Detecting the node-density artifact in phylogeny reconstruction

The node-density effect is an artifact of phylogeny reconstruction that can cause branch lengths to be underestimated in areas of the tree with fewer taxa. Webster, Payne, and Pagel (2003, Science 301:478) introduced a statistical procedure (the "delta" test) to detect this artifact, and here we report the results of computer simulations that examine the test's performance. In a sample of 50,000 random data sets, we find that the delta test detects the artifact in 94.4% of cases in which it is present. When the artifact is not present (n = 10,000 simulated data sets) the test showed a type I error rate of approximately 1.69%, incorrectly reporting the artifact in 169 data sets. Three measures of tree shape or "balance" failed to predict the size of the node-density effect. This may reflect the relative homogeneity of our randomly generated topologies, but emphasizes that nearly any topology can suffer from the artifact, the effect not being confined only to highly unevenly sampled or otherwise imbalanced trees. The ability to screen phylogenies for the node-density artifact is important for phylogenetic inference and for researchers using phylogenetic trees to infer evolutionary processes, including their use in molecular clock dating. [Delta test; molecular clock; molecular evolution; node-density effect; phylogenetic reconstruction; speciation; simulation.]

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Phylogenomics of eukaryotes: Impact of missing data on large alignments

Resolving the relationships between Metazoa and other eukaryotic groups as well as between metazoan phyla is central to the understanding of the origin and evolution of animals. The current view is based on limited data sets, either a single gene with many species (e.g., ribosomal RNA) or many genes but with only a few species. Because a reliable phylogenetic inference simultaneously requires numerous genes and numerous species, we assembled a very large data set containing 129 orthologous proteins (similar to30,000 aligned amino acid positions) for 36 eukaryotic species. Included in the alignments are data from the choanoflagellate Monosiga ovata, obtained through the sequencing of about 1,000 cDNAs. We provide conclusive support for choanoflagellates as the closest relative of animals and for fungi as the second closest. The monophyly of Plantae and chromalveolates was recovered but without strong statistical support. Within animals, in contrast to the monophyly of Coelomata observed in several recent large-scale analyses, we recovered a paraphyletic Coelamata, with nematodes and platyhelminths nested within. To include a diverse sample of organisms, data from EST projects were used for several species, resulting in a large amount of missing data in our alignment (about 25%). By using different approaches, we verify that the inferred phylogeny is not sensitive to these missing data. Therefore, this large data set provides a reliable phylogenetic framework for studying eukaryotic and animal evolution and will be easily extendable when large amounts of sequence information become available from a broader taxonomic range.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Phylogenetic relationships within the moss family Bryaceae based on chloroplast DNA evidence

The Bryaceae are a large cosmopolitan family of mosses containing genera of considerable taxonomic difficulty. Phylogenetic relationships within the family were inferred using data from chloroplast DNA sequences (rps4 and trnL-trnF region). Parsimony and maximum likelihood optimality criteria, and Bayesian phylogenetic inference procedures were employed to reconstruct relationships. The genera Bryum and Brachymenium are not monophyletic groups. A clade comprising Plagiobryum, Acidodontium, Mielichhoferia macrocarpa, Bryum sects. Bryum, Apalodictyon, Limbata, Leucodontium, Caespiticia, Capillaria (in part: sect. Capillaria), and Brachymenium sect. Dicranobryum, is well supported in all analyses and represents a major lineage within the family. Section Dicranobryum of Brachymenium is more closely related to section Bryum than to the other sections of Brachymenium, as are Mielichhoferia macrocarpa and M. himalayana. Species of Acidodontium form a clade with Anomobryum julaceum. The grouping of species with a rosulate gametophytic growth form suggests the presence of a 'rosulate' clade similar in circumscription to the genus Rosulabryum. Mielichhoferia macrocarpa and M. himalayana are transferred to Bryum as B. porsildii and B. caucasicum, respectively.

Population subdivision and molecular sequence variation: Theory and analysis of Drosophila ananassae data

Population subdivision complicates analysis of molecular variation. Even if neutrality is assumed, three evolutionary forces need to be considered: migration, mutation, and drift. Simplification can be achieved by assuming that the process of migration among and drift within subpopulations is occurring fast compared to Mutation and drift in the entire population. This allows a two-step approach in the analysis: (i) analysis of population subdivision and (ii) analysis of molecular variation in the migrant pool. We model population subdivision using an infinite island model, where we allow the migration/drift parameter Theta to vary among populations. Thus, central and peripheral populations can be differentiated. For inference of Theta, we use a coalescence approach, implemented via a Markov chain Monte Carlo (MCMC) integration method that allows estimation of allele frequencies in the migrant pool. The second step of this approach (analysis of molecular variation in the migrant pool) uses the estimated allele frequencies in the migrant pool for the study of molecular variation. We apply this method to a Drosophila ananassae sequence data set. We find little indication of isolation by distance, but large differences in the migration parameter among populations. The population as a whole seems to be expanding. A population from Bogor (Java, Indonesia) shows the highest variation and seems closest to the species center.

