An experimental study of sliver exudation - Edelsbrunner, Herbert; Guoy, Damrong (Engineering with Computers)
We present results on a two-step improvement of mesh quality in three-dimensional Delaunay triangulations. The first step refines the triangulation by inserting sinks and eliminates tetrahedra with large circumradius over shortest edge length ratio. The second step assigns weights to the vertices to eliminate slivers. Our experimental findings provide evidence for the practical effectiveness of sliver exudation.

Fast software for box intersections - Zomorodian, Afra; Edelsbrunner, Herbert (International Journal of Computational Geometry and Applications)
We present fast implementations of a hybrid algorithm for reporting box and cube intersections. Our algorithm initially takes a divide-and-conquer approach and switches to simpler algorithms for low numbers of boxes. We use our implementations as engines to solve problems about geometric primitives. We look at two such problems in the category of quality analysis of surface triangulations.

Computing the writhing number of a polygonal knot - Agarwal, Pankaj; Edelsbrunner, Herbert; Wang, Yusu (Proceedings of the 13th annual ACM-SIAM symposium on Discrete algorithms)
The writhing number measures the global geometry of a closed space curve or knot. We show that this measure is related to the average winding number of its Gauss map. Using this relationship, we give an algorithm for computing the writhing number for a polygonal knot with n edges in time roughly proportional to n(1.6). We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.

Geometry of social relationships in the Old World wood mouse, Apodemus sylvaticus - Polechova, Jitka; Stopka, P. (Canadian Journal of Zoology)
Pilot studies in England by Stopka and Macdonald revealed that allogrooming in the Old World wood mouse, Apodemus sylvaticus, is a commodity that males can trade for reproductive benefits with females. This study, which used a combination of field study and observations in experimental enclosures, revealed that specific experimental conditions such as group-size and sex-ratio manipulations have a significant effect on the pattern of allogrooming exchanged between individuals. Furthermore, females from the Czech population were more likely to associate with each other as revealed by the clustering of activity centers of females (i.e., as opposed to almost exclusive ranges in English populations), and also by the higher intensity of allogrooming exchanged between females (i.e., virtually lacking in the previous experiment with English mice). Therefore, geographic variation and specific social conditions seem to be important driving factors for allogrooming behavior. Together with changes in overall grooming patterns, allogrooming between males and females remained invariably asymmetrical over all four experimental groups (i.e., two conditions for each sex) in that males provided more allogrooming to females than they received from them.

Non-canonical Wnt signalling and regulation of gastrulation movements - Tada, Masazumi; Concha, Miguel; Heisenberg, Carl-Philipp J (Seminars in Cell & Developmental Biology)
Members of the Wnt family have been implicated in a variety of developmental processes including axis formation, Patterning of the central nervous system and tissue morphogenesis. Recent studies have shown that a Wnt signalling pathway similar to that involved in the establishment of planar cell polarity in Drosophila regulates convergent extension movements during zebrafish and Xenopus gastrulation. This finding provides a good starting point to dissect the complex cell biology and genetic regulation of vertebrate gastrulation movements.

Establishment of the telencephalon during gastrulation by local antagonism of Wnt signaling - Houart, Corinne; Caneparo, Luca; Heisenberg, Carl-Philipp J; Barth, K Anukampa; Take Uchi, Masaya; Wilson, Stephen (Neuron)
Cells at the anterior boundary of the neural plate (ANB) can induce telencephalic gene expression when transplanted to more posterior regions. Here, we identify a secreted Frizzled-related Wnt antagonist, Tic, that is expressed in ANB cells and can cell nonautonomously promote telencephalic gene expression in a concentration-dependent manner. Moreover, abrogation of Tlc function compromises telencephalic development. We also identify Wnt8b as a locally acting modulator of regional fate in the anterior neural plate and a likely target for antagonism by Tic. Finally, we show that tlc expression is regulated by signals that establish early antero-posterior and dorso-ventral ectodermal pattern. From these studies, we propose that local antagonism of Wnt activity within the anterior ectoderm is required to establish the telencephalon.

