Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

Multifrequency VLA observations of the FR I radio galaxy 3C 31: morphology, spectrum and magnetic field

We present high-quality VLA images of the FR I radio galaxy 3C 31 in the frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40 arcsec. Our new images reveal complex, well resolved filamentary substructure in the radio jets and tails. We also use these images to explore the spectral structure of 3C 31 on large and small scales. We infer the apparent magnetic field structure by correcting for Faraday rotation. Some of the intensity substructure in the jets is clearly related to structure in their apparent magnetic field: there are arcs of emission where the degree of linear polarization increases, with the apparent magnetic field parallel to the ridges of the arcs. The spectral indices are significantly steeper (0.62) within 7 arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra of the jet edges are also slightly flatter than the average for their surroundings. At larger distances, the jets are clearly delimited from surrounding larger-scale emission both by their flatter radio spectra and by sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of 3C 31's jets is very close to that found in other FR I galaxies where their jets first brighten in the radio and where X-ray synchrotron emission is most prominent. Farther from the nucleus, where the spectra flatten, X-ray emission is fainter relative to the radio. The brightest X-ray emission from FR I jets is therefore not associated with the flattest radio spectra, but with a particle-acceleration process whose characteristic energy index is 2.24. The spectral flattening with distance from the nucleus occurs where our relativistic jet models require deceleration, and the flatter-spectra at the jet edges may be associated with transverse velocity shear. (Slightly abridged)Comment: 17 pages, 13 figures, accepted for publication in MNRA

The 74MHz System on the Very Large Array

The Naval Research Laboratory and the National Radio Astronomy Observatory completed implementation of a low frequency capability on the VLA at 73.8 MHz in 1998. This frequency band offers unprecedented sensitivity (~25 mJy/beam) and resolution (~25 arcsec) for low-frequency observations. We review the hardware, the calibration and imaging strategies, comparing them to those at higher frequencies, including aspects of interference excision and wide-field imaging. Ionospheric phase fluctuations pose the major difficulty in calibrating the array. Over restricted fields of view or at times of extremely quiescent ionospheric ``weather'', an angle-invariant calibration strategy can be used. In this approach a single phase correction is devised for each antenna, typically via self-calibration. Over larger fields of view or at times of more normal ionospheric ``weather'' when the ionospheric isoplanatic patch size is smaller than the field of view, we adopt a field-based strategy in which the phase correction depends upon location within the field of view. This second calibration strategy was implemented by modeling the ionosphere above the array using Zernike polynomials. Images of 3C sources of moderate strength are provided as examples of routine, angle-invariant calibration and imaging. Flux density measurements indicate that the 74 MHz flux scale at the VLA is stable to a few percent, and tied to the Baars et al. value of Cygnus A at the 5 percent level. We also present an example of a wide-field image, devoid of bright objects and containing hundreds of weaker sources, constructed from the field-based calibration. We close with a summary of lessons the 74 MHz system offers as a model for new and developing low-frequency telescopes. (Abridged)Comment: 73 pages, 46 jpeg figures, to appear in ApJ

Numerical simulation of bar and island morphodynamics in anabranching mega-rivers

Onlineopen article ©2013 American Geophysical Union.Bar and island morphodynamics in the world's largest anabranching rivers are investigated using a new numerical model of hydrodynamics, sediment transport, bank erosion, and floodplain development, operating over periods of several hundred years. Simulated channel morphology is compared to that of natural rivers and shown to be realistic, both in terms of the statistical characteristics of channel width, depth, and bar shape distributions, and mechanisms of unit bar, compound bar, and island evolution. Results demonstrate that bar and island stability may be sensitive to hydrologic regime, because greater variability in flood magnitude encourages the formation of emergent bars that can be stabilized by vegetation colonization. Simulations illustrate a range of mechanisms of unit bar generation that are linked to local bed or bank instabilities. This link may explain the reduced frequency of unit bars observed in some large anabranching rivers that are characterized by stable vegetated islands and slow rates of channel change. Model results suggest that the degree to which sand-sized bed material is carried in suspension likely represents an important control on bar morphodynamics and channel network evolution, because of its influence on sand transport direction. Consequently, differences in the partitioning of the total sand load between bed load and suspension may provide a partial explanation for contrasting styles of anabranching in the world's largest sand-bed rivers. These results highlight a need for spatially-distributed flow and sediment transport data sets from large rivers, in order to support improved parameterizations of sand transport mechanics in morphodynamic models.Natural Environment Research Council (NERC). Grant Numbers: NE/I023228/1, NE/E016022/

