Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.

Dating of divergences within the Rattus genus phylogeny using whole mitochondrial genomes

The timing and order of divergences within the genus Rattus have, to date, been quite speculative. In order to address these important issues we sequenced six new whole mitochondrial genomes from wild-caught specimens from four species, Rattus exulans, Rattus praetor, Rattus rattus and Rattus tanezumi. The only rat whole mitochondrial genomes available previously were all from Rattus norvegicus specimens. Our phylogenetic and dating analyses place the deepest divergence within Rattus at ∼3.5 million years ago (Mya). This divergence separates the New Guinean endemic R. praetor lineage from the Asian lineages. Within the Asian/Island Southeast Asian clade R. norvegicus diverged earliest at ∼2.9 Mya. R. exulans and the ancestor of the sister species R. rattus and R. tanezumi subsequently diverged at ∼2.2 Mya, with R. rattus and R. tanezumi separating as recently as ∼0.4 Mya. Our results give both a better resolved species divergence order and diversification dates within Rattus than previous studies.

The evolutionary history of cockatoos (Aves: Psittaciformes: Cacatuidae)

Cockatoos are the distinctive family Cacatuidae, a major lineage of the order of parrots (Psittaciformes) and distributed throughout the Australasian region of the world. However, the evolutionary history of cockatoos is not well understood. We investigated the phylogeny of cockatoos based on three mitochondrial and three nuclear DNA genes obtained from 16 of 21 species of Cacatuidae. In addition, five novel mitochondrial genomes were used to estimate time of divergence and our estimates indicate Cacatuidae diverged from Psittacidae approximately 40.7 million years ago (95% CI 51.6–30.3 Ma) during the Eocene. Our data shows Cacatuidae began to diversify approximately 27.9 Ma (95% CI 38.1–18.3 Ma) during the Oligocene. The early to middle Miocene (20–10 Ma) was a significant period in the evolution of modern Australian environments and vegetation, in which a transformation from mainly mesic to xeric habitats (e.g., fire-adapted sclerophyll vegetation and grasslands) occurred. We hypothesize that this environmental transformation was a driving force behind the diversification of cockatoos. A detailed multi-locus molecular phylogeny enabled us to resolve the phylogenetic placements of the Palm Cockatoo (Probosciger aterrimus), Galah (Eolophus roseicapillus), Gang-gang Cockatoo (Callocephalon fimbriatum) and Cockatiel (Nymphicus hollandicus), which have historically been difficult to place within Cacatuidae. When the molecular evidence is analysed in concert with morphology, it is clear that many of the cockatoo species’ diagnostic phenotypic traits such as plumage colour, body size, wing shape and bill morphology have evolved in parallel or convergently across lineages.

Evolutionary relationships and divergence times among the native rats of Australia

Background The genus Rattus is highly speciose and has a complex taxonomy that is not fully resolved. As shown previously there are two major groups within the genus, an Asian and an Australo-Papuan group. This study focuses on the Australo-Papuan group and particularly on the Australian rats. There are uncertainties regarding the number of species within the group and the relationships among them. We analysed 16 mitochondrial genomes, including seven novel genomes from six species, to help elucidate the evolutionary history of the Australian rats. We also demonstrate, from a larger dataset, the usefulness of short regions of the mitochondrial genome in identifying these rats at the species level. Results Analyses of 16 mitochondrial genomes representing species sampled from Australo-Papuan and Asian clades of Rattus indicate divergence of these two groups ~2.7 million years ago (Mya). Subsequent diversification of at least 4 lineages within the Australo-Papuan clade was rapid and occurred over the period from ~ 0.9-1.7 Mya, a finding that explains the difficulty in resolving some relationships within this clade. Phylogenetic analyses of our 126 taxon, but shorter sequence (1952 nucleotides long), Rattus database generally give well supported species clades. Conclusions Our whole mitochondrial genome analyses are concordant with a taxonomic division that places the native Australian rats into the Rattus fuscipes species group. We suggest the following order of divergence of the Australian species. R. fuscipes is the oldest lineage among the Australian rats and is not part of a New Guinean radiation. R. lutreolus is also within this Australian clade and shallower than R. tunneyi while the R. sordidus group is the shallowest lineage in the clade. The divergences within the R. sordidus and R. leucopus lineages occurring about half a million years ago support the hypotheses of more recent interchanges of rats between Australia and New Guinea. While problematic for inference of deeper divergences, we report that the analysis of shorter mitochondrial sequences is very useful for species identification in rats.

