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PubMed2004

Punctuated equilibrium in software evolution.

An approach based on the paradigm of self-organized criticality is proposed for experimental investigation and theoretical modeling of software evolution. The dynamics of modifications is studied for three free, open source programs MOZILLA, FREE-BSD, and EMACS using the data from version control systems. Scaling laws typical for self-organized criticality found. A model of software evolution presenting the natural selection principle is proposed. Results of numerical and analytical investigation of the model are presented. They are in good agreement with data collected for real-world software.

Journal Article↗

PubMed1997

Coevolutionary chase on exploiter-victim systems with polygenic characters.

I study the dynamics of a simple quantitative genetic model describing coevolution of two antagonistic species of the victim-exploiter type. In this model, individuals are different with respect to an additive polygenic character that is under direct stabilizing selection and which also determines the strength of within and between species interactions. The model assumes that between species interactions are most intense when the victim's and exploiter's phenotypes match. I show that a cyclic coevolutionary chase is possible under a broad range of conditions. In most cases, the system cycles if the "victim" has a stronger incentive to win and/or a larger genetic variance, and is under stronger stabilizing selection than the "exploiter". The results presented here provide counter-examples to recent studies that (1) question the applicability of "Red Queen" and "arms race" metaphors for continuously varying traits; (2) argue for the existence of crucial differences between major and minor loci dynamics; and (3) attribute a stabilizing role to coevolution.

Animals↗

PubMed2003

The evolution of genomic base composition in bacteria.

Guanine plus cytosine (GC) content ranges broadly among bacterial genomes. In this study, we explore the use of a Brownian-motion model for the evolution of GC content over time. This model assumes that GC content varies over time in a continuous and homogeneous manner. Using this model and a maximum-likelihood approach, we analyzed the evolution of GC content across several bacterial phylogenies. Using three independent tests, we found that the observed divergence in GC content was consistent with a homogeneous Brownian-motion model. For example, similar rates of GC content evolution were inferred in several different bacterial subclades, indicating that there is relatively little rate heterogeneity in GC content evolution over broad evolutionary time scales. We thus argue that the homogeneous Brownian-motion model provides a good working model for GC content evolution. We then use this model to determine the overall rate of GC content evolution among eubacteria. We also determine the time frame over which GC content remains similar in related taxa, using a flexible definition for "similarity" in GC content so that, depending on the context, more or less stringent criteria may be applied. Our results have implications for models of sequence evolution, including those used for phylogenetic reconstruction and for inferring unusual changes in GC content.

Bacteria↗

PubMed1990

Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes.

An unusual pattern in a nucleic acid or protein sequence or a region of strong similarity shared by two or more sequences may have biological significance. It is therefore desirable to know whether such a pattern can have arisen simply by chance. To identify interesting sequence patterns, appropriate scoring values can be assigned to the individual residues of a single sequence or to sets of residues when several sequences are compared. For single sequences, such scores can reflect biophysical properties such as charge, volume, hydrophobicity, or secondary structure potential; for multiple sequences, they can reflect nucleotide or amino acid similarity measured in a wide variety of ways. Using an appropriate random model, we present a theory that provides precise numerical formulas for assessing the statistical significance of any region with high aggregate score. A second class of results describes the composition of high-scoring segments. In certain contexts, these permit the choice of scoring systems which are "optimal" for distinguishing biologically relevant patterns. Examples are given of applications of the theory to a variety of protein sequences, highlighting segments with unusual biological features. These include distinctive charge regions in transcription factors and protooncogene products, pronounced hydrophobic segments in various receptor and transport proteins, and statistically significant subalignments involving the recently characterized cystic fibrosis gene.

Amino Acid Sequence↗

PubMed1998

Self-adaptation in evolving systems.

A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in certain model fitness landscapes. The resultant genotype-phenotype mapping is degenerate in fitness space, there being no direct selective advantage for one probability versus another. Thus there is a "symmetry" between various genotypes that all correspond to the same phenotype. We show that the action of mutation and crossover lifts this degeneracy, that is, the genetic operators induce a breaking of the genotype-phenotype symmetry, thus leading to a preference for those genotypes that propagate most successfully into future generations. We demonstrate that this induced symmetry breaking allows the system to self-adapt in a time-dependent environment.

Adaptation, Physiological↗

PubMed1999

The alpha-subunit of protein prenyltransferases is a member of the tetratricopeptide repeat family.

