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The Evolutionary Unfolding of Complexity  [PDF]
James P. Crutchfield,Erik van Nimwegen
Physics , 1999,
Abstract: We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.
Complexity of evolutionary equilibria in static fitness landscapes  [PDF]
Artem Kaznatcheev
Computer Science , 2013,
Abstract: A fitness landscape is a genetic space -- with two genotypes adjacent if they differ in a single locus -- and a fitness function. Evolutionary dynamics produce a flow on this landscape from lower fitness to higher; reaching equilibrium only if a local fitness peak is found. I use computational complexity to question the common assumption that evolution on static fitness landscapes can quickly reach a local fitness peak. I do this by showing that the popular NK model of rugged fitness landscapes is PLS-complete for K >= 2; the reduction from Weighted 2SAT is a bijection on adaptive walks, so there are NK fitness landscapes where every adaptive path from some vertices is of exponential length. Alternatively -- under the standard complexity theoretic assumption that there are problems in PLS not solvable in polynomial time -- this means that there are no evolutionary dynamics (known, or to be discovered, and not necessarily following adaptive paths) that can converge to a local fitness peak on all NK landscapes with K = 2. Applying results from the analysis of simplex algorithms, I show that there exist single-peaked landscapes with no reciprocal sign epistasis where the expected length of an adaptive path following strong selection weak mutation dynamics is $e^{O(n^{1/3})}$ even though an adaptive path to the optimum of length less than n is available from every vertex. The technical results are written to be accessible to mathematical biologists without a computer science background, and the biological literature is summarized for the convenience of non-biologists with the aim to open a constructive dialogue between the two disciplines.
Time Complexity Analysis of an Evolutionary Algorithm for Finding Nearly Maximum Cardinality Matching
Jun HE,Xin YAO,

计算机科学技术学报 , 2004,
Abstract: Most of works on the time complexity analysis of evolutionary algorithms have always focused on some artificial binary problems The time complexity of the algorithms for combinatorial optimisation has not been well understood. This paper considers the time complexity of an evolutionary algorithm for a classical combinatorial optimisation problem, to find the maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce, a matching with nearly maximum cardinality in average polynomial time. The work is partially supported by Engineering and Physical Sciences Research Council (GR/R52541/01) and State Key Lab of Software Engineering at Wuhan University. The work was reported at UK 2002 Workshop on Computational Intelligence. Jun He received his M.Sc. degree in mathematics and Ph.D. degree in computer science from Wuhan University, China, in 1992 and 1995 respectively. He is currently a research fellow at University of Birmingham, England. His research interests include evolutionary computation, network security and parallel algorithms. Xin Yao received the Ph.D. degree in computer science from the Univ. Sci. Tech. China in 1990. He is currently a professor of computer science at the University of Birmingham, England. He is a fellow of IEEE. His major research interests include evolutionary computation, neural network ensembles, co-evolution, evolvable hardware, time complexity of evolutionary algorithms, and data mining. He published extensively in these areas.
Drift Conditions for Time Complexity of Evolutionary Algorithms

HE Jun,YAO Xin,KANG Li-shan,

软件学报 , 2001,
Abstract: The computational time complexity is an important topic in the theory of evolutionary algorithms. This paper introduces drift analysis into analysing the average time complexity of evolutionary algorithms, which are applicable to a wide range of evolutionary algorithms and many problems. Based on the drift analysis, some useful drift conditions to determine the time complexity of evolutionary algorithms are studied. These conditions are applied into the fully deceptive problem to verify their efficiency.
An Integrated and Evolutionary Dynamical Systems View of Climate Complexity  [PDF]
Walter Ritter Ortíz, Lorena Cruz
International Journal of Geosciences (IJG) , 2013, DOI: 10.4236/ijg.2013.41006

The Earth shows a constant display of an organized complexity system, and its intrinsic capacity for sporadic self-organization constitutes its fundamental and profound mysterious property. A graphical method derived from the logistic phase space of precipitation is proposed to identify periods of abundance-scarcity of rain as well as El Nino presence in order to cope with climate change. The most striking result is that the majority of El Nino events on this graph are chaotic, in which the sign of the dominant eigenvalues of precipitation gives trends of scarcity on negative signs and abundance on positive signs, with eleven years periods.

