RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical structure. On such networks evolving populations split into subpopulations which diffuse independently in sequence space. This demands a distinction between two mutation thresholds: one at which genotypic information is lost and one at which phenotypic information is lost. In between diffusion enables the search of vast areas in genotype space, while still preserving the dominant phenotype. By this dynamics the success of phenotypic adaptation becomes much less sensitive to the initial conditions in genotype space. Introduction To explain the high fixation rate of nucleotide substitutions in a population, Motoo Kimura argued that the vast majority of genetic change at the level of a population must be neutral, rather than adaptive [1]. Sewall Wright's reaction to Kimura's point was politely neutral [2, page 474]: "Changes in wholly nonfunctional parts of the molecul...

. This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node functions are also separately numbered. The genotype is just a list of node connections and functions. The genotype is then mapped to an indexed graph that can be executed as a program. Evolutionary algorithms are used to evolve the genotype in a symbolic regression problem (sixth order polynomial) and the Santa Fe Ant Trail. The computational effort is calculated for both cases. It is suggested that hit effort is a more reliable measure of computational efficiency. A neutral search strategy that allows the fittest genotype to be replaced by another equally fit genotype (a neutral genotype) is examined and compared with non-neutral search for the Santa Fe ant problem. The neutral search...

The Breeder Genetic Algorithm BGA models artificial selection as performed by human breeders. The science of breeding is based on advanced statistical methods. In this paper a connection between genetic algorithm theory and the science of breeding is made. We show how the response to selection equation and the concept of heritability can be applied to predict the behavior of the BGA. Selection, recombination and mutation are analyzed within this framework. It is shown that recombination and mutation are complementary search operators. The theoretical results are obtained under the assumption of additive gene effects. For general fitness landscapes regression techniques for estimating the heritability are used to analyze and control the BGA. The method of decomposing the genetic variance into an additive and a nonadditive part connects the case of additive fitness functions with the general case.

Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any two different structures almost touch each other, and sequences folding into almost all "common" structures can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared with data obtained by folding large samples of RNA sequences. Differences are explained in terms of RNA molecular structures. 1.

RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical secondary structures. Fitness landscapes that are based on the mapping between RNA sequence and RNA secondary structure hence have many neutral paths. A neutral walk on these fitness landscapes gives access to a virtually unlimited number of secondary structures that are a single point mutation from the neutral path. This shows that neutral evolution explores phenotype space and can play a role in adaptation. Introduction Ever since Sewall Wright introduced the metaphor of an "adaptive landscape" (Wright, 1932) the view on adaptive evolution has been dominated by that of an uphill walk of a population on a mountainous fitness landscape in which it can get stuck on suboptimal peaks. The neutralist perspective that evolution at the molecular level is dominated by non-adaptive, neutral changes (Kimura, 1983) has hardly changed this picture. A notable exception is Maynard...

Metastability is a common phenomenon. Many evolutionary processes, both natural and artificial, alternate between periods of stasis and brief periods of rapid change in their behavior. In this paper an analytical model for the dynamics of a mutationonly genetic algorithm (GA) is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics. The GA’s population dynamics is described in terms of flows in the space of fitness distributions. The trajectories through fitness distribution space are derived in closed form in the limit of infinite populations. We then show how finite populations induce metastability, even in regions where fitness does not exhibit a local optimum. In particular, the model predicts the occurrence of “fitness epochs”—periods of stasis in population fitness distributions—at finite population size and identifies the locations of these fitness epochs with the flow’s hyperbolic fixed points. This enables exact predictions of the metastable fitness distributions during the fitness epochs, as well as giving insight into the nature of the periods of stasis and the innovations between them. All these results are obtained as closed-form expressions in terms of the GA’s parameters.

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...

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. We propose the application of a genotype-phenotype mapping to the solution of constrained optimization problems. The method consists of strictly separating the search space of genotypes from the solution space of phenotypes. A mapping from genotypes into phenotypes provides for the appropriate expression of information represented by the genotypes. The mapping is constructed as to guarantee feasibility of phenotypic solutions for the problem under study. This enforcing of constraints causes multiple genotypes to result in one and the same phenotype. Neutral variants are therefore frequent and play an important role in maintaining genetic diversity. As a specific example, we discuss Binary Genetic Programming (BGP), a variant of Genetic Programming that uses binary strings as genotypes and program trees as phenotypes. Published in: Proceedings PARALLEL PROBLEM SOLVING FROM NATURE III Y. Davidor, H.-P. Schwefel and R. Manner (Eds.) Springer, Berlin, 1994 pp. 322 --- 332 1 Introduction...

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 auto-correlation function. In this paper we demonstrate that auto-correlation 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...