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Documents  92D15 | enregistrements trouvés : 31

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

A new type of a simple iterated game with natural biological motivation is introduced. Two individuals are chosen at random from a population. They must survive a certain number of steps. They start together, but if one of them dies the other one tries to survive on its own. The only payoff is to survive the game. We only allow two strategies: cooperators help the other individual, while defectors do not. There is no strategic complexity. There are no conditional strategies. Depending on the number of steps we recover various forms of stringent and relaxed cooperative dilemmas. We derive conditions for the evolution of cooperation.
Specifically, we describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with simple, unconditional strategies. When both players are present, each step is a symmetric two-player game. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent’s type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit $(n \rightarrow \infty)$. Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner’s Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.
A new type of a simple iterated game with natural biological motivation is introduced. Two individuals are chosen at random from a population. They must survive a certain number of steps. They start together, but if one of them dies the other one tries to survive on its own. The only payoff is to survive the game. We only allow two strategies: cooperators help the other individual, while defectors do not. There is no strategic complexity. There ...

91A80 ; 91A40 ; 91A22 ; 91A12 ; 91A20 ; 92D15

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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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ISBN 978-0-8218-1176-4

Lectures on mathematics in the life sciences , 0025

Localisation : Colloque 1er étage (SNOW)

biomathématique # cycle cellulaire # écologie # évolution

92-06 ; 92D10 ; 92D15

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- 201 p.
ISBN 978-0-8218-0941-9

Lectures on mathematics in the life sciences , 0026

Localisation : Colloque 1er étage (AIZU)

algorithme # analyse du génome # autonéplicon # bioinformatique # biologie # biologie de l'évolution # complexité biologique # dynamique des popullations # espace euclidien # modèle mathématique # morphogénèse # propriété du code génétique # simulation informatique # symbiologénése

92-02 ; 92-06 ; 92B05 ; 92D15

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- 242 p.
ISBN 978-0-8218-3197-7

DIMACS series in discrete mathematics and theorerical computer science , 0061

Localisation : Collection 1er étage

biomathématique # mathématique appliquée à la biologie # arbre # bioconsensus # hypergraphe # ensemble ordonnée # classification # préférence de groupe # science comportementale # taxonomie # biologie moléculaire # évolution

00B25 ; 91F99 ; 92-06 ; 92B10 ; 05C05 ; 05C65 ; 06A99 ; 62H30 ; 92B05 ; 92C40 ; 92D15

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- 133 p.
ISBN 978-2-8218-3740-5

Contemporary mathematics , 0439

Localisation : Collection 1er étage

condition nécessaire et suffisante d'optimalité # équations NLS-like # théorie de Hamilton-Jacobi # viscosité # perturbation régulière # dynamique des populations # équations aux dérivées partielles # méthode des équations paraboliques

49K99 ; 35Q55 ; 49L25 ; 35B25 ; 92D15 ; 35R35 ; 35K60 ; 58J35

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

In this presentation, we shall discuss the reconstruction of demographic parameters based on the genetic variability observed within a sample of individual DNA. In the family of models that we consider, the statistics describing this genetic diversity (number of mutations, distribution of the mutations amongst individuals in the sample) depend on a more or less coarse ‘resolution of (i.e., level of information on) the hidden genealogical tree that relates the sampled individuals. Considering the optimal resolution thus allows to greatly improve the exploration of the space of possible genealogies when computing the likelihood of demographic parameters, compared to classical methods based on full labelled trees such as Kingmans coalescent. We shall focus on two examples, based on works with Raazesh Sainudiin (Uppsala Univ.) and with Julia Palacios (Stanford Univ.), Sohini Ramachandran (Brown Univ.) and John Wakeley (Harvard Univ.). In this presentation, we shall discuss the reconstruction of demographic parameters based on the genetic variability observed within a sample of individual DNA. In the family of models that we consider, the statistics describing this genetic diversity (number of mutations, distribution of the mutations amongst individuals in the sample) depend on a more or less coarse ‘resolution of (i.e., level of information on) the hidden genealogical tree ...

92D15 ; 92D20 ; 60J10 ; 60J27

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

A phylogenetic tree that has been reconstructed from a given gene can describe a different evolutionary history from its underlying species tree. The reasons for this include: error in inferring the gene tree, incomplete lineage sorting, lateral gene transfer, and the absence of the gene in certain species. In this talk, I discuss probabilistic models and mathematical results that help address basic questions concerning the consistency and efficiency of different methods for inferring a species phylogeny from gene trees. A phylogenetic tree that has been reconstructed from a given gene can describe a different evolutionary history from its underlying species tree. The reasons for this include: error in inferring the gene tree, incomplete lineage sorting, lateral gene transfer, and the absence of the gene in certain species. In this talk, I discuss probabilistic models and mathematical results that help address basic questions concerning the consistency and ...

