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# Documents  92D25 | enregistrements trouvés : 58

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## A non exchangeable coalescent arising in phylogenetics Lambert, Amaury | CIRM H

Post-edited

A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric spaces and give some applications of coalescent point processes to the phylogeny of bird species.

However, these models of diversification assume that species are exchangeable particles, and this always leads to the same (Yule) tree shape in distribution. Here, we propose a non-exchangeable, individual-based, point mutation model of diversification, where interspecific pairwise competition is only felt from the part of individuals belonging to younger species. As the initial (meta)population size grows to infinity, the properly rescaled dynamics of species lineages converge to a one-parameter family of coalescent trees interpolating between the caterpillar tree and the Kingman coalescent.

Keywords: ultrametric tree, inference, phylogenetic tree, phylogeny, birth-death process, population dynamics, evolution
A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric ...

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## Modeling and simulation of biological networks :american mathematical society short course#Jan. 10-11 Laubenbacher Reinhard C. | Amercian Mathematical Society 2007

Congrès

- 151 p.
ISBN 978-0-8218-3964-5

Proceedings of symposia in applied mathematics , 0064

Localisation : Collection 1er étage

bio-mathématiques # génétique # système dynamique # modélisation # simulation

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## Seminar on differential equations and dynamical systemsseminar lectures given in Aug. Jones, G. Stephen | Springer-Verlag 1968

Congrès

Lecture notes in mathematics , 0060

Localisation : Collection 1er étage

dynamique des fluides # extension de la seconde méthode de Liapunov # fonction de Liapunov non-Lipschitz # instabilité de Chetaev # modèle de croissance de population # point critique en système dynamique généralisé # principe du maximum de Pontriagin # stabilité asymptotique # stabilité et existence de solution périodique au presque pér # théorie des perturbations # équation différentielle # équation différentielle fonctionnelle linéaire # équivalence asymtotique dynamique des fluides # extension de la seconde méthode de Liapunov # fonction de Liapunov non-Lipschitz # instabilité de Chetaev # modèle de croissance de population # point critique en système dynamique généralisé # principe du maximum de Pontriagin # stabilité asymptotique # stabilité et existence de solution périodique au presque pér # théorie des perturbations # équation différentielle # équation différentielle fonctionnelle linéaire # ...

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## Mathematical modelling of population dynamics :conference on ... held at the Mathematical Conference Centre#June 24-28 Janeczko, Stanislaw ; Siersma, Dirk | Institute Of Mathematics;Polish Academy of Sciences 2004

Congrès

- 266 p.

Banach center publications , 0063

Localisation : Salle des périodiques 1er étage

modélisation # dynamique des populations # équation différentielle # probabilité # système dynamique # biologie

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## Modeling paradigms and analysis of disease transmission models.Selected papers based on the presentations at the U.S.-African advanced study institute on mathematical modeling of infectious desease in AfricaMuizenberg # june 11-22, 2007and the DIMACS workshopStellenbosch # june 25-27, 2007 Gumel, Abba B. ; Lenhart, Suzanne | American Mathematical Society 2010

Congrès

- xiv; 268 p.
ISBN 978-0-8218-4384-0

DIMACS series in discrete mathematics and theoretical computer science , 0075

Localisation : Collection 1er étage

mathématiques appliquées à la biologie # application médicale

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## Mathematical studies on human disease dynamics :emerging paradigms and challengesAMS-IMS-SIAM joint summer research conference on modeling the dynamics of human disease#July 17-21 Gumel, Abba B. ; Castillo-Chavez, Carlos ; Mickens, Ronald E. ; Clemence, Dominic P. | American Mathematical Society 2006

Congrès

- 389 p.
ISBN 978-0-8218-3775-7

Contemporary mathematics , 0410

Localisation : Collection 1er étage

epidemologie # maladie # modélisation mathématique # HIV # sida # rotavirus # influenza # stratégie de controle