A Parameterized Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms  [PDF]
Dogan Corus,Per Kristian Lehre,Frank Neumann,Mojgan Pourhassan
Computer Science , 2014,
Abstract: Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem (GMST), and the generalised travelling salesman problem (GTSP) in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) EA working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the global structure representation enables to solve the problem in fixed-parameter time. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other's hard instances very efficiently. For the generalised travelling salesman problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) EA working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem.
Hidden evolutionary complexity of Nucleo-Cytoplasmic Large DNA viruses of eukaryotes  [cached]
Yutin Natalya,Koonin Eugene V
Virology Journal , 2012, DOI: 10.1186/1743-422x-9-161
Abstract: Background The Nucleo-Cytoplasmic Large DNA Viruses (NCLDV) constitute an apparently monophyletic group that consists of at least 6 families of viruses infecting a broad variety of eukaryotic hosts. A comprehensive genome comparison and maximum-likelihood reconstruction of the NCLDV evolution revealed a set of approximately 50 conserved, core genes that could be mapped to the genome of the common ancestor of this class of eukaryotic viruses. Results We performed a detailed phylogenetic analysis of these core NCLDV genes and applied the constrained tree approach to show that the majority of the core genes are unlikely to be monophyletic. Several of the core genes have been independently acquired from different sources by different NCLDV lineages whereas for the majority of these genes displacement by homologs from cellular organisms in one or more groups of the NCLDV was demonstrated. Conclusions A detailed study of the evolution of the genomic core of the NCLDV reveals substantial complexity and diversity of evolutionary scenarios that was largely unsuspected previously. The phylogenetic coherence between the core genes is sufficient to validate the hypothesis on the evolution of all NCLDV from a common ancestral virus although the set of ancestral genes might be smaller than previously inferred from patterns of gene presence-absence.
Time Complexity of Evolutionary Algorithms for Combinatorial Optimization: A Decade of Results
Time Complexity of Evolutionary Algorithms for Combinatorial Optimization: A Decade of Results

Pietro S Oliveto,Jun He,Xin Yao,

国际自动化与计算杂志 , 2007,
Abstract: Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms,such as the (1 1)-EA,on toy problems.These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems.In fact,in recent years,it has been possible to analyze the (1 1)-EA on combinatorial optimization problems with practical applications and more realistic population-baeed EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines.The most common mathematical techniques are introduced,the basic ideas behind them are discussed and their elective applications are highlighted.Solved problems that were still open are enumerated as are those still awaiting for a solution.New questions and problems arisen in the meantime are also considered.
Saliency mapping in the optic tectum and its relationship to habituation  [PDF]
Arkadeb Dutta,Yoram Gutfreund
Frontiers in Integrative Neuroscience , 2014, DOI: 10.3389/fnint.2014.00001
Abstract: Habituation of the orienting response has long served as a model system for studying fundamental psychological phenomena such as learning, attention, decisions and surprise. In this article, we review an emerging hypothesis that the evolutionary role of the superior colliculus (SC) in mammals or its homologue in birds, the optic tectum (OT), is to select the most salient target and send this information to the appropriate brain regions to control the body and brain orienting responses. Recent studies have begun to reveal mechanisms of how saliency is computed in the OT/SC, demonstrating a striking similarity between mammals and birds. The saliency of a target can be determined by how different it is from the surrounding objects, by how different it is from its history (that is habituation) and by how relevant it is for the task at hand. Here, we will first review evidence, mostly from primates and barn owls, that all three types of saliency computations are linked in the OT/SC. We will then focus more on neural adaptation in the OT and its possible link to temporal saliency and habituation.
The Cladistic Basis for the Phylogenetic Diversity (PD) Measure Links Evolutionary Features to Environmental Gradients and Supports Broad Applications of Microbial Ecology’s “Phylogenetic Beta Diversity” Framework  [PDF]
Daniel P. Faith,Catherine A. Lozupone,David Nipperess,Rob Knight
International Journal of Molecular Sciences , 2009, DOI: 10.3390/ijms10114723
Abstract: The PD measure of phylogenetic diversity interprets branch lengths cladistically to make inferences about feature diversity. PD calculations extend conventional specieslevel ecological indices to the features level. The “phylogenetic beta diversity” framework developed by microbial ecologists calculates PD-dissimilarities between community localities. Interpretation of these PD-dissimilarities at the feature level explains the framework’s success in producing ordinations revealing environmental gradients. An example gradients space using PD-dissimilarities illustrates how evolutionary features form unimodal response patterns to gradients. This features model supports new application of existing species-level methods that are robust to unimodal responses, plus novel applications relating to climate change, commercial products discovery, and community assembly.
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