“A problem of versions” : laying down the law in the school playground

Purpose This chapter investigates an episode where a supervising teacher on playground duty asks two boys to each give an account of their actions over an incident that had just occurred on some climbing equipment in the playground. Methodology This paper employs an ethnomethodological approach using conversation analysis. The data are taken from a corpus of video recorded interactions of children, aged 7-9 years, and the teacher, in school playgrounds during the lunch recess. Findings The findings show the ways that children work up accounts of their playground practices when asked by the teacher. The teacher initially provided interactional space for each child to give their version of the events. Ultimately, the teacher’s version of how to act in the playground became the sanctioned one. The children and the teacher formulated particular social orders of behavior in the playground through multi-modal devices, direct reported speech and scripts. Such public displays of talk work as socialization practices that frame teacher-sanctioned morally appropriate actions in the playground. Value of paper This chapter shows the pervasiveness of the teacher’s social order, as she presented an institutional social order of how to interact in the playground, showing clearly the disjunction of adult-child orders between the teacher and children.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses

The mechanical vibration properties of single actin filaments from 50 to 288 nm are investigated by the molecular dynamics simulation in this study. The natural frequencies obtained from the molecular simulations agree with those obtained from the analytical solution of the equivalent Euler–Bernoulli beam model. Through the convergence study of the mechanical properties with respect to the filament length, it was found that the Euler–Bernoulli beam model can only be reliably used when the single actin filament is of the order of hundreds of nanometre scale. This molecular investigation not only provides the evidence for the use of the continuum beam model in characterising the mechanical properties of single actin filaments, but also clarifies the criteria for the effective use of the Euler–Bernoulli beam model.

The development of ground impact models for the analysis of the risks associated with Unmanned Aircraft Operations over inhabited areas

With the emergence of Unmanned Aircraft Systems (UAS) there is a growing need for safety standards and regulatory frameworks to manage the risks associated with their operations. The primary driver for airworthiness regulations (i.e., those governing the design, manufacture, maintenance and operation of UAS) are the risks presented to people in the regions overflown by the aircraft. Models characterising the nature of these risks are needed to inform the development of airworthiness regulations. The output from these models should include measures of the collective, individual and societal risk. A brief review of these measures is provided. Based on the review, it was determined that the model of the operation of an UAS over inhabited areas must be capable of describing the distribution of possible impact locations, given a failure at a particular point in the flight plan. Existing models either do not take the impact distribution into consideration, or propose complex and computationally expensive methods for its calculation. A computationally efficient approach for estimating the boundary (and in turn area) of the impact distribution for fixed wing unmanned aircraft is proposed. A series of geometric templates that approximate the impact distributions are derived using an empirical analysis of the results obtained from a 6-Degree of Freedom (6DoF) simulation. The impact distributions can be aggregated to provide impact footprint distributions for a range of generic phases of flight and missions. The maximum impact footprint areas obtained from the geometric template are shown to have a relative error of typically less than 1% compared to the areas calculated using the computationally more expensive 6DoF simulation. Computation times for the geometric models are on the order of one second or less, using a standard desktop computer. Future work includes characterising the distribution of impact locations within the footprint boundaries.

Removal of toxic metals in a multi metal system using sorbents for potential application to urban stormwater treatment