Lipidation catalyzed by protein prenyltransferases is essential for the biological function of a number of eukaryotic proteins, many of which are involved in signal transduction and vesicular traffic regulation. Sequence similarity searches reveal that the alpha-subunit of protein prenyltransferases (PTalpha) is a member of the tetratricopeptide repeat (TPR) superfamily. This finding makes the three-dimensional structure of the rat protein farnesyltransferase the first structural model of a TPR protein interacting with its protein partner. Structural comparison of the two TPR domains in protein farnesyltransferase and protein phosphatase 5 indicates that variation in TPR consensus residues may affect protein binding specificity through altering the overall shape of the TPR superhelix. A general approach to evolutionary analysis of proteins with repetitive sequence motifs has been developed and applied to the protein prenyltransferases and other TPR proteins. The results suggest that all members in PTalpha family originated from a common multirepeat ancestor, while the common ancestor of PTalpha and other members of TPR superfamily is likely to be a single repeat protein.

Alkyl and Aryl Transferases↗

PubMed1988

Primary and secondary structure of the 18S ribosomal RNA of the bird spider Eurypelma californica and evolutionary relationships among eukaryotic phyla.

The primary structure of the 18S rRNA of the bird spider Eurypelma californica has been determined in the framework of a study of metazoan phylogeny on the basis of ribosomal RNA structure. A secondary-structure model was derived by comparison of the sequence with that of 43 other eukaryotic small-ribosomal-subunit RNA sequences presently available. This comparison allows a rather detailed secondary-structure pattern to be postulated for a eukaryote-specific area of highly variable sequence and length for which no consensus model has hitherto been attained. A dendrogram, reflecting evolutionary relationships among the 40 eukaryotic species of known 18S rRNA structure, was constructed by a matrix method selecting the best-fitting tree on the basis of a least-squares criterion. The tree shows an early divergence of a microsporidium, an euglenoid, kinetoplastids and a slime mold. Among the remaining species, two main clusters are distinguishable, one comprising the Ciliata, the other comprising Metazoa, green plants, fungi and several protists. Among the Metazoa, the three phyla presently investigated, viz. Chordata, Arthropoda and Nemathelminthes, are distinguishable as three separate lines of descent.

Animals↗

PubMed2002

Evolutionarily stable leaf area production in plant populations.

Using an analytical model, it was shown that for a given amount of nitrogen in the canopy of a stand (N(T)), there exists an evolutionarily stable leaf area index (ES-LAI), and therefore an evolutionarily stable average leaf nitrogen content (n(ES)(av);n(ES)(av) =N(T)/ES-LAI), at which no individual plant in the stand can increase its photosynthesis by changing its leaf area. It was also shown that this ES-LAI is always greater than the optimal LAI that maximizes photosynthesis per unit N(T) of the stand. This illustrates that the canopy structure that maximizes photosynthesis of a population is not the same as the canopy structure that maximizes photosynthesis of individuals within a population. It was further derived that the ES-LAI at given N(T) increases with the ratio between the light-saturated photosynthesis and the N content per unit leaf area (leaf-PPNUE) and that it decreases with the canopy extinction coefficient for light (K(L)), the light availability and the apparent quantum yield (phi). These hypotheses were tested by comparing calculated ES-LAI and n(ES)(av) values to actual LAIs and leaf N contents measured for stands of a large variety of herbaceous plants. There was a close correspondence between the calculated and measured values. As predicted by the model, plants with high leaf-PPNUEs produced more leaf area per unit nitrogen than those with low leaf-PPNUEs while plants with horizontal leaves, forming stands with higher K(L) values, produced less leaf area than those with more vertically inclined leaves. These results suggest that maximization of individual plant photosynthesis per unit of nitrogen plays an important role in determining leaf area production of plants and the resulting canopy structure of stands of vegetation. They further suggest this optimization to be a mechanism by which leaf traits such as leaf-PPNUE and leaf inclination angle are causally related to structural characteristics of the population, i.e. the leaf area index of the stand.

Biological Evolution↗

PubMed1997

Evolutionary stagnation due to pattern-pattern interactions in a coevolutionary predator-prey model.