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## Some mathematical models from population genetics.Ecole d'été de probabilités de Saint-Flour XXXIX-2009 Etheridge, Alison | Springer 2011

Congrès

- viii; 119 p.
ISBN 978-3-642-16631-0

Lecture notes in mathematics , 2012

Localisation : Collection 1er étage

dynamique des popullations # modèlisation mathématique # processus aléatoire

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## Fluid flow and transport in porous media :mathematical and numerical treatment#proceedings of an AMS-IMS-SIAM joint summer research conference on ... held at Mount Holyoke College#June 17-21 Chen, Zhangxin ; Ewing, Richard E. | American Mathematical Society 2002

Congrès

- 524 p.
ISBN 978-0-8218-2807-6

Contemporary mathematics , 0295

Localisation : Collection 1er étage

dynamique des fluides # milieu poreu # perméabilité # modèle mathématique # équation de transport # analyse numérique # modélisation de réseau de flot # calcul parallèle # optimisation # phénomène à plusieurs échelles # méthode des éléments finis # méthode des caractèristiques # EDP # équation de la chaleur # dynamique des populations # programmation dynamique # altgorithme parallèle

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## Size matters for balancing energy supply and demand in aquatic ectotherms Verberk, Wilco C.E.P. | CIRM H

Multi angle

Oxygen is essential for burning food and generate energy, but may become limiting for aquatic organisms that rely on gas exchange under water. This is because breathing under water is challenging: the diffusion of oxygen is orders of magnitude lower in water than in air, while the higher density and viscosity of water greatly enhance the cost of breathing. Given that oxygen may be also be a limiting resource, respiration physiology may be relevant to understand energy budgets in aquatic ectotherms.
Traditionally, respiration physiology has focused on the benefits of extracting sufficient amounts of oxygen and thus prevent asphyxiation. However, breathing oxygen is intrinsically dangerous: while a shortage of oxygen quickly leads to asphyxiation, too much oxygen is toxic. Therefore, the ability to regulate oxygen consumption rates (i.e. respiratory control) is at a premium; good respiratory control will enable ectotherms to balance oxygen toxicity against the risk of asphyxiation across a wide range of temperatures.
In this presentation I will focus on the effects of body size and temperature on this balancing act with regard to oxygen uptake and consumption. Body size is intimately tied to oxygen budgets and hence energy budgets through size related changes in oxygen requirements and respiratory surfaces. Furthermore, a larger body size may represent a respiratory advantage that helps to overcome viscosity. Given that viscous forces are larger in cold water, this respiratory advantage represents a novel explanation for the pattern of larger body sizes in cold water, with polar gigantism as the extreme manifestation.
Temperature is also intimately tied to oxygen budgets and hence energy budgets through thermal controls on metabolism and temperature related changes in the availability of dissolved oxygen (notably diffusivity, viscosity and solubility). Thus, differences in temperatures may act more strongly on ectotherms that rely on aquatic rather than on aerial gas exchange. Comparing four different insect orders, I demonstrate that thermal tolerance is indeed affected more by the prevalent oxygen conditions in species with poor respiration control. In conclusion, the ability to regulate gas exchange (i.e. respiratory control) is thus a key attribute of species that helps to explain thermal responses from an oxygen perspective.
Oxygen is essential for burning food and generate energy, but may become limiting for aquatic organisms that rely on gas exchange under water. This is because breathing under water is challenging: the diffusion of oxygen is orders of magnitude lower in water than in air, while the higher density and viscosity of water greatly enhance the cost of breathing. Given that oxygen may be also be a limiting resource, respiration physiology may be ...

