A model of the lung structure and its validation

As a framework to describe the structure of the lung, a theory is presented under the assumptions that all alveoli are initially equal and space filling, are ventilated as uniformly as possible, and obey the laws of elasticity. A combination of the tetrakaidecahedron (14-hedron) and the order-2 14-hedron formed by 14 14-hedra surrounding a central one that is perforated for ventilation meets the requirements. Alveolar ductal tree is formed by these order-2 polyhedra. Equilibrium and elasticity require the alveolar mouths to be curved and convex toward the alveolar wall. Perforation of additional walls causes a variety of alveolar shapes. The predicted shapes of the alveoli, the shapes of alveolar mouths, the lengths of sacs and ducts, the statistics of the dihedral angles, stars, corners, lines, dots, and vertices compare well with available morphometric data. The vascular and bronchial trees are joined at the alveolar level: each arteriole supplies 0.75 and each venule drains 0.72 order-2 polyhedra.     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

Identifying the rooted species tree from the distribution of unrooted gene trees under the coalescent

Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals—each with many genes—splitting into new populations or species. The coalescent process, which models ancestry of gene copies within populations, is often used to model the probability distribution of gene trees given a fixed species tree. This multispecies coalescent model provides a framework for phylogeneticists to infer species trees from gene trees using maximum likelihood or Bayesian approaches. Because the coalescent models a branching process over time, all trees are typically assumed to be rooted in this setting. Often, however, gene trees inferred by traditional phylogenetic methods are unrooted. We investigate probabilities of unrooted gene trees under the multispecies coalescent model. We show that when there are four species with one gene sampled per species, the distribution of unrooted gene tree topologies identifies the unrooted species tree topology and some, but not all, information in the species tree edges (branch lengths). The location of the root on the species tree is not identifiable in this situation. However, for 5 or more species with one gene sampled per species, we show that the distribution of unrooted gene tree topologies identifies the rooted species tree topology and all its internal branch lengths. The length of any pendant branch leading to a leaf of the species tree is also identifiable for any species from which more than one gene is sampled.     

A dispersal-aggregation model for mountain pine beetle in lodgepole pine stands

In this paper a dispersal-attack theory for bark beetle attacking trees is developed from a set of simple assumptions, and the resulting theoretical model is fit to data from four epidemic studies. Implications of the theory are discussed in relation to the dynamics of lodgepole pine-mountain pine beetle interactions.     

Geometric morphometrics in entomology: Basics and applications

The recent expansion of a variety of morphometric tools has brought about a revolution in the comparison of morphology in the context of the size and shape in various fields including entomology. First, an overview of the theoretical issues of geometric morphometrics is presented with a caution about the usage of traditional morphometric measurements. Second, focus is then placed on two broad approaches as tools for geometric morphometrics; that is, the landmark‐based and the outline‐based approaches. A brief outline of the two methodologies is provided with some important cautions. The increasing trend of entomological studies in using the procedures of geometric morphometrics is then summarized. Finally, information is provided on useful toolkits such as computer software as well as codes and packages of the R statistical software that could be used in geometric morphometrics.     

Estimating phylogenetic relationships despite discordant gene trees across loci: the species tree of a diverse species group of feather mites (Acari: Proctophyllodidae)

With the increased availability of multilocus sequence data, the lack of concordance of gene trees estimated for independent loci has focused attention on both the biological processes producing the discord and the methodologies used to estimate phylogenetic relationships. What has emerged is a suite of new analytical tools for phylogenetic inference--species tree approaches. In contrast to traditional phylogenetic methods that are stymied by the idiosyncrasies of gene trees, approaches for estimating species trees explicitly take into account the cause of discord among loci and, in the process, provides a direct estimate of phylogenetic history (i.e. the history of species divergence, not divergence of specific loci). We illustrate the utility of species tree estimates with an analysis of a diverse group of feather mites, the pinnatus species group (genus Proctophyllodes). Discord among four sequenced nuclear loci is consistent with theoretical expectations, given the short time separating speciation events (as evident by short internodes relative to terminal branch lengths in the trees). Nevertheless, many of the relationships are well resolved in a Bayesian estimate of the species tree; the analysis also highlights ambiguous aspects of the phylogeny that require additional loci. The broad utility of species tree approaches is discussed, and specifically, their application to groups with high speciation rates--a history of diversification with particular prevalence in host/parasite systems where species interactions can drive rapid diversification.     

