Towards Understanding the Origin of Genetic Languages

Molecular biology is a nanotechnology that works--it has worked for billions of years and in an amazing variety of circumstances. At its core is a system for acquiring, processing and communicating information that is universal, from viruses and bacteria to human beings. Advances in genetics and experience in designing computers have taken us to a stage where we can understand the optimisation principles at the root of this system, from the availability of basic building blocks to the execution of tasks. The languages of DNA and proteins are argued to be the optimal solutions to the information processing tasks they carry out. The analysis also suggests simpler predecessors to these languages, and provides fascinating clues about their origin. Obviously, a comprehensive unraveling of the puzzle of life would have a lot to say about what we may design or convert ourselves into.Comment: (v1) 33 pages, contributed chapter to "Quantum Aspects of Life", edited by D. Abbott, P. Davies and A. Pati, (v2) published version with some editin

Self-Adaptive Stable Mutation Based on Discrete Spectral Measure for Evolutionary Algorithms, Journal of Telecommunications and Information Technology, 2011, nr 4

In this paper, the concept of a multidimensional discrete spectral measure is introduced in the context of its application to the real-valued evolutionary algorithms. The notion of a discrete spectral measure makes it possible to uniquely define a class of multivariate heavy-tailed distributions, that have recently received substantial attention of the evolutionary optimization community. In particular, an adaptation procedure known from the distribution estimation algorithms (EDAs) is considered and the resulting estimated distribution is compared with the optimally selected referential distribution

Average Convergence Rate of Evolutionary Algorithms

In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average convergence rate. It is a normalised geometric mean of the reduction ratio of the fitness difference per generation. The calculation of the average convergence rate is very simple and it is applicable for most evolutionary algorithms on both continuous and discrete optimization. A theoretical study of the average convergence rate is conducted for discrete optimization. Lower bounds on the average convergence rate are derived. The limit of the average convergence rate is analysed and then the asymptotic average convergence rate is proposed

The Evolution of Dispersal in Random Environments and The Principle of Partial Control

McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying these relationships in their two-environment model are investigated for arbitrary numbers of environments. The effect they described is quantified as the fitness-abundance covariance. The phase in the life cycle where the population is censused is crucial for the implications of the fitness-abundance covariance. These relationships are shown to connect to the population genetics literature on the Reduction Principle for the evolution of genetic systems and migration. Conditions that produce selection for increased unconditional dispersal are found to be new instances of departures from reduction described by the "Principle of Partial Control" proposed for the evolution of modifier genes. According to this principle, variation that only partially controls the processes that transform the transmitted information of organisms may be selected to increase these processes. Mathematical methods of Karlin, Friedland, and Elsner, Johnson, and Neumann, are central in generalizing the analysis. Analysis of the adaptive landscape of the model shows that the evolution of conditional dispersal is very sensitive to the spectrum of genetic variation the population is capable of producing, and suggests that empirical study of particular species will require an evaluation of its variational properties.Comment: Dedicated to the memory of Professor Michael Neumann, one of whose many elegant theorems provides for a result presented here. 28 pages, 1 table, 1 figur

Biological evolution through mutation, selection, and drift: An introductory review

Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and intends to bridge the gap between the biological and the physical literature. We first clarify the terminology and recapitulate the basic models of population genetics, which describe the evolution of the composition of a population under the joint action of the various evolutionary forces. Building on these foundations, we specify the ingredients explicitly, namely, the various mutation models and fitness landscapes. We then review recent developments concerning models of mutational degradation. These predict upper limits for the mutation rate above which mutation can no longer be controlled by selection, the most important phenomena being error thresholds, Muller's ratchet, and mutational meltdowns. Error thresholds are deterministic phenomena, whereas Muller's ratchet requires the stochastic component brought about by finite population size. Mutational meltdowns additionally rely on an explicit model of population dynamics, and describe the extinction of populations. Special emphasis is put on the mutual relationship between these phenomena. Finally, a few connections with the process of molecular evolution are established.Comment: 62 pages, 6 figures, many reference