We consider a spatially structured model of a coevolutionary predator-prey system with interactions in a one-dimensional phenotype space. We show that in phenotype space predators and prey organize themselves into distinct clusters of phenotypes called quasi-species. The prey quasi-species also cluster in patches in real space. As the prey quasi-species evolve away from the predator quasi-species (in phenotype space) the prey patch size reduces and the single predator quasi-species is inhibited from evolving toward either of the two prey species. We show that it is the interaction between the phenotype space patterns (quasi-species) and the real space patterns (patches) that inhibit the predators from evolving.

Biological Evolution↗

PubMed2006

Handling time promotes the coevolution of aggregation in predator-prey systems.

Predators often have type II functional responses and live in environments where their life history traits as well as those of their prey vary from patch to patch. To understand how spatial heterogeneity and predator handling times influence the coevolution of patch preferences and ecological stability, we perform an ecological and evolutionary analysis of a Nicholson-Bailey type model. We prove that coevolutionarily stable prey and searching predators prefer patches that in isolation support higher prey and searching predator densities, respectively. Using this fact, we determine how environmental variation and predator handling times influence the spatial patterns of patch preferences, population abundances and per-capita predation rates. In particular, long predator handling times are shown to result in the coevolution of predator and prey aggregation. An analytic expression characterizing ecological stability of the coevolved populations is derived. This expression implies that contrary to traditional theoretical expectations, predator handling time can stabilize predator-prey interactions through its coevolutionary influence on patch preferences. These results are shown to have important implications for classical biological control.

Animals↗

PubMed2005

Networks in phylogenetic analysis: new tools for population biology.

Phylogenetic analysis has changed greatly in the past decade, including the more widespread appreciation of the idea that evolutionary histories are not always tree-like, and may, thus, be best represented as reticulated networks rather than as strictly dichotomous trees. Reconstructing such histories in the absence of a bifurcating speciation process is even more difficult than the usual procedure, and a range of alternative strategies have been developed. There seem to be two basic uses for a network model of evolution: the display of real but unobservable evolutionary events (i.e. a hypothesis of the true phylogenetic history), and the display of character conflict within the data itself (i.e. a summary of the data). These two general approaches are briefly reviewed here, and the strengths and weaknesses of the different implementations are compared and contrasted. Each network methodology seems to have limitations in terms of how it responds to increasing complexity (e.g. conflict) in the data, and therefore each is likely to be more appropriate for one of the two uses than for the other. Several examples using parasitological data sets illustrate the uses of networks within the context of population biology.

Algorithms↗

PubMed2001

Genetics of human complement component C4 and evolution the central MHC.

The two classes of human complement component C4 proteins C4A and C4B manifest differential chemical reactivities and binding affinities towards target surfaces and complement receptor CR1. There are multiple, polymorphic allotypes of C4A and C4B proteins. A complex multiplication pattern of C4A and C4B genes with variations in gene size, gene dosage and flanking genes exists in the population. This is probably driven by the selection pressure to respond to a great variety of parasites efficiently and effectively, which the bony fish achieved through the multiplication and diversification of the related complement C3 proteins. Complement C4, C3 and C5 belong to the alpha2 macroglobulin protein family but acquired specific features that include an anaphylatoxin domain, a netrin (NTR) domain, and stretches of basic residues for proteolytic processings to form multiple chain structures. Complement C3 and C4 are important in the innate immune response as they opsonize parasites for phagocytosis. The emergence of complement C3 predates proteins involved in the adaptive immune response as C3 is present in deuterostome invertebrates such as echinoderms. The human C4 genes are located in the central MHC at chromosome 6p21.3. C3 and C5 are located at chromosome 19 and 9, respectively, with representatives of the other groups of genes paralogous to the MHC at 19p13.1-p13.3, 1q21-25, and 9q33-34. The central MHC also contains genes for complement components C2 and Bf. These genes appear to have similar evolutionary histories to C3/C4/C5 and are used here to illustrate stepwise processes resulting in co-location of diverse domains, chromosomal duplication, local segmental duplication and divergence of sequence and function. This model of evolution is useful in the investigation of innate and acquired immunity and in seeking explanations for diseases associated with MHC ancestral haplotypes.

Amino Acid Sequence↗

PubMed2000

[The first trees. The Archaeopteris model].

