Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages

One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this paper we propose a topology reconstruction method consistent with the most general Markov model of nucleotide substitution, which can also deal with data coming from mixtures on the same topology. It is based on an idea of Eriksson on using phylogenetic invariants and provides a system of weights that can be used as input of quartet-based methods. We study its performance on real data and on a wide range of simulated 4-taxon data (both time-homogeneous and nonhomogeneous, with or without among-site rate heterogeneity, and with different branch length settings). We compare it to the classical methods of neighbor-joining (with paralinear distance), maximum likelihood (with different underlying models), and maximum parsimony. Our results show that this method is accurate and robust, has a similar performance to ML when data satisfies the assumptions of both methods, and outperforms all methods when these are based on inappropriate substitution models or when both long and short branches are present. If alignments are long enough, then it also outperforms other methods when some of its assumptions are violated.Comment: 32 pages; 9 figure

Periodic orbits in tall laterally heated rectangular cavities

This study elucidates the origin of the multiplicity of stable oscillatory flows detected by time integration in tall rectangular cavities heated from the side. By using continuation techniques for periodic orbits, it is shown that initially unstable branches, arising at Hopf bifurcations of the basic steady flow, become stable after crossing Neimark-Sacker points. There are no saddle-node or pitchfork bifurcations of periodic orbits, which could have been alternative mechanisms of stabilization. According to the symmetries of the system, the orbits are either fixed cycles, which retain at any time the center symmetry of the steady flow, or symmetric cycles involving a time shift in the global invariance of the orbit. The bifurcation points along the branches of periodic flows are determined. By using time integrations, with unstable periodic solutions as initial conditions, we determine which of the bifurcations at the limits of the intervals of stable periodic orbits are sub- or supercritical.Postprint (author's final draft

Bryophytes from the Republic of Equatorial Guinea (West Central Africa) : 3., contribution to the bryoflora of Rio Muni (continental region)

First results of the identification work of the collections made by Patxi Heras on Río Muni, the continental part of Equatorial Guinea, are offered. A list of 155 taxa (85 liverworts and 70 mosses) is included, 90 of them being new records for the country.Se ofrecen los primeros resultados del trabajo de identificación realizado en el material recolectado por Patxi Heras en Río Muni o Región Continental (Guinea Ecuatorial). Se incluye una lista de 155 táxones (85 hepáticas y 70 musgos), de los cuales 90 son novedad para el país

Bryophytes from the Republic of Equatorial Guinea (West Central Africa) : 6., Cololejeunea iradieri sp. nov., Cololejeunea magna stat. nov. and their relations to similar species

The group of African Cololejeunea species with a heart-shaped perianth and elongate marginal leaf cells has been studied. Cololejeunea iradieri is described as new from Equatorial Guinea (West Central Africa), while Cololejeunea harrisii Pócs var. magna Tix. is raised to species level. Their relations to similar species, C. amaniensis Pócs, C. harrisii Pócs and C. tenuiparietata Tix., are discussed.Se ha estudiado el grupo de especies africanas del género Cololejeunea con periantio en forma de corazón y células foliares marginales elongadas. Se describe Cololejeunea iradieri como especie nueva de Guinea Ecuatorial (Africa Centro-Occidental), mientras C. harrisii Pócs var. magna Tix. es elevada al rango de especie. Se discuten sus relaciones con sus especies afines C. amaniensis Pócs, C. harrisii Pócs y C. tenuiparietata Tix

Bryophytes from the Republic of Equatorial Guinea (West-Central Africa) : 1., introduction and preliminary checklist

A preliminary list consisting of 159 bryophyte taxa (82 liverworts and 77 mosses) has been compiled from the bryological literature on the Republic of Equatorial Guinea (Central-Western Africa) until 1995. A general overview of the physical features and vegetation of the country, and an account of the history of its bryological exploration are also included.Se han reunido en un catálogo preliminar los 159 táxones de briófitos (82 hepáticas y 77 musgos) de la República de Guinea Ecuatorial (Africa Centro-Occidental) conocidos a partir de la bibliografía hasta 1995. Se ha actualizado la nomenclatura y se incluye una descripción general del medio físico y de la vegetación del país, así como un resumen de la historia de su exploración briológica

