Degeneracy: a link between evolvability, robustness and complexity in biological systems

A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as ecosystem services and resilience is well recognized, the broader relationship between robustness and evolution is only starting to be fully appreciated. A renewed interest in this relationship has been prompted by evidence that mutational robustness can play a positive role in the discovery of adaptive innovations (evolvability) and evidence of an intimate relationship between robustness and complexity in biology. This paper offers a new perspective on the mechanics of evolution and the origins of complexity, robustness, and evolvability. Here we explore the hypothesis that degeneracy, a partial overlap in the functioning of multi-functional components, plays a central role in the evolution and robustness of complex forms. In support of this hypothesis, we present evidence that degeneracy is a fundamental source of robustness, it is intimately tied to multi-scaled complexity, and it establishes conditions that are necessary for system evolvability

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves into a critical and constructive attitude in our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.Comment: 111 pages, 11 figures uses elsarticle latex clas

Online Diversity Control in Symbolic Regression via a Fast Hash-based Tree Similarity Measure

Diversity represents an important aspect of genetic programming, being directly correlated with search performance. When considered at the genotype level, diversity often requires expensive tree distance measures which have a negative impact on the algorithm's runtime performance. In this work we introduce a fast, hash-based tree distance measure to massively speed-up the calculation of population diversity during the algorithmic run. We combine this measure with the standard GA and the NSGA-II genetic algorithms to steer the search towards higher diversity. We validate the approach on a collection of benchmark problems for symbolic regression where our method consistently outperforms the standard GA as well as NSGA-II configurations with different secondary objectives.Comment: 8 pages, conference, submitted to congress on evolutionary computatio

Evolvability and rate of evolution in evolutionary computation

Evolvability has emerged as a research topic in both natural and computational evolution. It is a notion put forward to investigate the fundamental mechanisms that enable a system to evolve. A number of hypotheses have been proposed in modern biological research based on the examination of various mechanisms in the biosphere for their contribution to evolvability. Therefore, it is intriguing to try to transfer new discoveries from Biology to and test them in Evolutionary Computation (EC) systems, so that computational models would be improved and a better understanding of general evolutional mechanisms is achieved. -- Rate of evolution comes in different flavors in natural and computational evolution. Specifically, we distinguish the rate of fitness progression from that of genetic substitutions. The former is a common concept in EC since the ability to explicitly quantify the fitness of an evolutionary individual is one of the most important differences between computational systems and natural systems. Within the biological research community, the definition of rate of evolution varies, depending on the objects being examined such as gene sequences, proteins, tissues, etc. For instance, molecular biologists tend to use the rate of genetic substitutions to quantify how fast evolution proceeds at the genetic level. This concept of rate of evolution focuses on the evolutionary dynamics underlying fitness development, due to the inability to mathematically define fitness in a natural system. In EC, the rate of genetic substitutions suggests an unconventional and potentially powerful method to measure the rate of evolution by accessing lower levels of evolutionary dynamics. -- Central to this thesis is our new definition of rate of evolution in EC. We transfer the method of measurement of the rate of genetic substitutions from molecular biology to EC. The implementation in a Genetic Programming (GP) system shows that such measurements can indeed be performed and reflect well how evolution proceeds. Below the level of fitness development it provides observables at the genetic level of a GP population during evolution. We apply this measurement method to investigate the effects of four major configuration parameters in EC, i.e., mutation rate, crossover rate, tournament selection size, and population size, and show that some insights can be gained into the effectiveness of these parameters with respect to evolution acceleration. Further, we observe that population size plays an important role in determining the rate of evolution. We formulate a new indicator based on this rate of evolution measurement to adjust population size dynamically during evolution. Such a strategy can stabilize the rate of genetic substitutions and effectively improve the performance of a GP system over fixed-size populations. This rate of evolution measure also provides an avenue to study evolvability, since it captures how the two sides of evolvability, i.e., variability and neutrality, interact and cooperate with each other during evolution. We show that evolvability can be better understood in the light of this interplay and how this can be used to generate adaptive phenotypic variation via harnessing random genetic variation. The rate of evolution measure and the adaptive population size scheme are further transferred to a Genetic Algorithm (GA) to solve a real world application problem - the wireless network planning problem. Computer simulation of such an application proves that the adaptive population size scheme is able to improve a GA's performance against conventional fixed population size algorithms

Local Optima Networks of NK Landscapes with Neutrality

In previous work we have introduced a network-based model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. By using two known neutral variants of the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the non-neutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and non-neutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.Comment: IEEE Transactions on Evolutionary Computation volume 14, 6 (2010) to appea