Asymmetry in RNA pseudoknots: observation and theory

RNA can fold into a topological structure called a pseudoknot, composed of non-nested double-stranded stems connected by single-stranded loops. Our examination of the PseudoBase database of pseudoknotted RNA structures reveals asymmetries in the stem and loop lengths and provocative composition differences between the loops. By taking into account differences between major and minor grooves of the RNA double helix, we explain much of the asymmetry with a simple polymer physics model and statistical mechanical theory, with only one adjustable parameter.     

Long branch effects distort maximum likelihood phylogenies in simulations despite selection of the correct model

The aim of our study was to test the robustness and efficiency of maximum likelihood with respect to different long branch effects on multiple-taxon trees. We simulated data of different alignment lengths under two different 11-taxon trees and a broad range of different branch length conditions. The data were analyzed with the true model parameters as well as with estimated and incorrect assumptions about among-site rate variation. If length differences between connected branches strongly increase, tree inference with the correct likelihood model assumptions can fail. We found that incorporating invariant sites together with Γ distributed site rates in the tree reconstruction (Γ+I) increases the robustness of maximum likelihood in comparison with models using only Γ. The results show that for some topologies and branch lengths the reconstruction success of maximum likelihood under the correct model is still low for alignments with a length of 100,000 base positions. Altogether, the high confidence that is put in maximum likelihood trees is not always justified under certain tree shapes even if alignment lengths reach 100,000 base positions.     

An efficient algorithm for approximating geodesic distances in tree space

The increasing use of phylogeny in biological studies is limited by the need to make available more efficient tools for computing distances between trees. The geodesic tree distance-introduced by Billera, Holmes, and Vogtmann-combines both the tree topology and edge lengths into a single metric. Despite the conceptual simplicity of the geodesic tree distance, algorithms to compute it don't scale well to large, real-world phylogenetic trees composed of hundred or even thousand leaves. In this paper, we propose the geodesic distance as an effective tool for exploring the likelihood profile in the space of phylogenetic trees, and we give a cubic time algorithm, GeoHeuristic, in order to compute an approximation of the distance. We compare it with the GTP algorithm, which calculates the exact distance, and the cone path length, which is another approximation, showing that GeoHeuristic achieves a quite good trade-off between accuracy (relative error always lower than 0.0001) and efficiency. We also prove the equivalence among GeoHeuristic, cone path, and Robinson-Foulds distances when assuming branch lengths equal to unity and we show empirically that, under this restriction, these distances are almost always equal to the actual geodesic.     

Dynamical phase coexistence: A simple solution to the “savanna problem”

We introduce the concept of dynamical phase coexistence to provide a simple solution for a long-standing problem in theoretical ecology, the so-called “savanna problem”. The challenge is to understand why in savanna ecosystems trees and grasses coexist in a robust way with large spatiotemporal variability. We propose a simple model, a variant of the contact process (CP), which includes two key extra features: varying external (environmental/rainfall) conditions and tree age. The system fluctuates locally between a woodland and a grassland phase, corresponding to the active and absorbing phases of the underlying pure contact process. This leads to a highly variable stable phase characterized by patches of the woodland and grassland phases coexisting dynamically. We show that the mean time to tree extinction under this model increases as a power-law of system size and can be of the order of 10,000,000 years in even moderately sized savannas. Finally, we demonstrate that while local interactions among trees may influence tree spatial distribution and the order of the transition between woodland and grassland phases, they do not affect dynamical coexistence. We expect dynamical coexistence to be relevant in other contexts in physics, biology or the social sciences.     