The earliest self-supporting organisms exceeding 2 m in height evolved about 370 million years ago, approximately 100 million years after the rise of the first land plants. Evidence for the tree habit is usually indirect and assessed from the diameter of the available stem fragments. Four systematic groups of Devonian plants evolved the tree habit independantly: the Lycopsida, Cladoxylopsida, and progymnosperms in the Middle Devonian, the Equisetopsida in the Late Devonian. All share a free-sporing life cycle which limits their habitats to wet areas. Their branching pattern involves the strict division of their apices, whether equally or unequally. The progymnosperm genus Archaeopteris was widespread worldwide and evolved the highest trees of the Devonian (maximum height estimated at 40 m). Besides it ecological significance as the dominant component of the earliest forests, Archaeopteris currently represents the closest known relative to the seed plants with which it shares two derived characters, the heterosporous life cycle, and the possession of leaves. Another distinctive feature of Archaeopteris trees is represented by the double function of their wood for both support and conduction. New analyses involving vascular trace analysis in anatomically preserved specimens have demonstrated that Archaeopteris is not the simple tree reconstructed by Beck (1962). In this fate model, Archaeopteris consisted of an erect trunk bearing short-lived, flattened, leaf-like branch systems forming a terminal crown. New evidence indicates that laterally to these appendages of apical origin, a new type of branches, of adventitious origin, evolved which development compares to that of the axillary branches of the seed plants. These branches which were large and long-lived represent major architectural components of the tree. Evidence for vascular structures comparable to those produced on stem cuttings in modern plants suggest that Archaeopteris may have evolved vegetative strategies for propagation. The set of "modern" characters of Archaeopteris may explain its success until the Devonian/Carboniferous boundary when its extinction is correlated to the radiation of the earliest seed plants.

Biological Evolution↗

PubMed2005

Protein signatures distinctive of alpha proteobacteria and its subgroups and a model for alpha-proteobacterial evolution.

Alpha (alpha) proteobacteria comprise a large and metabolically diverse group. No biochemical or molecular feature is presently known that can distinguish these bacteria from other groups. The evolutionary relationships among this group, which includes numerous pathogens and agriculturally important microbes, are also not understood. Shared conserved inserts and deletions (i.e., indels or signatures) in molecular sequences provide a powerful means for identification of different groups in clear terms, and for evolutionary studies (see www.bacterialphylogeny.com). This review describes, for the first time, a large number of conserved indels in broadly distributed proteins that are distinctive and unifying characteristics of either all alpha-proteobacteria, or many of its constituent subgroups (i.e., orders, families, etc.). These signatures were identified by systematic analyses of proteins found in the Rickettsia prowazekii (RP) genome. Conserved indels that are unique to alpha-proteobacteria are present in the following proteins: Cytochrome c oxidase assembly protein Ctag, PurC, DnaB, ATP synthase alpha-subunit, exonuclease VII, prolipoprotein phosphatidylglycerol transferase, RP-400, FtsK, puruvate phosphate dikinase, cytochrome b, MutY, and homoserine dehydrogenase. The signatures in succinyl-CoA synthetase, cytochrome oxidase I, alanyl-tRNA synthetase, and MutS proteins are found in all alpha-proteobacteria, except the Rickettsiales, indicating that this group has diverged prior to the introduction of these signatures. A number of proteins contain conserved indels that are specific for Rickettsiales (XerD integrase and leucine aminopeptidase), Rickettsiaceae (Mfd, ribosomal protein L19, FtsZ, Sigma 70 and exonuclease VII), or Anaplasmataceae (Tgt and RP-314), and they distinguish these groups from all others. Signatures in DnaA, RP-057, and DNA ligase A are commonly shared by various Rhizobiales, Rhodobacterales, and Caulobacter, suggesting that these groups shared a common ancestor exclusive of other alpha-proteobacteria. A specific relationship between Rhodobacterales and Caulobacter is indicated by a large insert in the Asn-Gln amidotransferase. The Rhizobiales group of species are distinguished from others by a large insert in the Trp-tRNA synthetase. Signature sequences in a number of other proteins (viz. oxoglutarate dehydogenase, succinyl-CoA synthase, LytB, DNA gyrase A, LepA, and Ser-tRNA synthetase) serve to distinguish the Rhizobiaceae, Brucellaceae, and Phyllobacteriaceae families from Bradyrhizobiaceae and Methylobacteriaceae. Based on the distribution patterns of these signatures, it is now possible to logically deduce a model for the branching order among alpha-proteobacteria, which is as follows: Rickettsiales --> Rhodospirillales-Sphingomonadales --> Rhodobacterales-Caulobacterales --> Rhizobiales (Rhizobiaceaea-Brucellaceae-Phyllobacteriaceae, and Bradyrhizobiaceae). The deduced branching order is also consistent with the topologies in the 16 rRNA and other phylogenetic trees. Signature sequences in a number of other proteins provide evidence that alpha-proteobacteria is a late branching taxa within Bacteria, which branched after the delta,epsilon-subdivisions but prior to the beta,gamma-proteobacteria. The shared presence of many of these signatures in the mitochondrial (eukaryotic) homologs also provides evidence of the alpha-proteobacterial ancestry of mitochondria.