Virus Replication as a Phenotypic Version of Polynucleotide Evolution

In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. By taking into account beneficial effects we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium" and transient. Finally, based on these quantitative results we are able to draw some qualitative conclusions.Comment: 23 pages, 1 figure, 2 tables. arXiv admin note: substantial text overlap with arXiv:1110.336

Introducing a Pictographic Language for Envisioning a Rich Variety of Enactive Systems with Different Degrees of Complexity

Notwithstanding the considerable amount of progress that has been made in recent years, the parallel fields of cognitive science and cognitive systems lack a unifying methodology for describing, understanding, simulating and implementing advanced cognitive behaviours. Growing interest in ’enactivism’ - as pioneered by the Chilean biologists Humberto Maturana and Francisco Varela - may lead to new perspectives in these areas, but a common framework for expressing many of the key concepts is still missing. This paper attempts to lay a tentative foundation in that direction by extending Maturana and Varela’s pictographic depictions of autopoietic unities to create a rich visual language for envisioning a wide range of enactive systems - natural or artificial - with different degrees of complexity. It is shown how such a diagrammatic taxonomy can help in the comprehension of important relationships between a variety of complex concepts from a pan-theoretic perspective. In conclusion, it is claimed that visual language is not only valuable for teaching and learning, but also offers important insights into the design and implementation of future advanced robotic systems

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Spatio-structural granularity of biological material entities

<p>Abstract</p> <p>Background</p> <p>With the continuously increasing demands on knowledge- and data-management that databases have to meet, ontologies and the theories of granularity they use become more and more important. Unfortunately, currently used theories and schemes of granularity unnecessarily limit the performance of ontologies due to two shortcomings: (i) they do not allow the integration of multiple granularity perspectives into one granularity framework; (ii) they are not applicable to cumulative-constitutively organized material entities, which cover most of the biomedical material entities.</p> <p>Results</p> <p>The above mentioned shortcomings are responsible for the major inconsistencies in currently used spatio-structural granularity schemes. By using the Basic Formal Ontology (BFO) as a top-level ontology and Keet's general theory of granularity, a granularity framework is presented that is applicable to cumulative-constitutively organized material entities. It provides a scheme for granulating complex material entities into their constitutive and regional parts by integrating various compositional and spatial granularity perspectives. Within a scale dependent resolution perspective, it even allows distinguishing different types of representations of the same material entity. Within other scale dependent perspectives, which are based on specific types of measurements (e.g. weight, volume, etc.), the possibility of organizing instances of material entities independent of their parthood relations and only according to increasing measures is provided as well. All granularity perspectives are connected to one another through overcrossing granularity levels, together forming an integrated whole that uses the <it>compositional object perspective </it>as an integrating backbone. This granularity framework allows to consistently assign structural granularity values to all different types of material entities.</p> <p>Conclusions</p> <p>The here presented framework provides a spatio-structural granularity framework for all domain reference ontologies that model cumulative-constitutively organized material entities. With its multi-perspectives approach it allows querying an ontology stored in a database at one's own desired different levels of detail: The contents of a database can be organized according to diverse granularity perspectives, which in their turn provide different <it>views </it>on its content (i.e. data, knowledge), each organized into different levels of detail.</p

Beyond the public and private divide: Remapping transnational climate governance in de 21th century

This article provides a first step towards a better theoretical and empirical knowledge of the emerging arena of transnational climate governance. The need for such a re-conceptualization emerges from the increasing relevance of non-state and transnational approaches towards climate change mitigation at a time when the intergovernmental negotiation process has to overcome substantial stalemate and the international arena becomes increasingly fragmented. Based on a brief discussion of the increasing trend towards transnationalization and functional segmentation of the global climate governance arena, we argue that a remapping of climate governance is necessary and needs to take into account different spheres of authority beyond the public and international. Hence, we provide a brief analysis of how the public/private divide has been conceptualized in Political Science and International Relations. Subsequently, we analyse the emerging transnational climate governance arena. Analytically, we distinguish between different manifestations of transnational climate governance on a continuum ranging from delegated and shared public-private authority to fully non-state and private responses to the climate problem. We suggest that our remapping exercise presented in this article can be a useful starting point for future research on the role and relevance of transnational approaches to the global climate crisis