In the context of increasing demand for potable water and the depletion of water resources, stormwater is a logical alternative. However, stormwater contains pollutants, among which metals are of particular interest due to their toxicity and persistence in the environment. Hence, it is imperative to remove toxic metals in stormwater to the levels prescribed by drinking water guidelines for potable use. Consequently, various techniques have been proposed, among which sorption using low cost sorbents is economically viable and environmentally benign in comparison to other techniques. However, sorbents show affinity towards certain toxic metals, which results in poor removal of other toxic metals. It was hypothesised in this study that a mixture of sorbents that have different metal affinity patterns can be used for the efficient removal of a range of toxic metals commonly found in stormwater. The performance of six sorbents in the sorption of Al, Cr, Cu, Pb, Ni, Zn and Cd, which are the toxic metals commonly found in urban stormwater, was investigated to select suitable sorbents for creating the mixtures. For this purpose, a multi criteria analytical protocol was developed using the decision making methods: PROMETHEE (Preference Ranking Organisation METHod for Enrichment Evaluations) and GAIA (Graphical Analysis for Interactive Assistance). Zeolite and seaweed were selected for the creation of trial mixtures based on their metal affinity pattern and the performance on predetermined selection criteria. The metal sorption mechanisms employed by seaweed and zeolite were defined using kinetics, isotherm and thermodynamics parameters, which were determined using the batch sorption experiments. Additionally, the kinetics rate-limiting steps were identified using an innovative approach using GAIA and Spearman correlation techniques developed as part of the study, to overcome the limitation in conventional graphical methods in predicting the degree of contribution of each kinetics step in limiting the overall metal removal rate. The sorption kinetics of zeolite was found to be primarily limited by intraparticle diffusion followed by the sorption reaction steps, which were governed mainly by the hydrated ionic diameter of metals. The isotherm study indicated that the metal sorption mechanism of zeolite was primarily of a physical nature. The thermodynamics study confirmed that the energetically favourable nature of sorption increased in the order of Zn < Cu < Cd < Ni < Pb < Cr < Al, which is in agreement with metal sorption affinity of zeolite. Hence, sorption thermodynamics has an influence on the metal sorption affinity of zeolite. On the other hand, the primary kinetics rate-limiting step of seaweed was the sorption reaction process followed by intraparticle diffusion. The boundary layer diffusion was also found to limit the metal sorption kinetics at low concentration. According to the sorption isotherm study, Cd, Pb, Cr and Al were sorbed by seaweed via ion exchange, whilst sorption of Ni occurred via physisorption. Furthermore, ionic bonding is responsible for the sorption of Zn. The thermodynamics study confirmed that sorption by seaweed was energetically favourable in the order of Zn < Cu < Cd < Cr . Al < Pb < Ni. However, this did not agree with the affinity series derived for seaweed suggesting a limited influence of sorption thermodynamics on metal affinity for seaweed. The investigation of zeolite-seaweed mixtures indicated that mixing sorbents have an effect on the kinetics rates and the sorption affinity. Additionally, the theoretical relationships were derived to predict the boundary layer diffusion rate, intraparticle diffusion rate, the sorption reaction rate and the enthalpy of mixtures based on that of individual sorbents. In general, low coefficient of determination (R2) for the relationships between theoretical and experimental data indicated that the relationships were not statistically significant. This was attributed to the heterogeneity of the properties of sorbents. Nevertheless, in relative terms, the intraparticle diffusion rate, sorption reaction rate and enthalpy of sorption had higher R2 values than the boundary layer diffusion rate suggesting that there was some relationship between the former set of parameters of mixtures and that of sorbents. The mixture, which contained 80% of zeolite and 20% of seaweed, showed similar affinity for the sorption of Cu, Ni, Cd, Cr and Al, which was attributed to approximately similar sorption enthalpy of the metal ions. Therefore, it was concluded that the seaweed-zeolite mixture can be used to obtain the same affinity for various metals present in a multi metal system provided the metal ions have similar enthalpy during sorption by the mixture.

On the diversity analysis of the sequential slotted amplify-decode-and-forward protocol

In this paper, we review the sequential slotted amplify-decode-and-forward (SADF) protocol with half-duplex single-antenna and evaluate its performance in terms of pairwise error probability (PEP). We obtain the PEP upper bound of the protocol and find out that the achievable diversity order of the protocol is two with arbitrary number of relay terminals. To achieve the maximum achievable diversity order, we propose a simple precoder that is easy to implement with any number of relay terminals and transmission slots. Simulation results show that the proposed precoder achieves the maximum achievable diversity order and has similar BER performance compared to some of the existing precoders.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Influence of electrolyte cations on electron transport and electron transfer in dye-sensitized solar cells

The influence of different electrolyte cations ((Li+, Na+, Mg2+, tetrabutyl ammonium (TBA+)) on the TiO2 conduction band energy (Ec) the effective electron lifetime (τn), and the effective electron diffusion coefficient (Dn) in dye-sensitized solar cells (DSCs) was studied quantitatively. The separation between Ec and the redox Fermi level, EF,redox, was found to decrease as the charge/radius ratio of the cations increased. Ec in the Mg2+ electrolyte was found to be 170 meV lower than that in the Na+ electrolyte and 400 meV lower than that in the TBA+ electrolyte. Comparison of Dn and τn in the different electrolytes was carried out by using the trapped electron concentration as a measure of the energy difference between Ec and the quasi-Fermi level, nEF, under different illumination levels. Plots of Dn as a function of the trapped electron density, nt, were found to be relatively insensitive to the electrolyte cation, indicating that the density and energetic distribution of electron traps in TiO2 are similar in all of the electrolytes studied. By contrast, plots of τn versus nt for the different cations showed that the rate of electron back reaction is more than an order of magnitude faster in the TBA+ electrolyte compared with the Na+ and Li+ electrolytes. The electron diffusion lengths in the different electrolytes followed the sequence of Na+ > Li+ > Mg2+ > TBA+. The trends observed in the AM 1.5 current–voltage characteristics of the DSCs are rationalized on the basis of the conduction band shifts and changes in electron lifetime.