Alphaproteobacteria↗

PubMed2002

On the size distribution of live genera.

This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state of a homogeneous birth-and-death process after an exponentially distributed time. An ordinary differential equation for the generating function of the distribution is derived and solved and a recurrence relation for computing the probabilities in the distribution presented. Some properties of the distribution, including asymptotic behaviour, are examined and the distribution of the time since establishment of a genus of a given size derived. Fitting the distribution to empirical taxon size distributions by maximum likelihood is discussed and two examples are presented.

Animals↗

PubMed2002

Common origin and evolution of glycosyltransferases using Dol-P-monosaccharides as donor substrate.

On the basis of the analysis of 64 glycosyltransferases from 14 species we propose that several successive duplications of a common ancestral gene, followed by divergent evolution, have generated the mannosyltransferases and the glucosyltransferases involved in asparagine-linked glycosylation (ALG) and phosphatidyl-inositol glycan anchor (PIG or GPI), which use lipid-related donor and acceptor substrates. Long and short conserved peptide motifs were found in all enzymes. Conserved and identical amino acid positions were found for the alpha 2/6- and the alpha 3/4-mannosyltransferases and for the alpha 2/3-glucosyltransferases, suggesting unique ancestors for these three superfamilies. The three members of the alpha 2-mannosyltransferase family (ALG9, PIG-B, and SMP3) and the two members of the alpha 3-glucosyltransferase family (ALG6 and ALG8) shared 11 and 30 identical amino acid positions, respectively, suggesting that these enzymes have also originated by duplication and divergent evolution. This model predicts a common genetic origin for ALG and PIG enzymes using dolichyl-phospho-monosaccharide (Dol-P-monosaccharide) donors, which might be related to similar spatial orientation of the hydroxyl acceptors. On the basis of the multiple sequence analysis and the prediction of transmembrane topology we propose that the endoplasmic reticulum glycosyltransferases using Dol-P-monosaccharides as donor substrate have a multispan transmembrane topology with a first large luminal conserved loop containing the long motif and a small cytosolic conserved loop containing the short motif, different from the classical type II glycosyltransferases, which are anchored in the Golgi by a single transmembrane domain.

Amino Acid Motifs↗

PubMed1988

Influence of the hypercycle on the error threshold: a stochastic approach.

The role of fluctuations on the error threshold of the hypercycle has been studied by a stochastic approach on a very simplified model. For this model, the master equation was derived and its unique steady state calculated. This state implies the extinction of the system. But the actual time necessary to reach the steady state may be astronomically long whereas for times of experimental interest the system could be near some quasi-stationary states. In order to explore this possibility a Gillespie simulation of the stochastic process has been carried out. These quasi-stationary states correspond to the deterministic steady states of the system. The error threshold shifts towards higher values of the quality factor Q. Moreover, information about the fluctuations around the quasi-stationary states is obtained. The results are discussed in relation to the deterministic states.

Animals↗

PubMed2006

Occupancy modeling of coverage distribution for whole genome shotgun DNA sequencing.

Expected-value models have long provided a rudimentary theoretical foundation for random DNA sequencing. Here, we are interested in improving characterization of genome coverage in terms of its underlying probability distributions. We find that the mathematical notion of occupancy serves as a good model for evolution of the coverage distribution function and reveals new insights related to sequence redundancy. Established concepts, such as "full shotgun depth," have been assumed invariant, but actually depend on project size and decrease over time. For most microbial projects, the full shotgun milestone should be revised downward by about 30%. Accordingly, many already-completed genomes appear to have been over-sequenced. Results also suggest that read lengths for emerging high-throughput sequencing methods must be increased substantially before they can be considered as possible successors to the standard Sanger method. In particular, gains in throughput and sequence depth cannot be made to compensate for diminished read length. Limits are well approximated by a simple logarithmic equation, which should be useful in estimating maximum coverage-based redundancy for future projects.

Algorithms↗