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 non-independent 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 the...

The current implementation of the Neo-Darwinian 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 genotype-phenotype 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 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.

Abstract—Self-adaptation is used in all main paradigms of evolutionary computation to increase efficiency. We claim that the basis of self-adaptation is the use of neutrality. In the absence of external control neutrality allows a variation of the search distribution without the risk of fitness loss. I.

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely de ned base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The preimages of this map, called neutral networks, are uniquely associated with the shapes and vice versa. Random graph theory is used to construct networks in sequence space which are suitable models for neutral networks. The theory of molecular quasispecies has been applied to replication and mutation on single-peak tness landscapes. This concept is extended by considering evolution on degenerate multi-peak landscapes which originate from neutral networks by assuming that one particular shape is tter than all others. On such a singleshape landscape the superior tness value is assigned to all sequences belonging

In nature, phenotypic variability is highly structured with respect to correlations between different phenotypic traits. In this paper we argue that this structuredness can be understood as the outcome of an adaptive process of phenotypic exploration distributions, similar to the adaptation of the search distribution in heuristic search schemes or Estimation-of-Distribution Algorithms. The key ingredient of this process is a non-trivial genotype-phenotype mapping: We rigorously define non-triviality, in which case neutral traits (as a generalization of strategy parameters) influence phenotype evolution by determining exploration distributions. Our main result is the description of the evolution of exploration distributions themselves in terms of an ordinary evolution equation. Accordingly, the ``fitness'' of an exploration distribution is proportional to its similarity (in the sense of the Kullback-Leibler divergence) to the fitness distribution over phenotype space. Hence, exploration distributions evolve such that dependencies and correlations between phenotypic variables in selection are naturally adopted by the way evolution explores phenotype space.

re analyzed for RNA secondary structures. Optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of an uninterrupted series of phenotypes from initial stucture to target, called relay series. We give a novel definition of continuity in evolution which identifies discontinuities as major changes in molecular phenotypes. Evolutionary Dynamics --- Exploring the Interplay of Accident, Selection, Neutrality, and Function Edited by J. P. Crutchfield and P. Schuster, Oxford Univ. Press 1 2 Evolution of Phenotypes 1 GENOTYPES AND PHENOTYPES Evolutionary optimization in asexually multiplying populations follows Darwin 's principle and is determined by the interplay of two processes which exert counteracting influences on genetic heterogeneity: (i) Mutations increase di

We address a primary question of computational as well as biological research on evolution: How can an exploration strategy adapt in such a way as to exploit the information gained about the problem at hand? We first introduce an integrated formalism of evolutionary search which provides a unified view on different specific approaches. On this basis we discuss the implications of indirect modeling (via a ``genotype-phenotype mapping'') on the exploration strategy. Notions such as modularity, pleiotropy and functional phenotypic complex are discussed as implications. Then, rigorously reflecting the notion of self-adaptability, we introduce a new definition that captures self-adaptability of exploration: different genotypes that map to the same phenotype may represent (also topologically) different exploration strategies; self-adaptability requires a variation of exploration strategies along such a ``neutral space''. By this definition, the concept of neutrality becomes a central concern of this paper. Finally, we present examples of these concepts: For a specific grammar-type encoding, we observe a large variability of exploration strategies for a fixed phenotype, and a self-adaptive drift towards short representations with highly structured exploration strategy that matches the ``problem's structure''.

We suggest simulating evolution of complex organisms using...

A self-reproduction via description is discussed in a network model of machines and description tapes. Tapes consist of bit strings, encoding function of machines. A tape is replicated when it is read by an adequate machine. Generally, a machine rewrites a tape without doing correct replication. The variation in a reproduced tape is taken as mutation. Since this mutation is caused by a machine's program, we call it active mutation. Which machine is translated from a given tape is dependent on what kind of a machine reads the tape. External noise is introduced in machine's reading process to make errors. A new reaction pathway is induced by external noise via machine's error action. We nd that the induced pathways will be mimicked deterministically in an emerging core structure. This core structure will be remained stable after turning o external noise. Low external noise develops a core structure of minimal self-replicative loop. When external noise is elevated, a more complex network evolves. Machines composing a complex core network, which has been bred in high external noise, will actively rewrite tapes rather just replicate them. Self-replication not as an individual but as a network now becomes important.