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

Background  

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.     

Towards building the tree of life: a simulation study for all angiosperm genera

Comprehensive phylogenetic trees are essential tools to better understand evolutionary processes. For many groups of organisms or projects aiming to build the Tree of Life, comprehensive phylogenetic analysis implies sampling hundreds to thousands of taxa. For the tree of all life this task rises to a highly conservative 13 million. Here, we assessed the performances of methods to reconstruct large trees using Monte Carlo simulations with parameters inferred from four large angiosperm DNA matrices, containing between 141 and 567 taxa. For each data set, parameters of the HKY85+G model were estimated and used to simulate 20 new matrices for sequence lengths from 100 to 10,000 base pairs. Maximum parsimony and neighbor joining were used to analyze each simulated matrix. In our simulations, accuracy was measured by counting the number of nodes in the model tree that were correctly inferred. The accuracy of the two methods increased very quickly with the addition of characters before reaching a plateau around 1000 nucleotides for any sizes of trees simulated. An increase in the number of taxa from 141 to 567 did not significantly decrease the accuracy of the methods used, despite the increase in the complexity of tree space. Moreover, the distribution of branch lengths rather than the rate of evolution was found to be the most important factor for accurately inferring these large trees. Finally, a tree containing 13,000 taxa was created to represent a hypothetical tree of all angiosperm genera and the efficiency of phylogenetic reconstructions was tested with simulated matrices containing an increasing number of nucleotides up to a maximum of 30,000. Even with such a large tree, our simulations suggested that simple heuristic searches were able to infer up to 80% of the nodes correctly.     

A fast algorithm for computing geodesic distances in tree space

Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a euclidean-like structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained.     

Flat-Top Reflection Characteristics in Metal-Dielectric-Metal Plasmonic Waveguide Structure Side Coupled with Cascaded Double Cavities

Based on a metal-dielectric-metal (MDM) plasmonic waveguide side coupled with a single cavity, we rebuild such resonator system by cascading double side-coupled cavities to obtain flat-top reflection response over a frequency bandwidth. The increased coherent scattering path provides an additional freedom to engineer the complex interference between the cavity modes and the waveguide mode. By decomposing the compound cavity modes into two decoupled resonances, we analyze the conditions to realize flat-top reflection response. The physics behind the flat-top reflection characteristics is found to be originated from the interference interaction between the two cavities through examining the cavity excitations and the reflected power response. Temporal coupled-mode theory and finite difference time domain method are utilized as theoretical and numerical tools which convince each other.     

On the impossibility of reconstructing ancestral data and phylogenies.

We prove that it is impossible to reconstruct ancestral data at the root of "deep" phylogenetic trees with high mutation rates. Moreover, we prove that it is impossible to reconstruct the topology of "deep" trees with high mutation rates from a number of characters smaller than a low-degree polynomial in the number of leaves. Our impossibility results hold for all reconstruction methods. The proofs apply tools from information theory and percolation theory.     

Stretching short DNAs in electrolytes

This paper is aimed at a combined theoretical and numerical study of the force-extension relation of a short DNA molecule stretched in an electrolyte. A theoretical formula based on a recent discrete wormlike chain (WLC) model of Kierfeld et al. (Eur Phys. J. E, Vol. 14, pp.17-34, 2004) and the classical OSF mean-field theory on electrostatic stiffening of a charged polymer is numerically verified by a set of Brownian dynamics simulations based on a generalized bead-rod (GBR) model incorporating long-ranged electrostatic interactions via the Debye-Hueckel potential (DH). The analysis indicates that the stretching of a short DNA can be well described as a WLC with a constant effective persistent length. This contrasts the behavior of long DNA chains that are known to exhibit variable persistent lengths depending on the ion concentration levels and force magnitudes.     