Assessing reading at Key Stage 2: SATs as measures of children's inferential abilities

This article describes two studies. The first study was designed to investigate the ways in which the statutory assessments of reading for 11-year-old children in England assess inferential abilities. The second study was designed to investigate the levels of performance achieved in these tests in 2001 and 2002 by 11-year-old children attending state-funded local authority schools in one London borough. In the first study, content and questions used in the reading papers for the Standard Assessment Tasks (SATs) in the years 2001 and 2002 were analysed to see what types of inference were being assessed. This analysis suggested that the complexity involved in inference making and the variety of inference types that are made during the reading process are not adequately sampled in the SATs. Similar inadequacies are evident in the ways in which the programmes of study for literacy recommended by central government deal with inference. In the second study, scripts of completed SATs reading papers for 2001 and 2002 were analysed to investigate the levels of inferential ability evident in scripts of children achieving different SATs levels. The analysis in this article suggests that children who only just achieve the 'target' Level 4 do so with minimal use of inference skills. They are particularly weak in making inferences that require the application of background knowledge. Thus, many children who achieve the reading level (Level 4) expected of 11-year-olds are entering secondary education with insecure inference-making skills that have not been recognised.

Deciding the price of fame

Previous studies of ignorance-driven decision-making have either analyzed when ignorance should prove advantageous on theoretical grounds, or else they have examined whether human behavior is consistent with an ignorance driven inference strategy (e.g., the recognition heuristic). The current study merges these research goals by examining whether – under conditions where ignorance driven inference might be expected – the type of advantages theoretical analyses predict are evident in human performance data. A single experiment shows that, when asked to make relative wealth judgments, participants reliably use recognition as a basis for their judgments. Their wealth judgments under these conditions are reliably more accurate when some of the target names are unknown than when participants recognize all the names (the “less-is-more effect”). these data are robust against a number of variations on the size of the pool from which participants have to choose and the nature of the wealth judgment.

A fuzzy multi-criteria decision approach for enhanced auto-tracking of seismic events

The main activity carried out by the geophysicist when interpreting seismic data, in terms of both importance and time spent is tracking (or picking) seismic events. in practice, this activity turns out to be rather challenging, particularly when the targeted event is interrupted by discontinuities such as geological faults or exhibits lateral changes in seismic character. In recent years, several automated schemes, known as auto-trackers, have been developed to assist the interpreter in this tedious and time-consuming task. The automatic tracking tool available in modem interpretation software packages often employs artificial neural networks (ANN's) to identify seismic picks belonging to target events through a pattern recognition process. The ability of ANNs to track horizons across discontinuities largely depends on how reliably data patterns characterise these horizons. While seismic attributes are commonly used to characterise amplitude peaks forming a seismic horizon, some researchers in the field claim that inherent seismic information is lost in the attribute extraction process and advocate instead the use of raw data (amplitude samples). This paper investigates the performance of ANNs using either characterisation methods, and demonstrates how the complementarity of both seismic attributes and raw data can be exploited in conjunction with other geological information in a fuzzy inference system (FIS) to achieve an enhanced auto-tracking performance.

Efficient fuzzy control of a rotary inverted pendulum based on LQR mapping

This paper develops fuzzy methods for control of the rotary inverted pendulum, an underactuated mechanical system. Two control laws are presented, one for swing up and another for the stabilization. The pendulum is swung up from the vertical down stable position to the upward unstable position in a controlled trajectory. The rules for the swing up are heuristically written such that each swing results in greater energy build up. The stabilization is achieved by mapping a stabilizing LQR control law to two fuzzy inference engines, which reduces the computational load compared with using a single fuzzy inference engine. The robustness of the balancing control is tested by attaching a bottle of water at the tip of the pendulum.

Multimodal semantic-associative collateral labelling and indexing of still images

A novel framework for multimodal semantic-associative collateral image labelling, aiming at associating image regions with textual keywords, is described. Both the primary image and collateral textual modalities are exploited in a cooperative and complementary fashion. The collateral content and context based knowledge is used to bias the mapping from the low-level region-based visual primitives to the high-level visual concepts defined in a visual vocabulary. We introduce the notion of collateral context, which is represented as a co-occurrence matrix, of the visual keywords, A collaborative mapping scheme is devised using statistical methods like Gaussian distribution or Euclidean distance together with collateral content and context-driven inference mechanism. Finally, we use Self Organising Maps to examine the classification and retrieval effectiveness of the proposed high-level image feature vector model which is constructed based on the image labelling results.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Semantic-associative visual content labelling and retrieval: A multimodal approach

A novel framework referred to as collaterally confirmed labelling (CCL) is proposed, aiming at localising the visual semantics to regions of interest in images with textual keywords. Both the primary image and collateral textual modalities are exploited in a mutually co-referencing and complementary fashion. The collateral content and context-based knowledge is used to bias the mapping from the low-level region-based visual primitives to the high-level visual concepts defined in a visual vocabulary. We introduce the notion of collateral context, which is represented as a co-occurrence matrix of the visual keywords. A collaborative mapping scheme is devised using statistical methods like Gaussian distribution or Euclidean distance together with collateral content and context-driven inference mechanism. We introduce a novel high-level visual content descriptor that is devised for performing semantic-based image classification and retrieval. The proposed image feature vector model is fundamentally underpinned by the CCL framework. Two different high-level image feature vector models are developed based on the CCL labelling of results for the purposes of image data clustering and retrieval, respectively. A subset of the Corel image collection has been used for evaluating our proposed method. The experimental results to-date already indicate that the proposed semantic-based visual content descriptors outperform both traditional visual and textual image feature models. (C) 2007 Elsevier B.V. All rights reserved.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.