Research Centre for Mathematical Modelling

(Forschungsschwerpunkt Mathematisierung, FSPM)

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Seminars (Colloquium):


 

Winter Semester 2011/12

  • Friday, January 20th 2012, 16:15 in V3-204
    Leif Engqvist, Bielefeld

    Theoretical approaches to understanding male fertility evolution

    Abstract:
    When females mate with more than one male, a male reproductive success will to a large extent be determined by the fertilization success of his sperm. In this highly competitive situation, sperm with reduced capacity will only have minute chances to fertilize an egg cell. Genetic changes causing a decrease in semen quality should therefore be rapidly swept away by selection. At odds with this view are many studies demonstrating variation in sperm viability traits in natural populations. Why do males not manufacture sperm of the highest possible viability? One reason might be that producing highly viable sperm is costly. Thus, decreased sperm viability may be advantageous if males can afford to gain some other benefit. Furthermore, sperm cells key position in gene transfer between generations makes them the midpoint of a number of important genetic conflicts. Therefore, the evolution of optimal fertility might be highly constrained. Here I will present three recent theoretical models that take these considerations into account and aim to answer the following questions regarding male fertility evolution: (1) How is sperm ageing predicted to be influenced by female mating rate? (2) How does variation in fertility traits influence male investment in sperm competition? (3) When does selection lead to variation in fertility and evolution of alternative reproductive strategies? These analyses reveal some highly interesting and counterintuitive results that also show that male strategic investment in sperm traits are often in strong conflict with female fertility.

  • Friday, December 9th 2011, 16:15 in V3-204
    Sebastian Steinfartz, Bielefeld

    Ökologisch-bedingte adaptive Diversifizierung bei Feuersalamandern (Salamandra salamandra): eine Herausforderung für "maßgeschneiderte'' Simulationsmodelle

    Abstract:
    Die Entstehung biologischer Vielfalt auf ganz unterschiedlichen taxonomischen Niveaus ist ein zentrales Forschungsgebiet moderner Evolutionsforschung. Vor allem die Frage, auf welche Weise und mit welcher Geschwindigkeit neue Arten entstehen, hat Biologen seit jeher im besonderen Maße fasziniert und interessiert. Mitteleuropäische, nacheiszeitlich wiederbesiedelte Lebensraumgemeinschaften eignen sich besonders gut dafür, mögliche Artbildungsprozesse und deren zugrunde liegenden Mechanismen zu untersuchen, da viele der Populationen in diesen Gebieten sich erst vor vergleichsweise kurzer Zeit (ca. 6000-8000 Jahren) etabliert haben und Anpassungs- und Diversifizierungsprozesse noch nicht abgeschlossen sind und quasi in situ beobachtet und untersucht werden können. Die Arbeitsgruppe von Sebastian Steinfartz untersucht seit etwa 10 Jahren die ökologisch-bedingte Diversifizierung von Feuersalamander-Populationen im Rheinland mit besonderem Fokus auf den Kottenforst bei Bonn. Ökologische sowie populationsgenetische Studien konnten zeigen, dass sich die Feuersalamander in dieser Population aufgrund der Adaptation an unterschiedliche Larvalgewässer in zwei genetisch differenzierte Gruppen aufgespalten haben, und dass dieser Prozess der adaptiven Diversifizierung noch nicht abgeschlossen ist und eventuell zur Bildung neuer Arten führen könnte. Im Rahmen des Vortrages soll eine aktuelle Momentaufnahme des Wissenstandes dieses ökologisch-bedingten Differenzierungsprozesses gezeichnet werden. Gleichzeitig soll diskutiert werden inwieweit auf diese Population maßgeschneiderte Simulationsmodelle zum einen die festgestellte Diversität und Differenzierung erklären können und ob die ökologisch unterschiedlich angepassten Typen den Artbildungsprozess in Zukunft abschließen werden oder nicht.

  • Monday, November 28th 2011, 17:15 in H6
    Prof. Dr. Walter Steurer, ETH Zuerich

    Why are quasicrystals quasiperiodic?

    Abstract:
    To answer this question we have to distinguish between metallic quasicrystals and quasiperiodic self-assembled colloidal structures. In the latter case special pair potentials with two different length scales and three-body interactions seem to be the main driving factors besides entropy. In case of metallic quasicrystals, the underlying mechanism is quite different. Here, the packing of low-energy clusters with non-crystallographic symmetry seems to be the decisive factor. The way of overlapping of these clusters and some other factors lead to a much higher structural order than in the case of soft quasicrystals. The focus of the talk will be on the ordering principles of metallic quasicrystals.

  • Friday, November 4th 2011, 16:15 in V3-204
    Mathias Staudigl, IMW, Bielefeld

    Stochastic Stability: Approximation, Convergence and Optimal Control (joint with William H. Sandholm, University of Wisconsin-Maddison)

    Abstract:
    In this talk we will discuss some ongoing research on evolutionary equilibrium selection in games using stochastic methods which are frequently used in economics. Since the seminal papers of Kandori, Mailath and Rob (Econometrica, 1993) and Young (Econometrica, 1993) the Freidlin-Wentzell method to assess the stability of attractors has been frequently applied in game theoretic models. However, up to now a satisfactory analysis of these models was restricted to either very simple strategic situations (i.e. games), or very simple perturbations of the dynamics. In this talk we will present some new tools how to overcome these two obstacles by using ideas from stochastic and deterministic optimal control theory. We will conclude by pointing out that our methods are not only useful in the study of stochastic evolutionary game dynamics, but also can be applied to classical optimization problems, such as Markov decision processes. This is joint work with William H. Sandholm, University of Wisconsin-Maddison.

    • Summer Semester 2011

  • Friday, July 22nd 2011, 14:15 in U10-146
    Michael Kopp, University of Vienna

    Adaptation of a quantitative trait to a moving optimum

    Abstract:
    Biological population can adapt to new environments if established gene variants are substituted by beneficial mutations, but surprisingly little is known about the nature of these mutations. Recent modeling efforts have focused on predicting the distribution of phenotypic effect sizes of individual substitution events. While the majority of these models considers adaptation after an abrupt change in the environment, I will present results for adaptation to gradual environmental change. I will show that the rate of environmental change can have a strong impact on the statistical patterns of adaptive substitutions. These results may help our understanding of evolutionary responses to global change.

