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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 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...
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 62 (2 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
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...
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 48 (20 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...
Ruggedness and Neutrality  The NKp family of Fitness Landscapes
 Alive VI: Sixth International Conference on Articial Life
, 1998
"... It has come to be almost an article of faith amongst population biologists and GA researchers alike that the principal feature of a fitness landscape as regards evolutionary dynamics is "ruggedness", particularly as measured by the autocorrelation function. In this paper we demonstrate that autoco ..."
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Cited by 45 (2 self)
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It has come to be almost an article of faith amongst population biologists and GA researchers alike that the principal feature of a fitness landscape as regards evolutionary dynamics is "ruggedness", particularly as measured by the autocorrelation function. In this paper we demonstrate that autocorrelation alone may be inadequate as a mediator of evolutionary dynamics, specifically in the presence of large scale neutrality. We introduce the NKp family of landscapes (a variant on NK landscapes) which possess the remarkable property that varying the degree of neutrality has minimal effect on the correlation structure. It is demonstrated that NKp landscapes feature neutral networks which have a "constant innovation" property comparable with the neutral networks observed in models of RNA secondary structure folding landscapes. We show that evolutionary dynamics on NKp landscapes vary dramatically with the degree of neutrality  at high neutrality the dynamics are characterised by populat...
Landscapes And Molecular Evolution
, 1996
"... that allows to choose the direction for the next step at random from all directions along which fitness does not decrease. Stationary states of populations correspond to local optima of the fitness landscape. Evolution is seen as a series of transitions between optima with increasing fitness values. ..."
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Cited by 41 (5 self)
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that allows to choose the direction for the next step at random from all directions along which fitness does not decrease. Stationary states of populations correspond to local optima of the fitness landscape. Evolution is seen as a series of transitions between optima with increasing fitness values. Wright's metaphor saw a recent revival when sufficiently simple models of fitness landscapes became available [1, 41]. These models are based on spin glass theory [63, 66] or closely related to it like Kauffman's Nk model [42]. Evolution of RNA molecules has been studied by more realistic models that deal explicitly with molecular structures obtained from folding RNA sequences [23, 24]. Fitness values serving as input parameters for evolutionary dynamics were derived through evaluation of the structures. The complexity of RNA fitness landscapes originates from conflicting consequences of structural changes that are reminiscent of "frustration" in the theory of spin glasses [2]. Fitness in t
Effect of neutral selection on the evolution of molecular species
 In Proc. R. Soc. London B
, 1998
"... We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequencestructure maps are present also in ou ..."
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Cited by 39 (1 self)
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We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequencestructure maps are present also in our general model. Examples are the occurrence of “common ” structures which occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks which cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena which appear to be general properties of neutrally evolving systems. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network. 1
Fitness landscapes and evolvability
 Evolutionary Computation
, 2002
"... In this paper, we develop techniques based on evolvability statistics of the fitness landscape surrounding sampled solutions. Averaging the measures over a sample of equal fitness solutions allows us to build up fitness evolvability portraits of the fitness landscape, which we show can be used to co ..."
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Cited by 37 (2 self)
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In this paper, we develop techniques based on evolvability statistics of the fitness landscape surrounding sampled solutions. Averaging the measures over a sample of equal fitness solutions allows us to build up fitness evolvability portraits of the fitness 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 find 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 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.
Design of MultiStable RNA Molecules
, 2001
"... We show that the problem of designing RNA sequences that can fold into multiple stable secondary structures can be transformed into a combinatorial optimization problem that can be solved by means of simple heuristics. Hence it is feasible to design RNA switches with prescribed structural alternativ ..."
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Cited by 31 (7 self)
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We show that the problem of designing RNA sequences that can fold into multiple stable secondary structures can be transformed into a combinatorial optimization problem that can be solved by means of simple heuristics. Hence it is feasible to design RNA switches with prescribed structural alternatives. We discuss the theoretical background and present an effcient tool that allows the design of various types of switches. We argue that both the general properties of the sequencestructure map of RNA secondary structures and the ease with which our design tool finds bistable RNAs, strongly indicates that RNA switches are easily accessible in evolution. Thus RNA switches are likely not exceptional instances of interesting RNA behavior but rather examples of an ubiquitous paradigm. Keywords: RNA switches, sequence design, RNA folding, RNA secondary structure prediction