92D15 ; 92C37 ; 92C80 ; 05C05

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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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Outreach;Mathematics Education and Popularization of Mathematics;Mathematics in Science and Technology

dynamique adaptative - évolution

00A06 ; 92D15

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

Recent population genomics studies focus prevalently on the aspects of demography and adaptation, whereas age structure (for example, in plants via the maintenance of seed banks) has attracted less attention. Germ banking, that is, seed or egg dormancy, is a prevalent and important life-history trait in plants and invertebrates, which buffers against environmental variability and modulates species extinction in fragmented habitats. I will here summarize our recent findings investigating the intertwined effect of germ banking, time-varying population size and selection on genetic polymorphism in the wild tomato species. First, we examine the effect of seed banking on within species variability and local adaptation in the wild tomato Solanum chilense. Population genetic analyses and statistical inference of past demography was conducted on pooled-sequencing from 30 genes from an exhaustive sampling of 23 populations over Chile and Peru. We reveal a north-south colonization associated with relaxed purifying selection in the south as shown by a decrease of genetic variation and an increasing proportion of nonsynonymous polymorphism from north to south and population substructure with at least four genetic groups. We also uncover 1) a decreasing proportion of adaptive amino acid substitutions from north to south suggesting that adaptation is favoured in large populations, while 2) signatures of local adaptation predominantly occur in the smaller populations from the marginal ranges in the south. These results combined with additional germination data suggest that colonization of new habitats was accompanied by local adaptation for shorter seed banks in the marginal populations, shaping in return the available nucleotide diversity and effectiveness of purifying and positive selection. Second, we use ABC and polymorphism data to estimate population divergence times between two wild tomato species in presence of seed banks. We show that unknown seed banking also impedes our knowledge of the speciation process. Joint work with Katharina B. Böndel, Wolfgang Stephan. Recent population genomics studies focus prevalently on the aspects of demography and adaptation, whereas age structure (for example, in plants via the maintenance of seed banks) has attracted less attention. Germ banking, that is, seed or egg dormancy, is a prevalent and important life-history trait in plants and invertebrates, which buffers against environmental variability and modulates species extinction in fragmented habitats. I will here ...

92D40 ; 92C80 ; 92D15

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

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. I will describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a "linkage block"). I will describe how we can exploit this insensitivity in a new "coarse-grained" coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability. Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. I will describe a simple limit that emerges when interference is ...

92D10 ; 92D15

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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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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

35B40 ; 35Q20 ; 35K40 ; 35Q92 ; 35A01 ; 92D15

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- 127 p.

Actualité scientifiques et industrielles , 0917

Localisation : Ouvrage RdC (DAUV)

biosphère # chlorophylle # composition chimique du globe # cristal # génèse de la vie # matière albuminoïde # structure des organismes # structure du globe # évolution géochimique

92Cxx ; 92D15 ; 92Exx

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- 239 p.
ISBN 978-0-19-850942-4

Oxford lecture series in mathematics and its applications , 0024

Localisation : Ouvrage RdC (SEMP)

phylogénétique # évolution # arbre phylogénique # statistique # arbre # modèle de Markov

92D15 ; 62P10 ; 05C05 ; 62H30 ; 92D10

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- 378 p.
ISBN 978-0-521-65539-2

Localisation : Ouvrage RdC (HOUS)

adaptation # évolution # modèle mathématique # maximisation # jeu dynamique # optimisation dynamique # énergie # sélection naturelle

92D15 ; 91A40 ; 90C40 ; 90C39

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- 236 p.
ISBN 978-0-8218-3753-5

DIMACS series in discrete mathematics and theoretical computer science , 0071

Localisation : Collection 1er étage

épidémologie # maladie contagieuse # évolution # équation différentielle # EDP # statistiques appliquées à la biologie # médecine # biomathématiques # application biomédicale # génétique # dynamique des populations

34C60 ; 35Q80 ; 62P10 ; 92B05 ; 92C50 ; 92C60 ; 92D10 ; 92D15 ; 92D25 ; 92D30

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- 318 p.
ISBN 978-0-19-920822-7

Localisation : Ouvrage RdC (Reco)

mathématiques appliquées aux sciences naturelles # évolution # phylogénétique

92-06 ; 92D15 ; 00B25

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