Bryophytes from the Republic of Equatorial Guinea (West Central Africa) : 4., notes on some nomina nuda from Annobon

Eight moss species corresponding to nomina nuda recorded in the literature from Annobon Island are listed with their recent determination and current names. Leucophanes unguiculatum, Philonotis uncinata var. glaucescens and Vesicularia strephomischos are new records for the Equatorial Guinean bryoflora.Se citan con su identificación correcta y sus nombres actuales ocho especies de musgos procedentes de la isla de Annobón y registrados en la bibliografía como nomina nuda. Leucophanes unguiculatum, Philonotis uncinata var. glaucescens y Vesicularia strephomischos son nuevos registros para la brioflora de la República de Guinea Ecuatorial

Torsional solutions of convection in rotating fluid spheres

A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small Pr. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time- and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for E=10-4 at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with Ra. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.Postprint (published version

Local description of phylogenetic group-based models

Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group $G$, we provide an explicit construction of $codim X$ phylogenetic invariants (polynomial equations) of degree at most $|G|$ that define the variety $X$ on a Zariski open set $U$. The set $U$ contains all biologically meaningful points when $G$ is the group of the Kimura 3-parameter model. In particular, our main result confirms a conjecture by the third author and, on the set $U$, a couple of conjectures by Bernd Sturmfels and Seth Sullivant.Comment: 22 pages, 7 figure

On the development of the chondrocranium and the histological anatomy of the head in perinatal stages of marsupial mammals

An overview of the literature on the chondrocranium of marsupial mammals reveals a relative conservatism in shape and structures. We document the histological cranial anatomy of individuals representing Monodelphis domestica, Dromiciops gliroides, Perameles sp. and Macropus eugenii. The marsupial chondrocranium is generally characterized by the great breadth of the lamina basalis, absence of pila metoptica and large otic capsules. Its most anterior portion (cupula nasi anterior) is robust, and anterior to it there are well-developed tactile sensory structures, functionally important in the neonate. Investigations of ossification centers at and around the nasal septum are needed to trace the presence of certain bones (e.g., mesethmoid, parasphenoid) across marsupial taxa. In many adult marsupials, the tympanic floor is formed by at least three bones: alisphenoid (alisphenoid tympanic process), ectotympanic and petrosal (rostral and caudal tympanic processes); the squamosal also contributes in some diprotodontians. The presence of an entotympanic in marsupials has not been convincingly demonstrated. The tubal element surrounding the auditory tube in most marsupials is fibrous connective tissue rather than cartilage; the latter is the case in most placentals recorded to date. However, we detected fibrocartilage in a late juvenile of Dromiciops, and a similar tissue has been reported for Tarsipes. Contradictory reports on the presence of the tegmen tympani can be found in the literature. We describe a small tegmen tympani in Macropus. Several heterochronic shifts in the timing of development of the chondocranium and associated structures (e.g., nerves, muscles) and in the ossification sequence have been interpreted as largely being influenced by functional requirements related to the altriciality of the newborn marsupial during early postnatal life. Comparative studies of chondocranial development of mammals can benefit from a solid phylogenetic framework, research on non-classical model organisms, and integration with imaging and sectional data derived from computer-tomography.Fil: Sánchez Villagra, Marcelo R.. Universitat Zurich; SuizaFil: Forasiepi, Analia Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentin

Análisis de sensibilidad bayesiana a través de clases de distribuciones a priori: teoría y aplicaciones