  • Thursday, July 14th 2011, 10:15 in U10-146
    Mareike Fischer, Center for Integrative Bioinformatics, Vienna

    Reconstructing evolutionary trees - Chances and pitfalls in modern phylogenetics

    Abstract:
    Ever since Darwin published his first sketch of an evolutionary tree in 1859, scientists have been trying to reconstruct the Tree of Life. Such reconstructions are nowadays usually based on DNA data, which is interpreted with the help of tree inference methods. Maximum Parsimony (MP), Maximum Likelihood (ML) and distance-based methods (DB) are three such methods which are frequently used. In the first part of my talk, I will introduce MP and DB and I will show that even for the best possible DNA data, these methods can give contradictory results. In the second part of my talk, I will focus on the relationship between MP and ML, which has been widely discussed. For instance, it is well known that under a simple model of substitution, MP and ML always choose the same set of trees for DNA sequences. But some surprising properties of MP and ML have only recently been discovered: I will present examples for MP and ML favoring different trees when the underlying model is changed slightly - for example, when substitution probabilities are subject to an upper bound or when a molecular clock condition is imposed. Finally, I will show that, even though the two parts of my talk may seem unrelated at first glance, the same construction idea can be used to establish both results. This talk is based on joint work with Bhalchandra Thatte and Hans-Jürgen Bandelt.

  • Friday, June 24th 2011, 16:15 in V3-204
    Kristan Schneider, University of Vienna

    Genetic Hitchhiking and the Evolution of Anti-Malarial Drug Resistance

    Abstract:
    Malaria is among the most devastating human diseases, and it is still a threat to the public health in large areas of the developing world. Malaria control is highly dependent on the use of drugs, which clear out parasites in infected hosts. However, many important drugs have been rendered useless because parasites evolved resistance against them. Understanding the evolutionary history of the spread of drug resistance is the key to extend the lifespan of affordable and reliable anti-malarial drugs, and hence to guarantee successful malaria control. However, reconstructing the evolutionary history of drug resistance in the absence of reliable clinical and epidemiological data is difficult. Hence, theoretical models that predict the dynamics of the spread of resistance are urgently needed. While it is difficult to build mathematical models that consider the full complexity of malaria, we might be able to reconstruct the dynamics of drug resistance by analyzing empirical data. We introduce a model for the spread of drug resistance among human malaria parasites, which is designed to study genetic hitchhiking. It incorporates all characteristics of the complex malaria-transmission cycle and accounts for the fact that only a fraction of infected hosts receive drug treatment. It also incorporates that hosts can be co-infected by differently many parasites. The number of parasites co-infecting a host is either a constant or, more generally, follows a given frequency distribution. We show that the hitchhiking effect is similar but different from standard hitchhiking, and explain why standard hitchhiking theory cannot be applied to drug resistance in malaria. Furthermore, we show that a genome-wide reduction in relative heterozygosity occurs provided drug pressures are sufficiently high and sufficiently many hosts are infected by single haplotype strains.

  • Friday, June 17th 2011, 16:15 in V3-204
    Jan de Ruiter, Faculty of Linguistics and Literary Studies, Bielefeld University

    Modeling inter-channel dependencies using conditional entropy -- chasing the illusion of causality.

    Abstract:
    An intriguing problem in the field of human interaction is the mutual relationship between multiple signal "channels". An example is social eye-gaze ("Blickkontakt) and turn-taking. In order to get a formal handle on this problem, I have captured my empirical data in a state transition table of a Markov Model, combining turn-taking and eye-gaze states. This gives us a representation of a) how much time the communicating dyads spend in each state, and b) what the transitional probabilities are between different states. This representation turns out to be surprisingly useful to nail down and test vague and verbal theories about turn-taking and eye-gaze. A deeper and more challenging problem is to establish which channel determines ("dominates") the behavior of the other. It could be that turn-taking states cause certain patterns in eye-gaze states (as in Adam Kendon's 1967 standard theory), but it could also be that eye-gaze states have an effect on turn-taking states. This leads us to the more general, but very fishy problem of establishing causality from existing (historical) data sets, which is impossible for two reasons: first, as Bertrand Russell and others have convincingly argued, causality does not exist (except in our minds), and second, it is always possible that what looks like causality from A to B is actually a correlation between A and B caused by a third (unknown) factor C. Nevertheless, I am experimenting with conditional entropy used on partitionings of the transition probabilities of the Markov model, in an attempt to approximate the unattainable goal of establishing causality. Please note that this is work in progress, and not a completed thesis. I invite everyone to join and contribute to the discussion.

 

Winter Semester 2010/11

  • Thursday, February 3rd 2011, 14:15 in U10-146
    Lorens Imhof, Bonn University

    Phenotype Switching and Mutations in Random Environments

    Abstract:
    Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates and obtain a characterization of how the optimal switching rates depend on the frequency of environmental changes in a symmetric setting. Our results explain why the optimum is relatively insensitive to fitness in each environment. This is joint work with Drew Fudenberg.

  • Thursday, December 9th 2010, 14:15 in U10-146
    Evelyn Herrholz, Hochschule Neubrandenburg

    Parsimonious histograms

    Abstract:
    In the context of one-dimensional density estimation we are faced with the construction of histograms for given real-valued data. Even if a histogram is a rather simple density its construction is quite difficult. The number and width of the bins have to be specified in a satisfactory manner for a wide range of data sets. Therefore we consider tubes of functions with piecewise constant boundaries around the empirical cumulative distribution function. It is already known that the taut string minimizes typical smoothness functionals as well as the number of modes in such tubes. The latter provides an histogram with minimal number of local extremes. A related optimization problem is to obtain a histogram with the smallest number of (unequal length) bins. Its solution is subject of this talk.

  • Thursday, October 21st 2010, 15:00 in U10-146
    Marc Hellmuth, Leipzig University

    Approximate Graph Products

    Abstract:
    This talk is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected graphs is derived.

    Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the well-known "classical" prime factorization algorithm is strictly limited. This new PFD algorithm is based on a local approach that covers a graph by small factorizable subgraphs and then utilizes this information to derive the global factors. Therefore, we can take advantage of this approach and derive in addition a method for the recognition of approximate graph products.

  • Thursday, October 21st 2010, 14:15 in U10-146
    Atheer Matroud, Massey University, Neuseeland

    Nested tandem repeats- computation and analysis

    Abstract:
    Nested tandem repeat (NTR) is a complex repetitive structure, also referred to as Variable Length Tandem Repeats by [Hauth and Joseph, 2002]. NTRs structure contains two motifs repeated and interspersed with each other. In this presentation I will focus on illustrating some computation and analysis work I have done on this fascinating repetitive structure, highlighting the NTR that exists in the Taro plant and its possible use as a marker for intra-specific population study.

