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A pessimistic estimate of the time required for an eye to evolve.

Theoretical considerations of eye design allow us to find routes along which the optical structures of eyes may have evolved. If selection constantly favours an increase in the amount of detectable spatial information, a light-sensitive patch will gradually turn into a focused lens eye through continuous small improvements of design. An upper limit for the number of generations required for the complete transformation can be calculated with a minimum of assumptions. Even with a consistently pessimistic approach the time required becomes amazingly short: only a few hundred thousand years.

Animals↗

Inferring frequency dependent selection from the molecular evolution of a rapidly evolving virus: a theoretical investigation.

Hypotheses have been put forward suggesting that immune selection generates much of the intra-patient genetic diversity of rapidly evolving viruses. A Monte Carlo simulation is presented which models sequence evolution in an HIV-like virus under selection from the immune system. Measurements of evolutionary change are then made from the resulting sequences, generating predicted outcomes for each scenario. Frequency dependent immune selection is shown by two statistical measurements to have a significant effect on viral sequence evolution. The use of drawing inferences about underlying evolutionary processes from samples of viral diversity in infected individuals is discussed.

Evolution, Molecular↗

Language as an evolving word web.

Human language may be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and interacting words in sentences are connected by edges. The empirical distribution of the number of connections of words in this network is of a peculiar form that includes two pronounced power-law regions. Here we propose a theory of the evolution of language, which treats language as a self-organizing network of interacting words. In the framework of this concept, we completely describe the observed word web structure without any fitting. We show that the two regimes in the distribution naturally emerge from the evolutionary dynamics of the word web. It follows from our theory that the size of the core part of language, the 'kernel lexicon', does not vary as language evolves.

Humans↗

Evolving controllers for a homogeneous system of physical robots: structured cooperation with minimal sensors.

We report on recent work in which we employed artificial evolution to design neural network controllers for small, homogeneous teams of mobile autonomous robots. The robots were evolved to perform a formation-movement task from random starting positions, equipped only with infrared sensors. The dual constraints of homogeneity and minimal sensors make this a non-trivial task. We describe the behaviour of a successful system in which robots adopt and maintain functionally distinct roles in order to achieve the task. We believe this to be the first example of the use of artificial evolution to design coordinated, cooperative behaviour for real robots.

Adaptation, Physiological↗

Three functionally diverged major structural proteins of white spot syndrome virus evolved by gene duplication.

White spot syndrome virus (WSSV) is an invertebrate virus causing considerable mortality in penaeid shrimp. The oval-to-bacilliform shaped virions, isolated from infected Penaeus monodon, contain four major proteins: VP28, VP26, VP24 and VP19 (28, 26, 24 and 19 kDa, respectively). VP26 and VP24 are associated with the nucleocapsid and the remaining two with the envelope. Forty-one N-terminal amino acids of VP24 were determined biochemically allowing the identification of its gene (vp24) in the WSSV genome. Computer-assisted analysis revealed a striking similarity between WSSV VP24, VP26 and VP28 at the amino acid and nucleotide sequence level. This strongly suggests that these structural protein genes may have evolved by gene duplication and subsequently diverged into proteins with different functions in the WSSV virion, i.e. envelope and nucleocapsid. None of these three structural WSSV proteins showed homology to proteins of other viruses including baculoviruses, underscoring the distinct taxonomic position of WSSV among invertebrate viruses.

Amino Acid Sequence↗

The dynamic progression of evolved character states for aromatic amino acid biosynthesis in gram-negative bacteria.

A systematic analysis of the evolution of aromatic amino acid biosynthesis in the Proteobacteria, previously focussed mainly upon the gamma subdivision, has now been extended to the beta subdivision. Five lineages were studied, represented by Neisseria gonorrhoeae, Nitrosomonas europaea, Alcaligenes faecalis, rRNA Group-III pseudomonads/Rubrivivax gelatinosus, and rRNA Group-II pseudomonads/Rhodocyclus tenuis. Within the phenylalanine pathway, the bifunctional P-protein (chorismate mutase/prephenate dehydratase) was present in each lineage and must have evolved in a common ancestor of the beta and gamma subdivisions. Each P-protein was found to be subject to activation by L-tyrosine, and to feedback inhibition by L-phenylalanine. Phenylalanine-inhibited (DS-phe) and tyrosine-inhibited (DS-tyr) isoenzymes of 3-deoxy-D-arabino-heptulosonate-7-phosphate synthase probably existed in the common beta-subdivision ancestor, with DS-tyr being lost in N. gonorrhoeae and A. faecalis. The participation of DS-phe in a dissociable multienzyme complex with one or more other common-pathway enzymes is known to exist in N. gonorrhoeae. The same complex is indicated by two peaks of DS-phe seen in chromatographic profiles of Group-III pseudomonads and A. faecalis. It is concluded that the contemporary DS-phe species present in subdivision gamma and beta must have had independent origins. Tyrosine biosynthesis was found to be quite diverse within the beta subdivision. Nit. europaea possessed an arogenate dehydrogenase which was specific for NADP+. In all other lineages, a broad-specificity cyclohexadienyl dehydrogenase (CHD) was present. In N. gonorrhoeae the CDH was specific for NAD+ while the remaining CDH species could utilize either NAD+ or NADP+. Only the CDH species within the rRNA Group-II pseudomonad/R. tenuis lineage was feedback-inhibited by L-tyrosine, and this correlated with an allosteric pattern where activation of the prephenate dehydratase component of the P-protein by L-tyrosine was relatively poor. However, the CDH enzyme present in N. gonorrhoeae and A. faecalis was subject to inhibition by 4-hydroxyphenylpyruvate, this being competitive with respect to the cyclohexadienyl substrate. The monofunctional species of chorismate mutase (CM-F) and cyclohexadienyl dehydratase, widely distributed among the gamma-subdivision assemblage and recently shown to be periplasmic enzymes, were demonstrated in Pseudomonas pickettii, a member of rRNA homology Group-II.