Log Transformation Improves Dating of Phylogenies

Phylogenetic trees inferred from sequence data often have branch lengths measured in the expected number of substitutions and therefore, do not have divergence times estimated. These trees give an incomplete view of evolutionary histories since many applications of phylogenies require time trees. Many methods have been developed to convert the inferred branch lengths from substitution unit to time unit using calibration points, but none is universally accepted as they are challenged in both scalability and accuracy under complex models. Here, we introduce a new method that formulates dating as a nonconvex optimization problem where the variance of log-transformed rate multipliers is minimized across the tree. On simulated and real data, we show that our method, wLogDate, is often more accurate than alternatives and is more robust to various model assumptions.     

Comparative analysis of telomeric restriction fragment lengths in different tissues of <Emphasis Type="Italic">Ginkgo biloba</Emphasis> trees of different age

Ginkgo trees of four different ages were selected as experimental material. Telomeric restriction fragment (TRF) lengths, as an indicator of telomere length, were determined for different tissues by Southern hybridization analysis. Statistical analysis was performed to compare two aspects of TRF length. By determining TRF lengths for different tissues for each age, a latent tendency was found. TRF length varied from short to long in these tissues in the order microspore < embryonal callus < leaf < branchlet. TRF lengths for leaf tissue and branchlet tissue were dissimilar for female and male mature trees, although this difference between TRF lengths for the two sexes was not statistically significant. Evaluation of TRF lengths for each tissue for trees of all four ages revealed TRF lengths increased with age to some extent. Different rates of change were found for leaf tissue and for branchlet tissue, although tendencies to increase were not linear for either. Finally, a simple mathematical model was formulated to describe the relationship between telomere length and age for Ginkgo biloba L.     

The average common substring approach to phylogenomic reconstruction.

We describe a novel method for efficient reconstruction of phylogenetic trees, based on sequences of whole genomes or proteomes, whose lengths may greatly vary. The core of our method is a new measure of pairwise distances between sequences. This measure is based on computing the average lengths of maximum common substrings, which is intrinsically related to information theoretic tools (Kullback-Leibler relative entropy). We present an algorithm for efficiently computing these distances. In principle, the distance of two l long sequences can be calculated in O(l) time. We implemented the algorithm using suffix arrays our implementation is fast enough to enable the construction of the proteome phylogenomic tree for hundreds of species and the genome phylogenomic forest for almost two thousand viruses. An initial analysis of the results exhibits a remarkable agreement with "acceptable phylogenetic and taxonomic truth." To assess our approach, our results were compared to the traditional (single-gene or protein-based) maximum likelihood method. The obtained trees were compared to implementations of a number of alternative approaches, including two that were previously published in the literature, and to the published results of a third approach. Comparing their outcome and running time to ours, using a "traditional" trees and a standard tree comparison method, our algorithm improved upon the "competition" by a substantial margin. The simplicity and speed of our method allows for a whole genome analysis with the greatest scope attempted so far. We describe here five different applications of the method, which not only show the validity of the method, but also suggest a number of novel phylogenetic insights.     

Coupled Mode Theory for Surface Plasmon Polariton Waveguides

In allusion to special modes supported by surface plasmon polariton (SPP) waveguides, explicit expression for mode coupling coefficient which plays a central role in coupled mode theory is firstly redefined by adding the longitudinal electric field component. The mode coupling coefficients calculated by the proposed formula improve greatly compared with the coupled mode theory suited to conventional optical waveguides, and reasonable explanations from the point of view of physics and mathematics have been given. Afterwards, the coupling lengths, the transmission lengths, the normalized power exchanges, and the cross talk performances of adjacent parallel SPP waveguides with varying waveguide separation distances D and waveguide lengths L are investigated at telecom wavelength. The results are encouraging as they indicate that the coupled mode theory is developed in a self-consistent manner by retaining the longitudinal electric field component in the derivation and neglecting it only when the waveguides structure satisfies the weakly guiding situations. As a result, the new mode coupling coefficient formula for SPP waveguides considered in this paper is an important complement in the theory of SPP waveguides.