  • Thursday, October 14th 2010, 14:15 in U10-146
    Arndt Telschow, Helmholtz-Zentrum für Infektionsforschung, Braunschweig

    The role of Wolbachia and other reproductive parasites in eukaryotic evolution

    Abstract:
    Reproductive parasites are cytoplasmically inherited endosymbionts that manipulate the host reproductive system to their own advantage but to the disadvantage of their host. Common forms of reproductive parasitism are cytoplasmic incompatibility, male-killing, feminization, and parthenogenesis induction. Well-studied reproductive parasites belong to the bacterial groups Wolbachia, Rickettsia, Spiroplasma, and Cardinia. The wide distribution of these bacteria among arthropods, with Wolbachia estimated to infect 20-70% of all insect species, make the study of reproductive parasitism an important topic in evolution and ecology. In the first part of the presentation, it is discussed how reproduction parasites modify host gene flow and promote speciation. A mathematical modelling approach is used and analytical results for gene flow modification are presented. The results support the view that Wolbachia can promote host speciation, and, further, suggest strong impact of reproductive parasites on host gene flow. In the second part, results from the Nasonia genome project are presented which suggest horizontal gene transfer between Wolbachia, Nasonia, and pox viruses. These results suggest an important role of reproductive parasites in eukaryotic evolution.

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Summer Semester 2010

  • Thursday, June 10th, 2010, 14:15 in V3-204
    Volker Böhm, Bielefeld

    On the Dynamics of Asset Prices under Autoregressive Forecasting and Noise

    Abstract:
    The talk studies the impact of the interaction of two groups of heterogeneous investors (so called fundamentalists and chartists) on the dynamics of asset prices in the capital asset pricing model (CAPM). Members of both groups apply so called mean reverting autoregressive forecasting rules.

    Forecasts by chartists are made according to an adaptive mean reverting principle for the first two conditional moments using past asset price data. Fundamentalists' forecasts also use a mean reverting process, however, relative to a perceived so called fundamental value of asset price assumed to follow a stationary random walk. Different degrees of mean reversion have a strong impact on the dynamics of asset prices and returns showing the occurrence of a Neimark-Sacker bifurcation after a period doubling.

    An extensive numerical analysis shows that under these bifurcations highly cyclical time series of prices and returns occur which show the three typical features of empirically observed series of asset prices and returns, insignificant autocorrelation patterns of prices and returns for high order lags, which are non decaying for absolute and squared returns, as well as heavy tailed and skewed distributions. These results provide evidence that the non linearities induced by adaptive/autoregressive expectations are the major cause for overshooting features and fluctuating asset prices.

    The talk extends the analysis to study the impact of different random influences on aggregate asset supply, asset dividends, and on the fundamental asset price using numerical methods. For small enough noise, the period doubling and the Neimark-Sacker bifurcations are preserved inducing similar persistent autocorrelations. However, with larger perturbations and/or group switching, the bifurcations and autocorrelations disappear showing convergence to stationary solutions (random fixed points) without significant autocorrelations.

  • Thursday, May 27th, 2010, 14:15 in V3-204
    Reinhard Bürger, University of Vienna

    Multilocus migration-selection models

    Abstract:
    Most natural populations are geographically structured and experience spatially varying selection. We present a general population-genetic model that incorporates migration between local populations (demes) and selection acting within demes on multiple gene loci, each with an arbitrary number of alleles. The model is formulated in terms of a system of difference equations and describes the evolution of gamete frequencies in the demes. In the absence of selection, we prove global convergence to linkage equilibrium and to spatial homogeneity. This result is used to derive the weak-selection limit and to prove generic global convergence of trajectories if selection is weak relative to migration and recombination. Analogous results can be proved for the weak-migration limit and the Levene model.

  • Thursday, May 20th, 2010, 14:15 in V3-204
    Richard Gardner, Western Washington University

    Reconstruction in Geometric Tomography

    Abstract:
    Geometric tomography is the area of mathematics concerned with the retrieval of information about a geometric object from data about its orthogonal projections onto lines or planes or its intersections with lines or planes. In recent years, a number of algorithms have been developed for the purpose of reconstructing convex bodies from data of this sort. Examples are parallel and point X-rays, width or brightness functions, and support functions. In each case the algorithm takes as input a finite number of noisy (that is, corrupted by error) measurements and outputs a convex polytope that approximates the unknown convex body. The algorithms have all been proved to be strongly consistent, meaning that under suitable conditions, the Hausdorff distance from the output convex polytope to the unknown body converges, almost surely, to zero as the number of measurements increases. In some cases rates of convergence have also been obtained by applying the theory of empirical processes.
    The talk will survey these results, and briefly mention also a very recent one concerning reconstruction from covariograms, functions giving the volume of the intersection of a convex body with its translates. This reconstruction problem is closely related to the Phase Retrieval Problem for characteristic functions of convex bodies.
    The earliest algorithm to be discussed was proposed by electrical engineers in 1990, without proof of convergence. The mathematical methods involve convex geometry and probability, but the talk is intended to be accessible to a general audience. The algorithms have been implemented and pictures of typical computer reconstructions will be presented.

  • Part 1: Thursday, April 29th, 2010, 14:15 in V3-204
    Part 2: Thursday, May 6th, 2010, 14:15 in V3-204
    Michael Baake, Bielefeld

    Diffraction theory of deterministic and stochastic structures

    Abstract:
    Mathematical diffraction theory is concerned with the determination of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Moreover, the phenomenon of homometry shows various unexpected new facets. This is particularly so when systems with stochastic components are taken into account.
    This talk reviews some of the recent results, with focus on concrete examples, and is mainly based on joint work with U. Grimm and R.V. Moody. In particular, after giving a short introduction, we will discuss classic deterministic examples with singular continuous and with absolutely continuous spectra, and compare the latter with random systems. A systematic approach is proposed via the theory of stochastic processes.

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Winter Semester 2009/10

  • Friday, March 12th, 2010, 10:15 in V3-204
    Götz Gelbrich, Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig

    Herzinsuffizienz und Depression: Henne und Ei, oder interagierende Leiden?

    Abstract:
    Depression hat unter herzinsuffizienten Patienten eine deutlich erhöhte Prävalenz, ist mit erhöhter Mortalität verbunden und hat mit der Schwere der Herzinsuffizienz eine Reihe klinischer Korrelate. Es wird der Frage nachgegangen, ob die Depression nur ein Marker für die Progression der Herzinsuffizienz ist, oder ob zwischen beiden Erkrankungen durch diverse Pathomechanismen vermittelte Wechselwirkungen bestehen. Dazu werden anhand eines Strukturgleichungsmodells längsschnittliche wechselseitige Beziehungen der Herzinsuffizienz und der Depression untersucht.