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## Coevolution of habitat use in stochastic environments Schreiber, Sebastian J. | CIRM H

Multi angle

Species live and interact in landscapes where enviornmental conditions vary both in time and space. In the face of this spatial-temporal heterogeneity, species may co-evolve their habitat choices which determine their spatial distributions. To understand this coevolution, I present an analysis of a general class of stochastic Lotka-Volterra models that account for space implicitly. For these equations, a (stochastic) coevolutionarily stable strategy (coESS) is a set of habitat choice strategies for each species that, with high probability, resists invasion attempts from mutant subpopulations utilizing other habitat choice strategies. We show that the coESS is characterized by a system of second-order equations. This characterization implies that the stochastic per-capita growth rates are negative in all occupied patches for all species despite all of the species coexisting. Applying this characterization to the coevolution of habitat-choice of competitors and predator-prey systems identifies under what environmental conditions, natural selection excorcises "the ghost of competition past'' and generates enemy-free and victimless habitats. Collectively, these results highlight the importance of temporal fluctuations, spatial heterogeneity and species interactions on the evolution of species spatial distributions. Species live and interact in landscapes where enviornmental conditions vary both in time and space. In the face of this spatial-temporal heterogeneity, species may co-evolve their habitat choices which determine their spatial distributions. To understand this coevolution, I present an analysis of a general class of stochastic Lotka-Volterra models that account for space implicitly. For these equations, a (stochastic) coevolutionarily stable ...

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## De la géométrie à la dynamique de populations et des communautés Poggiale, Jean-Christophe | CIRM

Multi angle

Outreach

L'écologie est une discipline quantitative dans laquelle les mathématiques sont présentes sous différentes formes depuis très longtemps. En conséquence, l'arrivée massive d'ordinateurs de plus en plus puissants dans les laboratoires dans les dernières décennies, a conduit à une explosion de la modélisation dans ce domaine, sous forme de calculs numériques mais également par l'analyse mathématique de modèles relativement simples. Cette croissance importante de l'activité de modélisation mathématique a été accompagnée par une augmentation de la complexité des modèles d'écologie qui tentent d'intégrer la plus grosse quantité de processus connus possible. Parallèlement, les moyens d'expérimentations et d'observation du milieu naturel n'ont pas cessé de s'améliorer, produisant ainsi des bases de données de plus en plus complètes dans la description du fonctionnement des écosystèmes. Paradoxalement, la formulation de base des processus utilisée dans les modèles complexes est toujours la même et fondée sur des expérimentations réalisées dans des conditions homogènes de laboratoire au cours du XXème siècle. Nous posons la question de l'intérêt d'une description adéquate d'un écosystème pour comprendre ses réponses à différentes perturbations. Une approche consiste à utiliser des formulations mécanistes des processus, c'est à dire des formulations fondées sur des détails expliquant la cause de la réalisation des processus, plutôt que des formulations empiriques acquises dans des conditions différentes du milieu dans lequel on les applique. Cette prise en compte des mécanismes induit encore un surcroit de complexité. Les mathématiques fournissent un ensemble d'idées et de méthodes permettant tout d'abord de produire des formulations adaptées à la prise en compte des mécanismes et également d'aborder cette complexité des modèles écosystémiques, voire dans certains cas de la réduire. Nous illustrerons cette démarche à travers des exemples d'applications variés. L'écologie est une discipline quantitative dans laquelle les mathématiques sont présentes sous différentes formes depuis très longtemps. En conséquence, l'arrivée massive d'ordinateurs de plus en plus puissants dans les laboratoires dans les dernières décennies, a conduit à une explosion de la modélisation dans ce domaine, sous forme de calculs numériques mais également par l'analyse mathématique de modèles relativement simples. Cette croissance ...

