937 research outputs found

    A tractable genotype-phenotype map for the self-assembly of protein quaternary structure

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    The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a 2D lattice and exhibits a number of properties: redundancy\textit{redundancy} (genotypes vastly outnumber phenotypes), phenotype bias\textit{phenotype bias} (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity\textit{genotype component disconnectivity} (phenotypes consist of disconnected mutational networks) and shape space covering\textit{shape space covering} (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the HP lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.Comment: 12 pages, 6 figure

    Degeneracy: a design principle for achieving robustness and evolvability

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    Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.Comment: Accepted in the Journal of Theoretical Biology (Nov 2009

    Self-adaptive exploration in evolutionary search

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    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''.Comment: 24 pages, 5 figure

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

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    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

    New insights on neutral binary representations for evolutionary optimization

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    This paper studies a family of redundant binary representations NNg(l, k), which are based on the mathematical formulation of error control codes, in particular, on linear block codes, which are used to add redundancy and neutrality to the representations. The analysis of the properties of uniformity, connectivity, synonymity, locality and topology of the NNg(l, k) representations is presented, as well as the way an (1+1)-ES can be modeled using Markov chains and applied to NK fitness landscapes with adjacent neighborhood.The results show that it is possible to design synonymously redundant representations that allow an increase of the connectivity between phenotypes. For easy problems, synonymously NNg(l, k) representations, with high locality, and where it is not necessary to present high values of connectivity are the most suitable for an efficient evolutionary search. On the contrary, for difficult problems, NNg(l, k) representations with low locality, which present connectivity between intermediate to high and with intermediate values of synonymity are the best ones. These results allow to conclude that NNg(l, k) representations with better performance in NK fitness landscapes with adjacent neighborhood do not exhibit extreme values of any of the properties commonly considered in the literature of evolutionary computation. This conclusion is contrary to what one would expect when taking into account the literature recommendations. This may help understand the current difficulty to formulate redundant representations, which are proven to be successful in evolutionary computation. (C) 2016 Elsevier B.V. All rights reserved

    Associative memory in gene regulation networks

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    The pattern of gene expression in the phenotype of an organism is determined in part by the dynamical attractors of the organism’s gene regulation network. Changes to the connections in this network over evolutionary time alter the adult gene expression pattern and hence the fitness of the organism. However, the evolution of structure in gene expression networks (potentially reflecting past selective environments) and its affordances and limitations with respect to enhancing evolvability is poorly understood in general. In this paper we model the evolution of a gene regulation network in a controlled scenario. We show that selected changes to connections in the regulation network make the currently selected gene expression pattern more robust to environmental variation. Moreover, such changes to connections are necessarily ‘Hebbian’ – ‘genes that fire together wire together’ – i.e. genes whose expression is selected for in the same selective environments become co-regulated. Accordingly, in a manner formally equivalent to well-understood learning behaviour in artificial neural networks, a gene expression network will therefore develop a generalised associative memory of past selected phenotypes. This theoretical framework helps us to better understand the relationship between homeostasis and evolvability (i.e. selection to reduce variability facilitates structured variability), and shows that, in principle, a gene regulation network has the potential to develop ‘recall’ capabilities normally reserved for cognitive systems

    Compensatory evolution and the origins of innovations

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    Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to adaptation when co-opted - e.g. following a mutation increasing expression from a low, attenuated baseline. This view is described, for example, by the metaphor of the spread of a population across a neutral network in genotype space. As an alternative view, consider the fact that most phenotypic traits are affected by multiple sequences, including cryptic ones. Even in a strictly clonal population, the co-option of cryptic sequences at different loci may have different phenotypic effects and offer the population multiple adaptive possibilities. Here, we model the evolution of quantitative phenotypic characters encoded by cryptic sequences, and compare the relative contributions of genetic diversity and of variation across sites to the phenotypic potential of a population. We show that most of the phenotypic variation accessible through co-option would exist even in populations with no polymorphism. This is made possible by a history of compensatory evolution, whereby the phenotypic effect of a cryptic mutation at one site was balanced by mutations elsewhere in the genome, leading to a diversity of cryptic effect sizes across sites rather than across individuals. Cryptic sequences might accelerate adaptation and facilitate large phenotypic changes even in the absence of genetic diversity, as traditionally defined in terms of alternative alleles

    Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability.

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    Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps-a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure-to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.This work was funded under EP/P504287/1 by the Engineering and Physical Sciences Research Council (https://www.epsrc.ac.uk). SEA is supported by The Royal Society (https://royalsociety.org/).This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.pcbi.100477

    Degenerate neutrality creates evolvable fitness landscapes

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    Understanding how systems can be designed to be evolvable is fundamental to research in optimization, evolution, and complex systems science. Many researchers have thus recognized the importance of evolvability, i.e. the ability to find new variants of higher fitness, in the fields of biological evolution and evolutionary computation. Recent studies by Ciliberti et al (Proc. Nat. Acad. Sci., 2007) and Wagner (Proc. R. Soc. B., 2008) propose a potentially important link between the robustness and the evolvability of a system. In particular, it has been suggested that robustness may actually lead to the emergence of evolvability. Here we study two design principles, redundancy and degeneracy, for achieving robustness and we show that they have a dramatically different impact on the evolvability of the system. In particular, purely redundant systems are found to have very little evolvability while systems with degeneracy, i.e. distributed robustness, can be orders of magnitude more evolvable. These results offer insights into the general principles for achieving evolvability and may prove to be an important step forward in the pursuit of evolvable representations in evolutionary computation

    Evolvability signatures of generative encodings: beyond standard performance benchmarks

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    Evolutionary robotics is a promising approach to autonomously synthesize machines with abilities that resemble those of animals, but the field suffers from a lack of strong foundations. In particular, evolutionary systems are currently assessed solely by the fitness score their evolved artifacts can achieve for a specific task, whereas such fitness-based comparisons provide limited insights about how the same system would evaluate on different tasks, and its adaptive capabilities to respond to changes in fitness (e.g., from damages to the machine, or in new situations). To counter these limitations, we introduce the concept of "evolvability signatures", which picture the post-mutation statistical distribution of both behavior diversity (how different are the robot behaviors after a mutation?) and fitness values (how different is the fitness after a mutation?). We tested the relevance of this concept by evolving controllers for hexapod robot locomotion using five different genotype-to-phenotype mappings (direct encoding, generative encoding of open-loop and closed-loop central pattern generators, generative encoding of neural networks, and single-unit pattern generators (SUPG)). We observed a predictive relationship between the evolvability signature of each encoding and the number of generations required by hexapods to adapt from incurred damages. Our study also reveals that, across the five investigated encodings, the SUPG scheme achieved the best evolvability signature, and was always foremost in recovering an effective gait following robot damages. Overall, our evolvability signatures neatly complement existing task-performance benchmarks, and pave the way for stronger foundations for research in evolutionary robotics.Comment: 24 pages with 12 figures in the main text, and 4 supplementary figures. Accepted at Information Sciences journal (in press). Supplemental videos are available online at, see http://goo.gl/uyY1R
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