Zebrafish gastrulation movements: bridging cell and developmental biology - Heisenberg, Carl-Philipp J; Tada, Masazumi (Seminars in Cell & Developmental Biology)
During vertebrate gastrulation, large cellular rearrangements lead to the formation of the three germ layers, ectoderm, mesoderm and endoderm. Zebrafish offer many genetic and experimental advantages for studying vertebrate gastrulation movements. For instance, several mutants, including silberblick, knypek and trilobite, exhibit defects in morphogenesis during gastrulation. The identification of the genes mutated in these lines together with the analysis of the mutant phenotypes has provided new insights into the molecular and cellular mechanisms that underlie vertebrate gastrulation movements.

Wnt signalling: A moving picture emerges from van gogh - Heisenberg, Carl-Philipp J; Tada, Masazumi (Current Biology)
Recent studies on vertebrate homologues of the van gogh/strabismus (vang/stbm) gene, a key player in planar cell polarity signalling in Drosophila, show that vang/stbm is involved in patterning and morphogenesis during vertebrate gastrulation where it modulates two distinct Wnt signals.

Wnt signalling: Refocusing on Strabismus - Heisenberg, Carl-Philipp J (Current Biology)
Vertebrate homologues of the Strabismus/van Gogh (stbm/vang) gene have been implicated in patterning and morphogenesis during gastrulation. Recent work shows that stbm/vang is mutated in zebrafish trilobite mutants and that stbm/vang is required for morphogenesis but not patterning during zebrafish gastrulation.

Planar cell polarization requires Widerborst, a B′ regulatory subunit of protein phosphatase 2A - Hannus, Michael; Feiguin, Fabian; Heisenberg, Carl-Philipp J; Eaton, Suzanne (Development)
We have identified widerborst (wdb), a B' regulatory subunit of PP2A, as a conserved component of planar cell polarization mechanisms in both Drosophila and in zebrafish. In Drosophila, wdb acts at two steps during planar polarization of wing epithelial cells. It is required to organize tissue polarity proteins into proximal and distal cortical domains, thus determining wing hair orientation. It is also needed to generate the polarized membrane outgrowth that becomes the wing hair. Widerborst activates the catalytic subunit of PP2A and localizes to the distal side of a planar microtubule web that lies at the level of apical cell junctions. This suggests that polarized PP2A activation along the planar microtubule web is important for planar polarization. In zebrafish, two wdb homologs are required for convergent extension during gastrulation, supporting the conjecture that Drosophila planar cell polarization and vertebrate gastrulation movements are regulated by similar mechanisms.

The effects of multilocus balancing selection on neutral variability - Navarro, Arcadio; Barton, Nicholas H (Genetics)
We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.

Associations between cytoplasmic and nuclear loci in hybridizing populations - Orive, Maria; Barton, Nicholas H (Genetics)
We extend current multilocus models to describe the effects of migration, recombination, selection, and nonrandom mating on sets of genes in diploids with varied modes of inheritance, allowing us to consider the patterns of nuclear and cytonuclear associations (disequilibria) under various models of migration. We show the relationship between the multilocus notation recently presented by Kirkpatrick, Johnson, and Barton (developed from previous work by Barton and Turelli) and the cytonuclear parameterization of Asmussen, Arnold, and Avise and extend this notation to describe associations between cytoplasmic elements and multiple nuclear genes. Under models with sexual symmetry, both nuclear-nuclear and cytonuclear disequilibria are equivalent. They differ, however, in cases involving some type of sexual asymmetry, which is then reflected in the asymmetric inheritance of cytoplasmic markers. An example given is the case of different migration rates in males and females; simulations using 2, 3, 4, or 5 unlinked autosomal markers with a maternally inherited cytoplasmic marker illustrate how nuclear-nuclear and cytonuclear associations can be used to separately estimate female and male migration rates. The general framework developed here allows us to investigate conditions where associations between loci with different modes of inheritance are not equivalent and to use this nonequivalence to test for deviations from simple models of admixture.

The effect of deleterious alleles on adaptation in asexual populations - Johnson, Toby; Barton, Nicholas H (Genetics)
We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.

