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

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 sequence-structure 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

Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g. mutations) or non-heritable perturbations (e.g. the weather). Here we primarily focus on the first kind of robustness -- genetic robustness -- and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory, (2) understanding the evolution of genetic robustness, and (3) exploring the implications of genetic robustness for future evolution.

We tackle two problems of interest to the software assurance community. Firstly, existing models of software development (such as the waterfall and spiral models) are oriented towards one-off software development projects, while the growth of mass market computing has led to a world in which most software consists of packages which follow an evolutionary development model. This leads us to ask whether anything interesting and useful may be said about evolutionary development. We answer in the affirmative. Secondly, existing reliability growth models emphasise the Poisson distribution of individual software bugs, while the empirically observed reliability growth for large systems is asymptotically slower than this. We provide a rigorous explanation of this phenomenon. Our reliability growth model is inspired by statistical thermodynamics, but also applies to biological evolution. It is in close agreement with experimental measurements of the fitness of an evolving species a...

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

Evolution has created the complexity of the animate world and deciphering the language of evolution is the key towards understanding nature. The dynamics of evolution is simplified by considering it as a superposition of three less sophisticated processes: population dynamics, population support dynamics, and genotype-phenotype mapping. Evolution of molecules in laboratory assays provides a sufficiently simple system for the quantitative analysis of the three phenomena. Coarse-grained notions of structures like RNA secondary structures are used as model phenotypes. They provide an excellent tool for a comprehensive analysis of the entire complex of molecular evolution. The mapping from RNA genotypes into secondary structures is highly redundant. In order to find at least one sequence for every common structures one need only search a (relatively) small part of sequence space. The existence of selectively neutral phenotypes plays an important role for the the success and the efficiency ...

Recent experiments involving competition of clonal populations of RNA viruses have shown that competition among virus strains of approximately equal relative fitness can result in the eventual competitive exclusion of one of the species. As competition proceeds in time, both the winers and the losers exhibited absolute gains in fitness, consistent with the "Red Queen" hypothesis of evolution. Further experiments involving closely related evolving quasispecies revealed a highly predictable nonlinear behavior suggesting a deterministic component in the underlying quasispecies dynamics. In this paper we present a simple model of RNA virus populations which allows previous hypothesis to be tested and provides an interpretation for the observed experimental results. Submitted to Journal of Molecular Biology 1 Introduction RNA viruses, because of their intrinsic simplicity and adaptability offer a unique opportunity for exploring long term evolution under controlled conditions (Domingo an...

In this paper Lewontin's notion of "quasi-independence" of characters is formalized as the assumption that a region of the phenotype space can be represented by a product space of orthogonal factors. In this picture each character corresponds to a factor of a region of the phenotype space. We consider any region of the phenotype space that has a given factorization as a "type", i.e., as a set of phenotypes that share the same set of phenotypic characters. Using the notion of local factorizations we develop a theory of character identity based on the continuity of common factors among di#erent regions of the phenotype space. We also consider the topological constraints on evolutionary transitions among regions with di#erent regional factorizations, i.e., for the evolution of new types or body plans. It is shown that direct transition between di#erent "types" is only possible if the transitional forms have all the characters that the ancestral and the derived types have and are thus compatible with the factorization of both types. Transitional forms thus have to go over a "complexity hump" where they have more quasi-independent characters than either the ancestral as well as the derived type. The only logical, but biologically unlikely, alternative is a "hopeful monster" that transforms in a single step from the ancestral type to the derived type. Topological considerations also suggest a new factor that may contribute to the evolutionary stability of "types." It is shown that if the type is decomposable into factors which are vertex irregular (i.e. have states that are more or less preferred in a random walk), the region of phenotypes representing the type contains islands of strongly preferred states. In other words types have a statistical tendency of retaining evolu...

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...

Cultural psychology, and other social sciences (e.g. cultural anthropology, sociology), seek to document cultural variation, yet have difficulty providing strong empirical tests of explanations for that variation. It is argued here that an effective means of testing hypotheses regarding the origin of, and persistence and change in, cultural variation is by simulating cultural transmission in the lab using certain methods from experimental social psychology. Three experimental methods are reviewed: the transmission chain method, the replacement method, and the constant-group method. Although very few studies have explicitly simulated specific cross-cultural patterns, much potential exists for future investigations. This integration of small-scale experimental simulations and largescale observational or historical data is facilitated by an evolutionary framework for the study of culture, and has a precedent in the biological sciences, where experiments are used to simulate and explain the processes of biological evolution.