Alcaligenes↗

Fructan biosynthetic and breakdown enzymes in dicots evolved from different invertases. Expression of fructan genes throughout chicory development.

Fructans are fructose-based oligo- and polymers that serve as reserve carbohydrates in many plant species. The biochemistry of fructan biosynthesis in dicots has been resolved, and the respective cDNAs have been cloned. Recent progress has now succeeded in elucidating the biochemistry and molecular biology of fructan biodegradation in chicory, an economically important species used for commercial inulin extraction. Unlike fructan biosynthetic genes that originated from vacuolar-type invertase, fructan exohydrolases (FEHs) seem to have evolved from a cell-wall invertase ancestor gene that later obtained a low iso-electric point and a vacuolar targeting signal. Expression analysis reveals that fructan enzymes are controlled mainly at the transcriptional level. Using chicory as a model system, northern analysis was consistent with enzymatic activity measurements and observed carbohydrate changes throughout its development.

Cichorium intybus↗

Clusters of resistance genes in plants evolve by divergent selection and a birth-and-death process.

Classical genetic and molecular data show that genes determining disease resistance in plants are frequently clustered in the genome. Genes for resistance (R genes) to diverse pathogens cloned from several species encode proteins that have motifs in common. These motifs indicate that R genes are part of signal-transduction systems. Most of these R genes encode a leucine-rich repeat (LRR) region. Sequences encoding putative solvent-exposed residues in this region are hypervariable and have elevated ratios of nonsynonymous to synonymous substitutions; this suggests that they have evolved to detect variation in pathogen-derived ligands. Generation of new resistance specificities previously had been thought to involve frequent unequal crossing-over and gene conversions. However, comparisons between resistance haplotypes reveal that orthologs are more similar than paralogs implying a low rate of sequence homogenization from unequal crossing-over and gene conversion. We propose a new model adapted and expanded from one proposed for the evolution of vertebrate major histocompatibility complex and immunoglobulin gene families. Our model emphasizes divergent selection acting on arrays of solvent-exposed residues in the LRR resulting in evolution of individual R genes within a haplotype. Intergenic unequal crossing-over and gene conversions are important but are not the primary mechanisms generating variation.

Evolution, Molecular↗

Polymorphic phase transitions in systems evolving in a two-dimensional discrete space.

Polymorphic phase transitions in systems evolving in a two-dimensional discrete space have been studied. The driving force of the transitions appears to be a difference between two main energetic contributions: one, related to the thermal activation of the process, and another, being of quantum nature. The former (high temperature limit) is naturally assigned to the expansion (melting) part of the transition, while the latter (low temperature limit) has much in common with the contraction (solidification) part. Between the two main physical states distinguished, there exists a certain state, corresponding to a discontinuity point (pole) in the morphological phase diagram, represented by the well-known Bose-Einstein (Planck) formula, in which the system blows up. This point is related to an expected situation in which the contour of the object under investigation stands for the Brownian or purely diffusional path, with the fractal dimension dw=2, and the situation can be interpreted as some emergence of an intermediate "tetratic" phase. This, in turn, recalls a certain analogy to the equilibrium (order-disorder) phase transition of Kosterlitz-Thouless type, characteristic of, e.g., rough vs rigid interfaces in a two-dimensional space, with some disappearance of interface correlation length at dw=2. Otherwise, the contours of the objects are equivalent to fractional Brownian paths either in superlinear or "turbulent" (dw<2; the expansion case), or sublinear, viz., anomalously slow (dw>2; the contraction case) regimes, respectively. It is hoped that the description offered will serve to reflect properly the main subtleties of the dynamics of the polymorphic transitions in complex "soft-matter" systems, like formation of lipid mesomorphs or diffusional patterns, with nonzero line tension effect.

Journal Article↗

Origin of density clustering in a freely evolving granular gas.

The physical mechanisms leading to the development of density inhomogeneities in a freely evolving low density granular gas are investigated. By means of the direct simulation Monte Carlo method, numerical solutions of the inelastic Boltzmann equation are constructed for both a perturbed system and also for an initially homogeneous state. Analysis of the Fourier components of the fields indicates that the nonlinear coupling contributions of the transversal velocity play a crucial role in the initial setup of clustering. A simple hydrodynamic model is proposed to describe what is observed in the simulations. Finally, the nature of the inhomogeneous state is briefly discussed.