In situ SANS study of the surface and pore filling adsorption of subcritical and supercritical CO2 in porous silica as a function of pore size

We applied small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) to monitor evolution of the CO2 adsorption in porous silica as a function of CO2 pressure and temperature in pores of different sizes. The range of pressures (0 < P < 345 bar) and temperatures (T=18 OC, 35 OC and 60 OC) corresponded to subcritical, near critical and supercritical conditions of bulk fluid. We observed that the adsorption behavior of CO2 is fundamentally different in large and small pores with the sizes D > 100 Å and D < 30 Å, respectively. Scattering data from large pores indicate formation of a dense adsorbed film of CO2 on pore walls with the liquid-like density (ρCO2)ads≈0.8 g/cm3. The adsorbed film coexists with unadsorbed fluid in the inner pore volume. The density of unadsorbed fluid in large pores is temperature and pressure dependent: it is initially lower than (ρCO2)ads and gradually approaches it with pressure. In small pores compressed CO2 gas completely fills the pore volume. At the lowest pressures of the order of 10 bar and T=18 OC, the fluid density in smallest pores available in the matrix with D ~ 10 Å exceeds bulk fluid density by a factor of ~ 8. As pressure increases, progressively larger pores become filled with the condensed CO2. Fluid densification is only observed in pores with sizes less than ~ 25 – 30 Å. As the density of the invading fluid reaches (ρCO2)bulk~ 0.8 g/cm3, pores of all sizes become uniformly filled with CO2 and the confinement effects disappear. At higher densities the fluid in small pores appears to follow the equation of state of bulk CO2 although there is an indication that the fluid density in the inner volume of large pores may exceed the density of the adsorbed layer. The equivalent internal pressure (Pint) in the smallest pores exceeds the external pressure (Pext) by a factor of ~ 5 for both sub- and supercritical CO2. Pint gradually approaches Pext as D → 25 – 30 Å and is independent of temperature in the studied range of 18 OC ≤ T ≤ 60 OC. The obtained results demonstrate certain similarity as well as differences between adsorption of subcritical and supercritical CO2 in disordered porous silica. High pressure small angle scattering experiments open new opportunities for in situ studies of the fluid adsorption in porous media of interest to CO2 sequestration, energy storage, and heterogeneous catalysis.

Load-unloading response of intact and artificially degraded articular cartilage correlated with near infrared (NIR) absorption spectra

The conventional mechanical properties of articular cartilage, such as compressive stiffness, have been demonstrated to be limited in their capacity to distinguish intact (visually normal) from degraded cartilage samples. In this paper, we explore the correlation between a new mechanical parameter, namely the reswelling of articular cartilage following unloading from a given compressive load, and the near infrared (NIR) spectrum. The capacity to distinguish mechanically intact from proteoglycan-depleted tissue relative to the "reswelling" characteristic was first established, and the result was subsequently correlated with the NIR spectral data of the respective tissue samples. To achieve this, normal intact and enzymatically degraded samples were subjected to both NIR probing and mechanical compression based on a load-unload-reswelling protocol. The parameter δ(r), characteristic of the osmotic "reswelling" of the matrix after unloading to a constant small load in the order of the osmotic pressure of cartilage, was obtained for the different sample types. Multivariate statistics was employed to determine the degree of correlation between δ(r) and the NIR absorption spectrum of relevant specimens using Partial Least Squared (PLS) regression. The results show a strong relationship (R(2)=95.89%, p<0.0001) between the spectral data and δ(r). This correlation of δ(r) with NIR spectral data suggests the potential for determining the reswelling characteristics non-destructively. It was also observed that δ(r) values bear a significant relationship with the cartilage matrix integrity, indicated by its proteoglycan content, and can therefore differentiate between normal and artificially degraded proteoglycan-depleted cartilage samples. It is therefore argued that the reswelling of cartilage, which is both biochemical (osmotic) and mechanical (hydrostatic pressure) in origin, could be a strong candidate for characterizing the tissue, especially in regions surrounding focal cartilage defects in joints.