Understanding quantitative genetic variation - Barton, Nicholas H; Keightley, Peter (Nature Reviews Genetics)
Until recently, it was impracticable to identify the genes that are responsible for variation in continuous traits, or to directly observe the effects of their different alleles. Now, the abundance of genetic markers has made it possible to identify quantitative trait loci (QTL) — the regions of a chromosome or, ideally, individual sequence variants that are responsible for trait variation. What kind of QTL do we expect to find and what can our observations of QTL tell us about how organisms evolve? The key to understanding the evolutionary significance of QTL is to understand the nature of inherited variation, not in the immediate mechanistic sense of how genes influence phenotype, but, rather, to know what evolutionary forces maintain genetic variability.

Extending the coalescent to multilocus systems: the case of balancing selection - Barton, Nicholas H; Navarro, Arcadio (Genetical Research)
Natural populations are structured spatially into local populations and genetically into diverse ‘genetic backgrounds’ defined by different combinations of selected alleles. If selection maintains genetic backgrounds at constant frequency then neutral diversity is enhanced. By contrast, if background frequencies fluctuate then diversity is reduced. Provided that the population size of each background is large enough, these effects can be described by the structured coalescent process. Almost all the extant results based on the coalescent deal with a single selected locus. Yet we know that very large numbers of genes are under selection and that any substantial effects are likely to be due to the cumulative effects of many loci. Here, we set up a general framework for the extension of the coalescent to multilocus scenarios and we use it to study the simplest model, where strong balancing selection acting on a set of n loci maintains 2n backgrounds at constant frequencies and at linkage equilibrium. Analytical results show that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. However, simulation results reveal that the structured coalescent approach breaks down when the number of backgrounds approaches the population size, because of stochastic fluctuations in background frequencies. A new method is needed to extend the structured coalescent to cases with large numbers of backgrounds.

Neutral evolution in spatially continuous populations - Barton, Nicholas H; Depaulis, Frantz; Etheridge, Alison (Theoretical Population Biology)
We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, σe; the effective population density, ρe; and a local scale, κ, at which local interactions become significant. The results are illustrated by simulations.

Inferring the root of a phylogenetic tree - Huelsenbeck, John; Bollback, Jonathan P; Levine, Amy (Systematic Biology)
Phylogenetic trees can be rooted by a number of criteria. Here, we introduce a Bayesian method for inferring the root of a phylogenetic tree by using one of several criteria: the outgroup, molecular clock, and nonreversible model of DNA substitution. We perform simulation analyses to examine the relative ability of these three criteria to correctly identify the root of the tree. The outgroup and molecular clock criteria were best able to identify the root of the tree, whereas the nonreversible model was able to identify the root only when the substitution process was highly nonreversible. We also examined the performance of the criteria for a tree of four species for which the topology and root position are well supported. Results of the analyses of these data are consistent with the simulation results.

Bayesian model adequacy and choice in phylogenetics - Bollback, Jonathan P (Molecular Biology and Evolution)
Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.

Axioms for real-time logics - Raskin, Jean; Schobbens, Pierre; Henzinger, Thomas A (Theoretical Computer Science)
This paper presents a complete axiomatization of two decidable propositional real-time linear temporal logics: Event Clock Logic (EventClockTL) and Metric Interval Temporal Logic with past (MetricIntervalTL). The completeness proof consists of an effective proof building procedure for EventClockTL. From this result we obtain a complete axiomatization of MetricIntervalTL by providing axioms translating MetricIntervalTL formulae into EventClockTL formulae, the two logics being equally expressive. Our proof is structured to yield axiomatizations also for interesting fragments of these logics, such as the linear temporal logic of the real numbers (TLR).

Convertibility verification and converter synthesis: Two faces of the same coin - Passerone, Roberto; De Alfaro, Luca; Henzinger, Thomas A; Sangiovanni Vincentelli, Alberto (Proceedings of the 11th IEEE/ACM international conference on Computer-aided design)
An essential problem in component-based design is how to compose components designed in isolation. Several approaches have been proposed for specifying component interfaces that capture behavioral aspects such as interaction protocols, and for verifying interface compatibility. Likewise, several approaches have been developed for synthesizing converters between incompatible protocols. In this paper, we introduce the notion of adaptability as the property that two interfaces have when they can be made compatible by communicating through a converter that meets specified requirements. We show that verifying adaptability and synthesizing an appropriate converter are two faces of the same coin: adaptability can be formalized and solved using a game-theoretic framework, and then the converter can be synthesized as a strategy that always wins the game. Finally we show that this framework can be related to the rectification problem in trace theory.