Journal Article↗

Convergence to equilibrium in a class of interacting particle systems evolving in discrete time.

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely, conservative cellular automata with piecewise linear flow diagrams, relaxation to the limit set follows the same power law at critical points. We further describe the structure of the limit sets of such systems as unions of shifts of finite type. Relaxation to the equilibrium resembles ballistic annihilation, with "defects" propagating in opposite directions annihilating upon collision.

Journal Article↗

Crashes, recoveries, and "core shifts" in a model of evolving networks.

A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self- organizes into an autocatalytic structure, which consists of an irreducible "core" surrounded by a parasitic "periphery." Crashes typically occur when the existing autocatalytic set becomes fragile and suffers a "core shift," defined graph theoretically. The nature of the recovery after a crash, in particular, the time of recovery, depends upon the organizational structure that survives the crash. The largest eigenvalue of the adjacency matrix of the graph is an important signal of network fragility or robustness.

Journal Article↗

Vertex overload breakdown in evolving networks.

We study evolving networks based on the Barabási-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case) is also studied. Implications on the growth of the Internet are discussed.

Journal Article↗

Evolving networks with distance preferences.

We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected ("make friends with the friends of your present friends"). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare them with the parameter values for random and scale-free networks. We find that for the shortest distance rule we obtain a power-law degree distribution as in scale-free networks, while the other parameters are significantly different, especially the clustering coefficient.

Journal Article↗

Software systems as complex networks: structure, function, and evolvability of software collaboration graphs.

Software systems emerge from mere keystrokes to form intricate functional networks connecting many collaborating modules, objects, classes, methods, and subroutines. Building on recent advances in the study of complex networks, I have examined software collaboration graphs contained within several open-source software systems, and have found them to reveal scale-free, small-world networks similar to those identified in other technological, sociological, and biological systems. I present several measures of these network topologies, and discuss their relationship to software engineering practices. I also present a simple model of software system evolution based on refactoring processes which captures some of the salient features of the observed systems. Some implications of object-oriented design for questions about network robustness, evolvability, degeneracy, and organization are discussed in the wake of these findings.

Journal Article↗

Stochastically evolving networks.

We discuss a class of models for the evolution of networks in which new nodes are recruited into the network at random times, and links between existing nodes that are not yet directly connected may also form at random times. The class contains both models that produce "small-world" networks and less tightly linked models. We produce both trees, appropriate in certain biological applications, and networks in which closed loops can appear, which model communication networks and networks of human sexual interactions. One of our models is closely related to random recursive trees, and some exact results known in that context can be exploited. The other models are more subtle and difficult to analyze. Our analysis includes a number of exact results for moments, correlations, and distributions of coordination number and network size. We report simulations and also discuss some mean-field approximations. If the system has evolved for a long time and the state of a random node (which thus has a random age) is observed, power-law distributions for properties of the system arise in some of these models.

Journal Article↗

Accelerated growth in outgoing links in evolving networks: deterministic versus stochastic picture.

In several real-world networks such as the Internet, World Wide Web, etc., the number of links grow in time in a nonlinear fashion. We consider growing networks in which the number of outgoing links is a nonlinear function of time but new links between older nodes are forbidden. The attachments are made using a preferential attachment scheme. In the deterministic picture, the number of outgoing links m (t) at any time t is taken as N (t)(theta) where N (t) is the number of nodes present at that time. The continuum theory predicts a power-law decay of the degree distribution: P (k) proportional to k-(1-2/ (1-theta ) ), while the degree of the node introduced at time t(i) is given by k(t(i),t)=t(theta)(i) [t/t(i) ]((1+theta)/2) when the network is evolved till time t. Numerical results show a growth in the degree distribution for small k values at any nonzero theta. In the stochastic picture, m (t) is a random variable. As long as is independent of time, the network shows a behavior similar to the Barabási-Albert (BA) model. Different results are obtained when is time dependent, e.g., when m (t) follows a distribution P (m) proportional to m(-lambda). The behavior of P (k) changes significantly as lambda is varied: for lambda>3, the network has a scale-free distribution belonging to the BA class as predicted by the mean field theory; for smaller values of lambda it shows different behavior. Characteristic features of the clustering coefficients in both models have also been discussed.

Journal Article↗

Approach to equilibrium in adiabatically evolving potentials.

For a potential function (in one dimension) which evolves from a specified initial form V(i)(x) to a different V(f)(x) asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibrium. There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form V(x,t) = V(f)(x) + (V(i) - V(f)) e(-lambda t). For a V(f)(x), which is double welled and a V(i)(x) which is simple harmonic, we show that, in particular, if the evolution is adiabatic, this results in a decrease in the Kramers time characteristic of V(f)(x). Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when V(i)(x) and V(f)(x) are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterizing the potential variation and the Kramers time. Both these features are illustrated through representative examples.

Journal Article↗