937 research outputs found
A tractable genotype-phenotype map for the self-assembly of protein quaternary structure
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: (genotypes vastly outnumber phenotypes),
(genotypic redundancy varies greatly between
phenotypes), (phenotypes consist
of disconnected mutational networks) and (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
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
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
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
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
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
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.
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
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
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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