  • Thursday, February 4th, 2010, 14:15 in V3-204
    Thomas Wiehe, University of Cologne

    Testing for genomic signatures of adaptive events

    Abstract:
    Identifying genome sites which underwent recent adaptive evolution - and distinguishing these genetic from demographic signals - is still a major challenge in computational population genomics. Here, I will discuss two approaches, one based on microsatellite variability and one based on haplotype structure, to address this question. Furthermore, I will present a method of alignment-free genome comparison and applications.

  • Thursday, January 28th, 2010, 14:15 in V3-204
    Eva Buchkremer, Bielefeld

    Should I stay or should I go? Foraging decisions under uncertainty

    Abstract:
    Experiments testing for variance-sensitivity (also called risk-sensitivity) usually offer two options delivering identical expected payoffs, with one option providing a constant and the other one a variable reward or delay. Animals often show a preference for the constant option when variance is in amount (variance-aversion) and a preference for the variable option when variance is in delay (variance-proneness). Variance-sensitivity is a taxonomically widespread phenomenon. Variance-sensitive foraging preferences contradict predictions derived from evolutionarily-motivated models that emphasize long-term energetic benefits. We discuss a new approach of explaining variance-sensitive preferences. We hypothesize that decision mechanisms are primarily supposed to ensure optimal responses to the environment in which the animal forages. This paper demonstrates that simple decision rules ensure long-term rate maximization and exhibit variance-sensitive behavior when tested in a classical risk-sensitivity situation. We also show that behavioral patterns observed in experiments like preferences for constant reward amounts and variable time delays are produced by the decision rules. The decision rules presented here are a first step towards a decision mechanism that is psychologically plausible, is advantageous in natural foraging situations and explains irrational behavior like variance-sensitivity.

  • Thursday, January 14th, 2010, 14:15 in V3-204
    Jens Stoye, Bielefeld

    Rearrangement Models and Single-Cut Operations

    Abstract:
    At an abstract level, genomes can be compared based on their gene order, yielding a number of interesting combinatorial and algorithmical problems. These include the calculation of the minimum number of rearrangements that are necessary to transform one genome into another one, where different rearrangement models have been considered in the past, such as reversals (REV), Hannenhalli-Pevzner (HP), and Double-Cut and Join (DCJ). Though each one can be precisely defined, the general notion of a model so far remained undefined. In this talk, we give a formal set-theoretic definition, which allows us to investigate and prove relationships between distances under various existing and new models. Somewhat surprisingly, we observe an asymmetry within the space of models we study, that might be due to an underlying combinatorial structure that still needs to be elucidated.

    This is joint work with Anne Bergeron (Montreal) and Paul Medvedev (Toronto).

  • New date soon...
    Reinhard Bürger, University of Vienna

    Multilocus migragtion-selection models

    Abstract:
    Most natural populations are geographically structured and experience spatially varying selection. We present a general population-genetic model that incorporates migration between local populations (demes) and selection acting within demes on multiple gene loci, each with an arbitrary number of alleles. The model is formulated in terms of a system of difference equations and describes the evolution of gamete frequencies in the demes. In the absence of selection, we prove global convergence to linkage equilibrium and to spatial homogeneity. This result is used to derive the weak-selection limit and to prove generic global convergence of trajectories if selection is weak relative to migration and recombination. Analogous results can be proved for the weak-migration limit and the Levene model.

  • Thursday, November 12th, 2009, 14:15 in V3-204
    Arndt von Haeseler, University of Vienna

    A different view of sequence evolution

    Abstract:
    Models to describe the evolution of biological sequences abound. With the increased number of models statistical procedures have been suggested to select the "best" model from a large class of typically nested models. While these procedures are widely used, the Litmus test, whether the best model really describes the observed data, is typically not carried out. We will present a method to do exactly this. Moreover, we will suggest an algorithm that gives a biologically interpretation to explain the difference between observed data and predicted data by the model. Several examples will illustrate the strategy.

    This is joint work with Tanja Gesell, Steffen Klaere, and Minh Anh Thi Nguyen.

  • Wednesday, November 4th, 2009, 16:15 in V3-201
    Dieter Joseph, Infineon, Munich

    Entwicklungen der Patentwelt in Industrie und Forschung

    Abstract:
    Ein Erfahrungsbericht aus der Praxis.


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Summer Semester 2009

  • Thursday, August 27th, 2009, 14:15 in V3-204
    Peter Pfaffelhuber, University of Freiburg

    Bacterial population genomics

    Abstract:
    The genome of bacteria is less stable than the genome of eucariotes. In particular, it is an empirical observation that bacteria from the same population carry different genes. We study a model where new genes are introduced from the environment and can be lost along ancestral lines. By randomizing the genealogy according to a Kingman coalescent this mutation model, which appears to be new in the population genetic literature, can be analyzed. Moreover, empirical data fit well with our theoretical results. This is joint work with Franz Baumdicker, Wolfgang Hess, University of Freiburg.

  • Thursday, July 2nd, 2009, 14:15 in V3-204
    Mike Steel, University of Canterbury, Christchurch, New Zealand

    Mixed up trees: The geometry of phylogenetic mixtures

    Abstract:
    Increasingly complex (and 'realistic') models of sequence evolution carry with them a risk. Namely, as models become more parameter rich, the ability to accurately infer evolutionary history from sequence data can decrease unless the additional parameters can somehow be independently estimated. In extreme cases two quite different scenarios (e.g. different trees, or the same tree with quite different branch lengths) can quite perfectly describe the same data if the background parameters are adjusted suitably. This talk will describe some fundamental mathematical limitations in some recent approaches to inferring evolutionary history, and discuss their relevance for molecular systematics.

  • Thursday, June 25th, 2009, 14:15 in V3-204
    Arne Traulsen, MPI for evolutionary biology in Plön

    From Game Theory to Populations Genetics (and back?)

    Abstract:
    In the past five years, evolutionary game dynamics has made significant advances by considering finite populations. Many unexpected and novel results have been obtained that are not compatible with the usual deterministic framework of evolutionary game dynamics. The new dynamics is intimately connected to population genetics, but adds a new perspective that stresses frequency dependent selection. An important problem of game theory is the evolution of costly cooperation among selfish individuals. In population genetics, this is often described by inclusive fitness methods. It turns out, however, that the underlying assumptions are in general very different from the approach of evolutionary game theory.

