding problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which of one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.
Quasiindependence, homology and the unity of type: A topological theory of characters
 J. THEOR. BIOL
, 2002
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Genetic Measurement Theory of Epistatic Effects
, 1997
"... Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. As such it plays a crucial role in a variety of evolutionary phenomena such as speciation, population bottle necks and the evolution of genetic architecture (i.e. the evolution of dominan ..."
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Cited by 14 (3 self)
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Epistasis is defined as the influence of the genotype at one locus on the effect of a mutation at another locus. As such it plays a crucial role in a variety of evolutionary phenomena such as speciation, population bottle necks and the evolution of genetic architecture (i.e. the evolution of dominance, canalization and genetic correlations). In mathematical population genetics, however, epistasis is often represented as a mere noise term in an additive model of gene effects. In this paper it is argued that epistasis needs to be scaled in a way that is more directly related to the mechanisms of evolutionary change. A review of general measurement theory shows that the scaling of a quantitative concepts has to reflect the empirical relationships among the objects. To apply these ideas to epistatic mutation effects it is proposed to scale AxA epistatic effects as the change in the magnitude of the additive effect of a mutation at one locus due to a mutation at a second locus. It is shown ...