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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

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 ...

34E13 ; 34E15 ; 34E20 ; 92D25 ; 92D40

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

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

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 ...

92D25 ; 92D50 ; 92C15 ; 92C30

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...

92D25 ; 92D40

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

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

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 ...

92D25 ; 92D40

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