  • Tuesday, June 16th, 2009, 18:15 in W9-109
    Yeneng Sun, National University of Singapore

    Modeling large societies with uncertainty

    No abstract available.

  • Thursday, May 7th, 2009, 12:30 in V3-201
    H.-G. Purwins, Münster

    Lokalisierte Lösungen der erweiterten FitzHugh-Nagumo Gleichungen

    Abstract:
    Selbstorganisierte dissipative Strukturen sind in Natur und Technik weit verbreitet und nicht wenige Wissenschaftler sind der Ansicht, dass deren Verständnis und Anwendung eine der ganz großen Herausforderungen der modernen Naturwissenschaften darstellen. Der vorliegende Vortrag beschäftigt sich mit derartigen Strukturen in der Form von solitären lokalisierten Spots, die auch "Dissipative Solitonen" (DSen) genannt werden. Diese Objekte zeigen in vieler Hinsicht teilchenhaftes Verhalten und werden sowohl experimentell als auch als Lösungen von Reaktions-Diffusions-Systemen vom FitzHugh-Nagumo-Typ beobachtet. Im ersten Teil des Vortrags wird an Hand von experimentellen elektrischen Transportsystemen dargelegt, dass DSen z.B. als stationäre und laufende isolierte Pulse, als stationäre, laufende und rotierende "Moleküle" und als "kristalline", "flüssige" und "gasförmige" Vielteilchensysteme auftreten. Die dabei entdeckten Wechselwirkungsphänomen umfassen sowohl Streunung und Clusterbildung als auch Generation und Annihilation. Numerische Untersuchungen zeigen, dass sich alle experimentellen Beobachtungen qualitativ durch die verallgemeinerte FitzHugh-Nagumo-Gleichung beschreiben lassen. Es erweist sich, dass diese Gleichung als eine Art "Normalform" für eine größere Universalitätsklasse DSen tragender Systeme betrachtet werden kann.
    Im zweiten Teil des Vortrags wird besprochen, wie sich unter bestimmten Voraussetzungen aus der verallgemeinerte FitzHugh-Nagumo-Gleichung Teilchengleichungen ableiten lassen, die das dynamische Verhalten schwach wechselwirkender DSen sehr gut beschreiben.


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Winter Semester 2008/09

  • Thursday, February 5th, 2009, 14ct in V3-204
    Wilfried Gabriel, LMU Muenchen

    When is reversible phenotypic plasticity advantageous?

    Abstract:
    The ability of a genotype to express different phenotypes in variable environments often leads to a fitness advantage. Such adaptive phenotypic plasticity occurs in traits ranging from morphology to physiology and behavior and can be observed in nearly all classes of organisms. Understanding the selective advantage and the limits of plasticity is crucial to numerous issues in evolution and ecology. Environmental tolerance functions describe how fitness of an organism depends on the environmental state. Mode and variance of tolerance functions can be treated as quantitative genetic traits and its values may be altered if an organism performs phenotypic plastic changes induced by environmental cues. Non-plastic, irreversible plastic or reversible plastic genotypes are favored depending on time pattern and variance of environmental changes, on the reliability of the environmental cues, on the time spans needed to perform plastic shifts and on the costs of plasticity.

  • December 12th, 2008 14ct in V3-204
    Aernoud van Enter, Uni Groningen

    First-order transitions for nonlinear n-vector models

    Abstract:
    I discuss the occurrence of first-order transitions in temperature in various short-range lattice models with a rotation symmetry in d at least 2. Such transitions turn out to be widespread under the condition that the interaction potentials are sufficiently nonlinear. Some extensions to annealed models, and to the phenomenon of chaotic temperature dependence will be also discussed.

  • November 6th, 2008 14ct in V3-204
    Lars Koch, IMW, Bielefeld

    Persistent Ideologies in an Evolutionary Setting

    Abstract:
    We analyse finite two player games in which agents are unable to verify payoffs. Agents believe in ideologies that specify virtual payoff matrices of the game. We may, but do not need to assume the presence of ideologies that are equivalent to the true payoffs. There may be infinitely many different ideologies present at the same time. Given ideologies, agents maximize and choose actions. We define an equilibrium concept and prove existence. We assume equilibrium play at each point in time, however we refrain from assuming a particular equilibrium selection. Based on this setup, we define an evolutionary dynamic on the distribution of ideologies within the population. In this meta game agents adapt new ideologies. We assume a monotonic imitation dynamic, i.e. ideologies that lead to actions which are relatively successful in terms of true payoffs spread faster in the population than ideologies that recommend relatively unsuccessful actions. We characterize the set of stable distributions on the space of ideologies. For any finite 2 player normal form game we show that there is an open set of ideologies being not equivalent to the true payoffs that is not selected against by evolutionary monotonic dynamics based on the true payoffs of the game. If the game has a strict equilibrium set, we show stability of non-equivalent ideologies. We illustrate these results for generic 2X2-games.

  • SPECIAL: Lecture series in context of "Jahr der Mathematik"
    Mathematik ist überall: Mathematische Modellbildung

    • December 17th, 2008, 18:00 in H13
      Klaus Reinhold, Bielefeld
      Wie variabel ist die Variabilität biologischer Merkmale?

    • December 8th, 2008, 18:00 in H15(!)
      Karl Sigmund, Wien
      Zwischen Zwang und Freiwilligkeit: Die Spieltheorie der Kooperation

    • November 26th, 2008, 18:00 in H13
      Ellen Baake, Bielefeld
      Sind Mutationen spontan oder gerichtet?
      Das Luria-Delbrück-Experiment

    • November 12th, 2008, 18:00 in H13
      Frank Riedel, Bielefeld
      Total smart und auch noch reich - hohe Mathematik in der Wirtschaft

    • October 29th, 2008, 18:00 in H13
      Philippe Blanchard, Bielefeld
      Komplexe Netzwerke und zufällige Graphen in und jenseits der Physik

      (For abstracts visit "Jahr der Mathematik")

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Summer Semester 2008

  • July 2nd, 2008
    Werner Kirsch, Hagen

    Mathematik und Politik: Von Macht, Ministern und Quadratwurzeln

    Abstract:
    Die Frage nach einer angemessenen Vertretung aller Beteiligten am demokratischen Entscheidungsprozess ist eine der Grundfragen der Demokratie. So haben zum Beispiel im Ministerrat der Europäischen Union die Mitgliedsstaaten - je nach ihrer Bevölkerungsgröße - unterschiedlich viele Stimmen. Immer wieder gibt es bei Gipfeltreffen der EU Streit und Gezerre um diese Stimmgewichte; erst im vergangenen Jahr überraschte die polnische Regierung die Öffentlichkeit mit ihrer Forderung nach der ,,Quadratwurzel-Verteilung'' der Stimmen. Ähnliche Probleme ergeben sich bei anderen internationalen Organisationen (Weltbank, UNO), bei Länderkammern, wie dem Bundesrat, oder bei der Machtverteilung in großen Wirtschaftsunternehmen (z.B. VW).
    Kann man solche Machtverteilungen mit Hilfe der Mathematik analysieren? Ist es möglich, mit mathematischen Methoden eine Stimmverteilung als besonders ,,gerecht'' auszuzeichnen? Der Vortrag wird versuchen, diese Fragen zu beantworten und Denkanstöße für die politische Praxis zu liefern.
    Dieser Vortrag ist der Auftakt zu einer Veranstaltungsreihe im Rahmen des Jahres der Mathematik mit dem Titel ,,Mathematik ist überall: Mathematische Modellbildung''. Diese Reihe wird im Wintersemester fortgesetzt.

  • July 1st, 2008
    Mike Steel, Christchurch, New Zealand

    The Joys of Being Mean: Tricks for (Evolutionary) Trees

    Abstract:
    I describe how one can sometimes obtain useful insights into the properties of phylogenetic models -- both old and new -- that at first seem quite complex, by exploiting standard properties of expectation (the 'mean' of an appropriate random variable).

  • April 24th, 2008
    Tanja Gernhard, TU Munich

    A statistic for detecting lineage-specific bursts in a tree

    Abstract:
    In this talk I discuss tree statistics. First, the most common tree statistics are reviewed. We will see that lineage-specific speciation bursts cannot be detected with those statistics. I present a new statistic summarizing the timing of branching events, the runs statistic, which detects lineage-specific bursts. The statistic is applied to two example applications: we show that the evolution of the Hepatitis C virus appears to proceed in a lineage-specific bursting fashion; the ant phylogeny shows a speciation burst, but there is no evidence for lineage-specific bursting.
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Winter Semester 2007/08

  • January 31st, 2008
    Joachim Krug, University of Cologne

    Adaptation dynamics in smooth and rugged fitness landscapes

    Abstract:
    The talk will begin by briefly introducing key concepts of population genetics such as fitness landscapes, sequence space and fixation in the context of the Wright-Fisher model for the asexual evolution of finite populations, which provides a basic description of evolution experiments with bacteria and viruses. I then identify the parameters which allow for a broad classification of evolutionary regimes in rugged fitness landscapes with many peaks [1], and provide a detailed analysis of the phenomenon of clonal interference in a smooth (non-epistatic) landscape [2]. Finally, I will describe recent work on the house-of-cards model in finite populations [3], which is the simplest realization of a fitness landscape with strong epistasis. The talk is based on joint work with Kavita Jain and Su-Chan Park.

    [1] K. Jain, JK, Genetics 175, 1275 (2007)
    [2] S.C. Park, JK, PNAS 104, 18135 (2007)
    [3] S.C. Park, JK, submitted to JSTAT (arXiv:0711.1989)

  • December 13th, 2007
    Eva Maria Griebeler, University of Mainz

    Effekte der globalen Temperaturerhöhung auf die Populationsdynamik von Arten am Beispiel der Westlichen Beißschrecke (Platycleis albopunctata) und der Dreikantmuschel (Dreissena polymorpha)

    Abstract:
    Die globale Klimaveränderung wird die Habitate vieler Arten dramatisch verändern. Falls es ihnen nicht gelingt sich an die geänderten Umweltbedingungen anzupassen, werden sie möglicherweise langfristig aussterben. In meinem Vortrag möchte ich den Effekt von Temperaturerhöhung auf die Populationsdynamik exemplarisch für eine terrestrische und eine aquatisch lebende Art analysieren. Freilandstudien haben gezeigt, dass sowohl die Westliche Beißschrecke (Platycleis albopunctata) als auch die Dreikantmuschel (Dreissena polymorpha) in Habitaten mit sehr unterschiedlichen Temperaturbedingungen überleben können. Man kann daher vermuten, dass die beiden Arten auch unter der zukünftig zu erwartenden Temperaturerhöhung überleben werden. Diese Hypothese habe ich mit Hilfe von zwei Simulationsmodellen überprüft.

  • December 4th, 2007
    Achim Klenke, University of Mainz

    Infinite Rate Mutually Catalytic Branching

    Abstract:
    In 1998 Dawson and Perkins introduced a model of continuous state mutually catalytic branching on some countable Abelian group $S$ as site space. At each colony $k$ at time $t$ there is a continuous amount $X_t^i(k)$ of particles of type $i=1,2$. Time evolution is governed by
    • migration on $S$ according to some symmetric random walk kernel $a$,
    • random fluctuations of each type that are modelled locally by Feller's branching diffusion but at a rate proportional to the mass of the respective other type.
    Formally, the evolution can be described by a system of stochastic differential equations,
    $$ dX^i_t(k)=\sum_{l\in S}a(k,l)\big[X_t^i(l)-X^i_t(k)\big]dt +\sqrt{\gamma X1_t(k)X2_t(k)\,}dW^i_t(k),$$

    where $i=1,2$, $k\in S$, $\gamma>0$ is a parameter, and $(W^i(k))_{i=1,2,\;k\in S}$ is an independent family of Brownian motions.
    For the investigation of the longtime behaviour of this model it is useful to understand the limit model of $\gamma=\infty$. In a first step we construct this limit model via a martingale problem involving a Lévy-type jump measure on the state space $[0,\infty)2\setminus(0,\infty)2$ of each colony. In a second step we derive a sufficient condition for global coexistence of both types when started from a finite initial state. We show that it is sufficient that
    1. $$G_{\log}(k,l):=\int_0^\infty a_t(k,l)\,|\log(a_t(k,l))|\,dt <\infty\quad\mbox{for} k,l\in S, $$
      where $a_t$ is the continuous time kernel of the $a$-random walk, and

    2. the initial masses of type 1 and 2 are placed at sites $k_1$ and $k_2$ such that $G_{\log}(k_1,k_2)$ is small.

    In contrast, for the $\gamma<\infty$ model, Dawson and Perkins showed that for coexistence of types the weaker condition that $a$ is transient is necessary and sufficient.

    This is joint work with Leonid Mytnik.