This Ph.D. dissertation provides contributions in the study of robustness in decision-making problems from a Bayesian point of view. We bring interesting results related with robust Bayesian analysis which make this studies easier. Then, these results are applied in the study of real problems in different contexts: actuarial or financial risk, metrology and reliability theory. Consequently, the thesis is divided into three chapters, where each of them are involved in these different backgrounds. Roughly speaking, Bayesian Statistics obtain the posterior distribution of an underlying univariate or multivariate parameter as a consequence of the likelihood function from an initial sample and a prior information of the parameter according to the Bayes' rule. So, the main interest of the Bayesian point of view is the contribution not only the initial sample that we have but also introducing more information stemming from some experts. That prior information may come in different forms, although it is usually based on the experts' knowledge, which will give enough information to make decisions. In Bayesian inference is fundamental a high precision in the decision maker's judgement, specially regarding his beliefs and preferences. In the Bayesian decision framework, the prior distribution is determined in the set of states given by the experts and it is used to obtain a posterior distribution and a posterior quantity of interest depending on the problem. Usually, that quantity is such that minimizes the expected loss, which is known as the Bayes action, especially in the univariate case. It is common in the Bayesian decision framework starting from a unique prior distribution. However, there are plenty of criticism on that issue: has been well selected the prior distribution from the prior knowledge? Has been introduced any biased information, i.e., there exist any subjectivity in the specific prior distribution? How difficult is to express mathematically the experts' prior knowledge? So, the problem gets more complicated when there exist inaccuracies in the choice of the prior distribution. Therefore, a Bayesian robust analysis seems to be essential. The main goal of Bayesian robustness is to quantify and interpret the uncertainty induced by partial knowledge of one (or more) of the three elements in the analysis. Those three elements are the prior distribution, the loss function and the likelihood function. However, thorough this work, we will mainly focus on prior uncertainty for two major reasons. First, use of priors have been criticized by detractors of the Bayesian approach and Bayesian robustness provides a way to address such issue. Second, there is a practical difficulty in specifying exactly a prior corresponding to the experts' knowledge. Bayesian analysis in complex problems typically entails messy computations, and most times one cannot afford the additional computational burden that would be imposed by a formal robustness analysis. Particularly when one try to compute the range of a posterior quantity of interest. So, we can find many papers in the literature where authors try to simplify that procedures. In particular, this work has focused on it. On the other hand, the Markov Chain - Monte Carlo (MCMC) algorithms appears as an essential tool in the Bayesian decision problem. We refer to the enormous impact that MCMC methods have had on Bayesian analysis, and taking into account that Bayesian robustness methodology will need to be compatible with MCMC methods to become widely used. Though much additional work needs to obtain good results of the robust Bayesian techniques by using MCMC, it is the best way to obtain quality samples and values for the quantity of interest. Then, this work is focused on replacing a single prior distribution by a class of priors but developing classes of prior distribution which make easier the computation of the classes of posterior distribution and, therefore, the computation of the set of the quantity of interest. In order to carry out the Bayesian sensitivity analysis, it will be important to define some useful tools: the univariate and multivariate stochastic orders and the distortion functions. First, stochastic orderings are specially important, providing information about how two distributions can be compared depending on what we are looking for. For example, the simplest one is by considering classical characteristics of the distributions, as the mean value or the standard deviation. However, these comparisons are not good enough because we summarize all information in just a single measure. In this way, stochastic orders represent a powerful tool which allows us to compare two random variables in terms of different criteria. Here we list some of the stochastic orders which we will use along this dissertation: the univariate and multivariate usual stochastic order, the increasing convex (concave) order, the univariate and multivariate likelihood ratio order and the uniform conditional variability order. We will see their formal definitions and some interesting properties, including the chain of implication among all of them. In addition, distortion functions play an important role not only in this dissertation but also in different fields that appear on it, as in actuarial theory. A distortion function h is a non-decreasing continuous function such that h(0)=0 and h(1)=1. For each distortion, we can find a distorted distribution function. This idea will be explained better in the introduction, besides more interesting properties of it. It is worth mentioning that in the multivariate case there exist different ways to define the distortion functions. So, rather than choice the more suitable option every time, we will use a natural extension given by the concept of weight functions and weighted densities in the multivariate case. We provide its definition and the main properties. To summarize, this PhD dissertation will focus on develop new ways to study Bayesian robustness in the prior distribution using different tools as the classical ones. Among all these tools, we will use stochastic orders, distortion functions and weight functions. It will be considered as the starting point of this work a new class of prior distribution that they show: the Distorted Band. We will find more information about this class along the dissertation. Also, this work gives several examples and ideas to indicate the importance and uses of robustness in a Bayesian setting. The main idea is to develop new results that allow us to make sensitivity analysis in different fields of application: actuarial risk, metrology and reliability theory. Finally, the key idea is to obtain a new multivariate class of prior distribution likewise the Distorted Band