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## Catching ghosts with a coarse net: real and imaginary effects in ecological monitoring routine based on sparse sampling Petrovskaya, Natalia | CIRM H

Multi angle

Mathematics in Science and Technology

Data collection and subsequent interpretation plays an important role in many ecological problems. Quantities such as the total population size and/or average population density are often evaluated based on data collected as a result of a sampling procedure. Accurate evaluation of the above quantities is crucial in ecological applications where they are used for making decision about means of control. Examples include management of pest insects in agricultural fields, prevention of plant diseases and control of geographic spread of invasive species.
One essential feature of ecological data is that the data are often sparse due to financial, labour, and other restrictions on the sampling routine. Meanwhile it is usually assumed by practitioners that estimates of ecological quantities obtained are representative, no matter how coarse a sampling grid is. This assumption is, however, not necessarily true. It will be discussed in the talk that evaluation from sparse data can lead to a loss of important information about the population dynamics. I argue that conclusions about data quality are not always obvious and practitioners can be mislead by the results of standard validation tests. It will then be shown that accuracy of the population size estimation is strongly affected by pattern formation and the number of samples required for accurate evaluation should be related to the properties of a spatial pattern. I will also discuss the effect of synchronization of population dynamics on disjoint habitats in order to demonstrate that the pattern formation, if not taken into account by a sampling procedure, may lead to unjustified or even false conclusions about the absence/presence of synchronization.
Data collection and subsequent interpretation plays an important role in many ecological problems. Quantities such as the total population size and/or average population density are often evaluated based on data collected as a result of a sampling procedure. Accurate evaluation of the above quantities is crucial in ecological applications where they are used for making decision about means of control. Examples include management of pest insects ...

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## Dynamic Energy Budget Theory as integrative hub for evaluating organismal performance in multivariate environments Muller, Erik B. | CIRM H

Multi angle

The statement that organisms in their natural environments are subject to a multitude of environmental factors - some beneficial, some adverse and some either favorable or neutral or detrimental depending on their intensity or that of other factors - is a truism that nonetheless stresses a major challenge for ecologists. Societal needs press us to find answers to questions such as “What will be the implications of rising sea surface temperatures, acidifying oceans, increasing run-off and intensifying storms expected due to climate change on reef-building corals?” and “How will materials emerging through technological innovation, such as the rapid development of nanotechnology, compound with existing stress factors to affect organisms in their natural environment and food crops?”.

Perhaps somewhat less of a commonplace statement, a single environmental factor can have multiple physiological effects on a single organism. For instance, ocean acidification, i.e. the changes in the ocean carbonate system due to an increasing atmospheric pCO2, may have physiological impacts that are both positive, e.g. stimulating photosynthesis through CO2 enrichment, and negative, e.g. inducing pH stress and increasing the costs for calcification. As another example, toxic compounds often interfere with several organismal processes; e.g. cadmium may enhance the production of reactive oxygen species, inhibit enzymes via binding to sulfhydryl groups and cause zinc deficiencies, among other potential interferences.

Complex problems such as those outlined abovecall for an integrative metabolic theory, such as Dynamic Energy Budget (DEB) theory, that considers a multivariate environment with stressors that are potentially interfering with several physiological processes simultaneously. I will illustrate how those kinds of complex problems can be addressed in DEB theory with various examples, including the impact of global change induced stress on marine calciferous organisms, the impact of engineered nanoparticles on the stability of symbioses of plants and nitrogen-fixing bacteria with generalized, process-based DEBtox theory.
The statement that organisms in their natural environments are subject to a multitude of environmental factors - some beneficial, some adverse and some either favorable or neutral or detrimental depending on their intensity or that of other factors - is a truism that nonetheless stresses a major challenge for ecologists. Societal needs press us to find answers to questions such as “What will be the implications of rising sea surface tem...

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## Competitive populations with vertical and horizontal transmissions Méléard, Sylvie | CIRM H

Multi angle

Mathematics in Science and Technology;Probability and Statistics

Horizontal transfer of information is recognized as a major process in the evolution and adaptation of population, especially micro-organisms. There is a large literature but the previous models are either based on epidemiological models or population genetics stochastic models with constant population size. We propose a general stochastic eco-evolutionary model of population dynamics with horizontal and vertical transfers, inspired by the transfer of plasmids in bacteria. The transfer rates are either density-dependent (DD) or frequency-dependent (FD) or of Michaelis-Menten form (MM). Our model allows eco-evolutionary feedbacks. In the first part we present a two-traits (alleles or kinds of plasmids, etc.) model with horizontal transfer without mutation and study a large population limit. It’s a ODEs system. We show that the phase diagrams are different in the (DD), (FD) and (MM) cases. We interpret the results for the impact of horizontal transfer on the maintenance of polymorphism and the invasion or elimination of pathogens strains. We also propose a diffusive approximation of adaptation with transfer. In a second part, we study the impact of the horizontal transfer on the evolution. We explain why it can drastically affect the evolutionary outcomes. Joint work with S. Billiard,P. Collet, R. Ferrière, C.V. Tran. Horizontal transfer of information is recognized as a major process in the evolution and adaptation of population, especially micro-organisms. There is a large literature but the previous models are either based on epidemiological models or population genetics stochastic models with constant population size. We propose a general stochastic eco-evolutionary model of population dynamics with horizontal and vertical transfers, inspired by the ...

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## Near-criticality in mathematical models of epidemics Luczak, Malwina | CIRM H

Multi angle

Probability and Statistics

In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can cross the threshold from supercritical to subcritical (for instance, due to control measures such as vaccination) or from subcritical to supercritical (for instance, due to a virus mutation making it easier for it to infect hosts). Therefore, near-criticality can be thought of as a paradigm for disease emergence and eradication, and understanding near-critical phenomena is a key epidemiological challenge.
In this talk, we explore near-criticality in the context of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homogeneous populations.
In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can ...

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## Large deviations for Poisson driven processes in epidemiology Kratz, Peter | CIRM H

Multi angle

Mathematics in Science and Technology;Probability and Statistics

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## Evolutionary branching: trade-offs and magic traits Kisdi, Eva | CIRM H

Multi angle

Mathematics in Science and Technology

Adaptive dynamics has shaped our understanding of evolution by demonstrating that, via the process of evolutionary branching, ecological interactions can promote diversification. The classical approach to study the adaptive dynamics of a system is to specify the ecological model including all trade-off functions and other functional relationships, and make predictions depending on the parameters of these functions. However, the choice of trade-offs and other functions is often the least well justified element of the model, and examples show that minor variations in these functions can lead to qualitative changes in the model predictions. In the first part of this talk, I shall revisit evolutionary branching and other evolutionary phenomena predicted by adaptive dynamics using an inverse approach: I investigate under which conditions a trade-off function exists that yields a given evolutionary outcome.
Evolutionary branching can amount to the birth of new species, but only if reproductive isolation evolves between the emerging branches. Recent studies show that mating is often assortative with respect to the very trait that is under ecological selection. Such "magic traits" can ensure reproductive isolation, yet they are by far not free tickets to speciation. In the second half of my talk, I discuss the consequences of sexual selection emerging from assortative mating, and show how a perfect female should search for mates.
Adaptive dynamics has shaped our understanding of evolution by demonstrating that, via the process of evolutionary branching, ecological interactions can promote diversification. The classical approach to study the adaptive dynamics of a system is to specify the ecological model including all trade-off functions and other functional relationships, and make predictions depending on the parameters of these functions. However, the choice of ...

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## Non-local Lokta-Volterra cross diffusion systems - Part 1 Fontbona, Joaquin | CIRM H

Multi angle

Partial Differential Equations;Mathematical Physics;Probability and Statistics

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## Non-local Lokta-Volterra cross diffusion systems - Part 2 Fontbona, Joaquin | CIRM H

Multi angle

Partial Differential Equations;Mathematics in Science and Technology;Probability and Statistics

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## Spatially structured population dynamics: the point of view of PDEs - Part 1 Desvillettes, Laurent | CIRM H

Multi angle

Partial Differential Equations;Mathematics in Science and Technology;Probability and Statistics

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