  • October 25th, 2007
    Joachim Krug, University of Cologne

    Adaption dynamics in smooth and rugged fitness landscapes

    Abstract:
    The talk will begin by briefly introducing key concepts of population genetics such as fitness landscapes, sequence space and fixation in the context of the Wright-Fisher model for the asexual evolution of finite populations, which provides a basic description of evolution experiments with bacteria and viruses. I then identify the parameters which allow for a broad classification of evolutionary regimes in rugged fitness landscapes with many peaks [1], and provide a detailed analysis of the phenomenon of "clonal interference" in a smooth (non-epistatic) landscape [2]. The talk is based on joint work with Kavita Jain and Su-Chan Park.

    [1] K. Jain, JK, Genetics 175, 1275 (2007)
    [2] S.C. Park, JK, PNAS (in press)

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Summer Semester 2007

  • June 18th, 2007
    Marc Steinbach, University of Hannover

    Nonlinear Optimization on Scenario Trees

    Abstract:
    Multistage stochastic programming models are becoming vital in decision support for planning under uncertainty in various areas. While linear scenario tree models are widely used, well understood, and tractable by (almost) mature large scale optimization codes, comparably well developed solvers for nonlinear models do not yet exist. We present an approach that combines a suitable interior point method (handling nonlinearity and nonconvexity) with a "tree-sparse KKT solver" for the expensive linear-indefinite Newton step subproblems (handling the excessive size of multistage models by exploiting their rich structure). The approach is motivated and illustrated with examples from portfolio optimization, robust process control, and electricity trading, for which computational results will be presented.

  • June 14th, 2007
    Iwan Jensen, Melbourne University

    Exact solutions for models of punctured staircase polygons

    Abstract:
    In many cases real life phenomena are modelled by simplified solvable models, which despite the simplifications can give us great insight into the behaviour of the more complicated fully-fledged problem. A well-known long standing problem in statistical mechanics is to find the perimeter generating function for self-avoiding polygons on two-dimensional lattices. Several simplifications of this problem are solvable, but all the simpler models impose an effective directedness or other constraint that reduces the problem, in essence, to a one-dimensional problem. A very important and interesting insight gained from these simple models (staircase polygons in particular) is a conjecture for the limit distribution of area and scaling function for self-avoiding polygons. Here we report on the discovery of the exact perimeter generating function for two models of punctured staircase polygons. We started by counting the exact number of punctured polygons. Using this series we found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation. In one case we managed to solve the ODE and find a closed form expression for the generating function. We have since been able to prove this results exactly using combinatorial arguments. This solution allows a generalisation to a model with any fixed number of nested punctures as well as to other types of polygons. This is joint work with Andrew Rechnitzer (University of British Columbia), Mike Zabrocki (York University) and Anthony Guttmann (Melbourne University) and contains significant results from work with Christoph Richard.

  • May 24th, 2007
    Frank Riedel, Bielefeld University

    Evolutionary Game Theory - Theory and Applications for Continuum Strategy Models

    Abstract:
    We give an overview of evolutionary reasoning in Game Theory, with a special emphasis on games with a continuum of strategies. Whereas traditional game theory relies on the concepts of rationality, common knowledge and Nash equilibrium, evolutionary models use only the forces of selection and mutation to decsribe long run outcomes in games. Interestingly, the ``folk theorem of evolutionary game theory'' shows that stable states of such dynamics frequently are (very robust) Nash equilibria. In this sense, evolution leads to rationality. The talk discusses in which sense this can be rationalized to games with a continuum of strategies.

  • May 10th, 2007
    Carmen Molina-Paris, University of Leeds

    Peripheral T cell repertoire maintenance -- the quasi-stationary distribution

    Abstract:
    A healthy immune system requires a T cell population that responds promptly to foreign antigen. This is achieved by using a variety of self-peptides to (i) select a receptor repertoire in the thymus and (ii) keep naive T cells alive and ready for action in the periphery. In this talk I will present a stochastic mathematical model to study T cell repertoire diversity maintenance. The model incorporates the concept of survival stimuli emanating from self antigen presenting cells. I will show that in the mean field approximation clonotype extinction is guaranteed and compute extinction times of T cell clonotypes without thymic input. I will introduce the concept of the mean niche overlap and make use of the quasi-stationary distribution to compute average clonotype numbers for different values of the niche overlap.

  • April 5th, 2007
    Bernd Kugelmann, University of Greifswald

    Optimale Steuerung am Beispiel von Fischfangquoten

    Abstract:
    Im Vortrag wird ein Modell für die zeitliche Entwicklung von einer oder mehrerer Fischpopulationen in der Ostsee unter dem Einfluss von Erntemaßnahmen vorgestellt. Diese Fangbemühungen sollen so gesteuert werden, dass ein rein ökonomisches Zielkriterium optimiert wird. Mit steigender Komplexität des Modells wird die analytische Lösung des Problems immer schwieriger. Im Vortrag wird eine Methode zur numerischen Lösung dieses Optimalsteuerungsproblems erläutert und die Ergebnisse werden diskutiert.


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Winter Semester 2006/07

  • January 23rd, 2007
    Erwin Frey, Ludwig-Maximilians-Universität Munich

    Soft Materials and Collective Phenomena in Cellular Systems

    Abstract:
    Rapid developments in molecular biology and single molecule methods have provided evidence that soft interactions and fluctuation phenomena play a vital role in biology, in particular on the level of the very fundamental processes such as cytoskeletal organization, force generation by molecular motors, and cell motility.
    In this talk I will review our understanding of fibrous materials that are ubiquitious in nature, and collective phenomena which may arise in intracellular transport processes. The elastic properties of fibrous biomaterials result from a subtle interplay between the architecture of the network and the elastic properties of its building blocks. A description of these systems requires novel concepts in polymer physics. Brownian motion governs the transport along molecular multi-lane highways in cells. Exploring these systems' behavior, we find that it can be tuned by controlling particle fluxes at the boundaries and the bulk of the track. In addition to their biological relevance these systems may also be viewed as novel nonequilibrium devices.

  • January 18th, 2007
    Marc Timme, Max Planck Institute for Dynamics and Self-Organization and Bernstein Center for Computational Neuroscience Göttingen

    Speed Limits in Spiking Neural Networks Explained by Random Matrix Theory

    Abstract:
    Precisely coordinated spatio-temporal spiking dynamics have been observed experimentally in different neuronal systems and are discussed to be an essential part of computation in the brain. Their dynamical origin, however, remains unknown.
    Here we study the dynamics of neural network models and reveal basic mechanisms underlying the neurons' precise temporal coordination. We focus on the synchronization dynamics of neural networks exhibiting a complicated connection topology. In such networks, an irregular, balanced state coexists with a synchronous state of regular activity. Using a random matrix approach we predict the speed of synchronization in such networks in dependence of properties of individual neurons and their interaction network. We find that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strengths between neurons become infinitely large. We offer an intuitive explanation of this phenomenon.