Evolutionary dynamics of populations with genotype-phenotype map

In this thesis we develop a multi-scale model of the evolutionary dynamics of a population of cells, which accounts for the mapping between genotype and phenotype as determined by a model of the gene regulatory network. We study topological properties of genotype-phenotype networks obtained from the multi-scale model. Moreover, we study the problem of evolutionary escape and survival taking into account a genotype-phenotype map. An outstanding feature of populations with genotype-phenotype map is that selective pressures are determined by the phenotype, rather than genotypes. Our multi-scale model generates the evolution of a genotype-phenotype network represented by a pseudo-bipartite graph, that allows formulate a topological definition of the concepts of robustness and evolvability. We further study the problem of evolutionary escape for cell populations with genotype-phenotype map, based on a multi-type branching process. We present a comparative analysis between genotype-phenotype networks obtained from the multi-scale model and networks constructed assuming that the genotype space is a regular hypercube. We compare the effects on the probability of escape and the escape rate associated to the evolutionary dynamics between both classes of graphs. We further the study of evolutionary escape by analysing the long term survival conditioned to escape. Traditional approaches to the study of escape assume that the reproduction number of the escape genotype approaches infinity, and, therefore, survival is a surrogate of escape. Here, we analyse the process of survival upon escape by taking advantage of the fact that the natural setting of the escape problem endows the system with a separation of time scales: an initial, fast-decaying regime where escape actually occurs, is followed by a much slower dynamics within the (neutral network of) the escape phenotype. The probability of survival is analysed in terms of topological features of the neutral network of the escape phenotype.En aquesta tesi es desenvolupa un model multi-escala de la dinàmica evolutiva d'una població de cèl·lules, tenint en compte la correspondència entre el genotip i el fenotip determinat per un model de la xarxa de regulació genètica. Estudiem les propietats topològiques de les xarxes genotip-fenotip obtingudes a partir del model multi-escala. D'altra banda, s'estudia el problema de la fugida evolutiva i la supervivència, tenint en compte una aplicació entre genotip i fenotip. Una característica destacable de les poblacions amb aplicació genotip-fenotip és que les pressions selectives actuen sobre els fenotips, en lloc dels genotips. El nostre model multi-escala genera l'evolució d'una xarxa genotip-fenotip representada per un graf pseudo-bipartit, el qual permet formular una definició topològica dels conceptes de robustesa y capacitat evolutiva. A més a més, estudiem el problema de fugida evolutiva de poblacions de cèl¿lules amb una aplicació genotip-fenotip, basat en en un procés de ramificació multi-tipus. Presentem un anàlisi comparatiu entre les xarxes de genotip-fenotip obtingudes a partir del model multi-escala i les xarxes construïdes assumint un espai de genotips de tipus hipercub regular. Comparem els efectes de la probabilitat de fugida i la freqüència d'escapament associades a la dinàmica evolutiva entre ambdues classes de grafs. Anem més enllà de l'estudi de fugida evolutiva mitjançant l'anàlisi de la supervivència a llarg plaç condicionat a fugir. Els enfocaments tradicionals per a l'estudi de la fugida o escapament suposen una taxa de reproducció en el genotip de fugida propera a infinit. Per tant, la supervivència és equivalent a la fugida. Aquí analitzem el procés de supervivència suposant fugida aprofitant el fet que l'entorn natural del problema de fugida dota al sistema amb una separació d'escales de temps: un règim inicial, de temps ràpid, on la fugida realment es produeix; seguit d'una dinàmica molt més lenta dins de la (xarxa neutra del) fenotip de fugida. La probabilitat de supervivència s'analitza en termes de les característiques topològiques de la xarxa neutra del fenotip de fugidaPostprint (published version

`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms

We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation