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Research talks;Mathematics in Science and Technology;Probability and Statistics;Topology

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 ...

60J80 ; 60J85 ; 92D15 ; 92D25 ; 54E45 ; 54E70

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- 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

76-06 ; 00B25 ; 76S05 ; 76M25 ; 65M60 ; 65M25 ; 65N55 ; 35R60 ; 35K05 ; 92D25 ; 49L20 ; 68W10

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- 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

92-02 ; 92D25 ; 60K40 ; 00A71

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- 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

92-01 ; 92D25 ; 92D40 ; 93A30 ; 92D30

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- 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

34D05 ; 34D20 ; 34D23 ; 92B05 ; 92-01 ; 92-02 ; 92-06 ; 92D25 ; 92D30

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- 266 p.

Banach center publications , 0063

Localisation : Salle des périodiques 1er étage

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

92D25 ; 35Q80 ; 37N25

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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 # ...

58F10 ; 58F32 ; 58Fxx ; 92D25 ; 93D05

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- 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

92B05 ; 00B25 ; 92-06 ; 92D10 ; 92D25 ; 92-08

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Research talks;Dynamical Systems and Ordinary Differential Equations;Mathematics in Science and Technology

Energy investment into maturation encompasses any expenses linked to tissue differentiation, i.e. re-organization of body structure during development. This is different from growth which can be conceptualized as synthesis of more of the same. Energy invested into growth is fixed into the biomass of the organism (with some overheads), but energy invested in maturation is oxidized as metabolic work making it more difficult to quantify in practice. Nonetheless it can be quantified and it can even represent a substantial part of the energy budget of living organisms. In this talk I will give an overview of different studies where investment in maturity was quantified. The focus will be on 4 different types of organisms: cnidarians, ctenophores, teleost fish and frogs. I will further discuss what type of eco-physiological effects might be expected when an organism modifies its investment into these processes. Some intriguing literature studies will be presented which can be re-interpreted in perhaps unexpected ways when investment into maturation is taken into account. This raises the question of just how important and how flexible such costs might actually be. Maturity can be used as a quantifier for internal time. Seven criteria were proposed which should be respected by any such metric: (1) independent of morphology, (2) independent of body size, (3) depend on one a priori homologous event, (4) unaffected by changes in temperature, (5) similar between closely related species, (6) increase with clock time, and (7) physically quantifiable (Reiss 1989). We showed that the maturity concept of Dynamic Energy Budget theory complies with all those criteria and on the basis of this information and the studies presented above I will finish by discussing the potential role of maturity in shaping metabolic flexibility. Energy investment into maturation encompasses any expenses linked to tissue differentiation, i.e. re-organization of body structure during development. This is different from growth which can be conceptualized as synthesis of more of the same. Energy invested into growth is fixed into the biomass of the organism (with some overheads), but energy invested in maturation is oxidized as metabolic work making it more difficult to quantify in ...

92D25 ; 92D40 ; 92C30

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Research talks;Mathematics in Science and Technology;Probability and Statistics

Maladapted individuals can only colonise a new habitat if they can evolve a positive growth rate fast enough to avoid extinction - evolutionary rescue. We use the infinitesimal model to follow the evolution of the growth rate, and find that the probability that a single migrant can establish depends on just two parameters: the mean and genetic variance of fitness. With continued migration, establishment is inevitable. However, above a threshold migration rate, the population may be trapped in a sink state, in which adaptation is held back by gene flow. By assuming a constant genetic variance, we develop a diffusion approximation for the joint distribution of population size and trait mean. Maladapted individuals can only colonise a new habitat if they can evolve a positive growth rate fast enough to avoid extinction - evolutionary rescue. We use the infinitesimal model to follow the evolution of the growth rate, and find that the probability that a single migrant can establish depends on just two parameters: the mean and genetic variance of fitness. With continued migration, establishment is inevitable. However, above a threshold ...

92D15 ; 92D10 ; 92D25

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Research talks;Dynamical Systems and Ordinary Differential Equations;Mathematics in Science and Technology

Dynamic Energy Budget (DEB) models describe how individual organisms acquire and use energy from food and have therefore been argued to consistently link different levels of biological organisation. Various types of DEB models, differing in the organisation and precedence of metabolic processes such as growth, maintenance and reproduction, have been proposed and investigated, although recently the term DEB theory has become more and more identified with the framework developed by Kooijman.
In this lecture I will address the question to what extent differences between DEB models affect the dynamics at the population and community level. I will show that maintenance costs, which are accounted for in all DEB models, have a crucial influence, but that metabolic organisation is of lesser importance. I will furthermore show that population and community dynamics are mostly determined by differences in the capacity of individuals with different body sizes or in different stages of their life history to transform food into new biomass. Such differences, which I refer to as ontogenetic asymmetry in energetics, are however influenced more by the types of food that individuals forage on in different stages of their life history than by their internal energetics. Ontogenetic shifts in resource use during life history are therefore likely to have a larger influence on population and community dynamics than the details of the individual energy budget.
Dynamic Energy Budget (DEB) models describe how individual organisms acquire and use energy from food and have therefore been argued to consistently link different levels of biological organisation. Various types of DEB models, differing in the organisation and precedence of metabolic processes such as growth, maintenance and reproduction, have been proposed and investigated, although recently the term DEB theory has become more and more ...

92D25 ; 37N25

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Research talks

How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments?
Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for non-small cell lung cancer have been performed.
In silico experiments confirm that the selection of proper infusion schedules plays a key role in the success of anti-cancer therapies. The outcomes of protocols of chemotherapy and immunotherapy (separately and in combination) differing in doses and timing of the treatments are analyzed.
In particular, we highlight how exploiting the competition between cancer populations seems to be an effective recipe to limit the insurgence of resistant populations. In some cases, combination of low doses therapies could yield a substantial control of the total tumor population without imposing a massive selective pressure that would suppress the sensitive clones leaving unchecked the clonal types resistant to therapies.
How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments?
Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for ...

92D25 ; 92C37 ; 92C50 ; 37N25 ; 35Q92

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

35K57 ; 92D25 ; 35Q92

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

35K57 ; 92D25 ; 35Q92

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Research schools;Partial Differential Equations;Mathematical Physics;Probability and Statistics

92D25 ; 35Q92 ; 60J85 ; 60H30 ; 35K57 ; 35K55

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

92D25 ; 35Q92 ; 60J85 ; 60H30 ; 35K57 ; 35K55

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Research talks;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 ...

92D25 ; 92D15 ; 91A40 ; 91A22

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Research talks;Mathematics in Science and Technology;Probability and Statistics

60F10 ; 92D30 ; 92D25

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Research talks

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 ...

92D30 ; 05C80 ; 92D25 ; 60J28

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Research talks;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 ...

60J75 ; 60J80 ; 92D25 ; 92D15

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