  • January 15th, 2007
    Hans-Otto Georgii, University of Munich

    The two-dimensional Ising model: What can we learn from its typical configurations?

    Abstract:
    The Ising model on the square lattice Z^2 is a primary example of a statistical mechanics model showing phase transition. The interplay between its local and global behaviour is clearly displayed by the random geometry of clusters appearing in its typical configurations. In conjunction with the attractiveness and nearest-neigbour character of the interaction, this geometry allows a detailed analysis of the possible equilibrium states. In particular, it follows that - at any temperature - there exist either one or two extremal equilibrium states. The talk will give an introduction to the model and describe some central results and techniques.

  • December 7th, 2006
    Sven Wiesinger, Bielefeld University

    Two mathematical models for stochastic resonance in an asymmetric double-well potential

    Abstract:
    After an introduction to the concept of stochastic resonance and some notes about applications, the talk will concentrate on an overview of two mathematical approaches to stochastic resonance in an asymmetric double-well potential: The classical approach, based on the Freidlin-Wentzell theory for random perturbations of dynamical systems, and a newer approach based on research results by N. Berglund and B. Gentz.


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Summer Semester 2006

  • August 21st, 2006
    Ulrich Gerland, LMU Munich

    Physical, functional, and evolutionary aspects of transcription factor-DNA interaction

    Abstract:
    To regulate the transcription of a gene, one or more transcription factors bind to closeby sites on the DNA, which they recognize through their specific sequences. The aim of this talk is to illustrate how the physical process of target site location and discrimination from the genomic background is entangled with the biological function. This interplay of physics and function can also shed some light on the evolutionary aspects of these interactions.

  • August 3rd, 2006
    Jay Taylor, Oxford University, U.K.

    The common ancestor process via diffusion theory

    Abstract:
    One strategy for incorporating population genetic processes into a phylogenetic framework is through the common ancestor process, which describes the sequence of mutations along the unique lineage from which all extant individuals are descended. Although the common ancestor process in a population evolving according to a multitype branching process has been studied in some depth (e.g., Georgii and Baake (2003)), analysis of the CAP for a population of constant size is complicated by the lack of independence between individuals. In particular, if there are fitness differences between individuals, then the CAP fails to satisfy the Markov property. Fearnhead (2002) was able to characterize the CAP for a population with two fitness classes using the ancestral selection graph, obtaining a Markov process by introducing a family of virtual lineages representing those necessarily out-competed by the common ancestor (which is guaranteed to survive for all time).
    In this talk we will describe an alternative characterization of the common ancestor process using the coupled allele frequency-coalescent process introduced by Kaplan, Darden and Hudson (1988). Here we obtain a Markov process by keeping track not only of the type of the common ancestor but also of the frequencies of the types segregating in the population. We show that our results complement those obtained by Fearnhead in the case of constant fitnesses. In addition, the diffusion theoretic approach readily extends to other one-dimensional population genetic models and we use it to study the common ancestor process in populations subject to frequency-dependent selection, fluctuating selection, and bottlenecks.

  • July 18th, 2006
    Mike Steel, University of Canterbury, Christchurch, New Zealand

    Combinatorial approaches in phylogenetics

    Abstract:
    Phylogenetics is the reconstruction and analysis of 'evolutionary' trees and graphs in biology (and related areas of classification, such as linguistics). Discrete mathematics plays an important role in the underlying theory. We will describe some of the ways in which concepts from combinatorics (e.g. poset theory, greedoids, cyclic permutations, Menger's theorem, closure operators, chordal graphs) play a central role. As well as providing an overview, we also describe some recent and new results, and outline some open problems.

  • July 6th, 2006
    Ellen Baake, Bielefeld University

    Der Gordische DNA-Knoten: Enzymscheren und Geometrie

    Abstract:
    Im Laufe des Lebens einer Zelle wird ihre DNA mehrfach verknäult und wieder entwirrt. Dafür verantwortlich sind gewisse Enzyme, sogenannte Topoisomerasen, die, wie der Name schon sagt, bestimmte topologische Operationen an DNA-Molekülen durchführen. Ihre Funktionsweise wurde in enger Kooperation zwischen Biochemikern und Mathematikern aufgeklärt; wesentliches Werkzeug war dabei der Satz von White zur Geometrie von Bändern.
    Der Vortrag gibt einen Überblick über diesen 'Klassiker' der mathematischen Biologie.

  • June 27th, 2006
    Gaby Schneider, University of Frankfurt

    A stochastic model for near-synchronous neuronal firing activity

    Abstract:
    The precise timing of the firing of cortical neurons may be central for information processing in the brain. Recently, very small delays have been discovered between pairs of neurons, invisible in the raw processes but detectable in their cross correlation function. A stochastic model for the parallel firing activity of multiple neurons is presented which offers a possible explanation for the mechanism of the observed delays.

  • June 22nd, 2006
    Jochen Blath, TU Berlin

    Lambda-Coalescents as stochastic models in population genetics: Are they really out there?

    Abstract:
    Stochastic processes form a cornerstone of quantitative population genetics. Of particular interest in this talk are so-called coalescent processes, which can be used to model the genealogical tree of a population.
    Since their introduction in 1999, the structure of so-called Lambda-Coalescents and of their corresponding population models, the generalised Fleming-Viot (super-)processes, has been thoroughly studied. Special cases, e.g. Beta-coalescents with Beta strictly between 1 and 2, allowing multiple genealogical mergers, can be considered as models for the genealogy of populations with rather extreme reproductive behaviour, in so far as, e.g., single individuals are able, within a single reproductive step, to produce a number of offspring potentially of the same order of magnitude as the size of the original population.
    However, for the genealogy of many populations (in the domain of attraction of the so-called classical Fleming-Viot process), the reasonable (and very succesful) standard model in population genetics is Kingman´s Coalescent, which allows binary genealogical mergers only. Methods developed on the basis of this model admit, e.g. via importance sampling or MCMC methods, efficient likelyhood-based inference of evolutionary parameters from relatively large samples in population genetics.
    Recently, Eldon and Wakely provided evidence that the Kingman Coalescent as traditional null-model, in certain situations (e.g. for some marine species), might need to be replaced by more general models, since such species do exhibit the extreme reproductive behaviour described above.
    In a joint project with Matthias Birkner (WIAS Berlin), we address the question whether, how and which Lambda Coalescents can provide better models as basis for fully likelihood based inference in such situations.


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last modified: 24/11/2010