Eco-evolutionary dynamics integrates the reciprocal interactions betweenecology and evolution. These two branches of biology traditionally assumethe other as static for simplicity. However, increasing evidence shows thatthis simplification may not always hold because ecology and evolution canoperate in similar timescales. This thesis theoretically explores how thereciprocal interactions may influence ecological and evolutionary outcomesin four different eco-evolutionary contexts.Many species of non-social animals live in groups. Aggregating ingroups often has both benefits and costs that depend on group size. Thanksto the benefits of aggregation, population growth likely depends positivelyon population density when it is small. This phenomenon, the Allee effect,has been hypothesized to explain the evolution of aggregation behavior. Ifind that the Allee effect alone does not lead to the evolution whenpopulation dynamics is explicitly accounted for. Some other mechanisms,such as frequent needs for colonizing new patches or anti-aggregation,should be invoked to explain why aggregation behavior could evolve.Phenotypic plasticity is the ability of a genotype to express distinctphenotypes when exposed to different environments. Although it is oftenshown to be adaptive and not costly, highly plastic organisms are rare. Paststudies demonstrated some potential reasons. I test another possibility; costsmay arise from sexual selection because highly plastic individuals may beless preferred as a mate. I show that, even in the absence of the direct cost ofplasticity, the level of plasticity remained low at intermediate strengths ofassortative mating. This pattern is robust across wide ranges of parametervalues.Ecological speciation occurs when ecologically divergent selectionbetween environments causes reproductive isolation between divergingsubpopulations. Several verbal models of ecological speciation emphasizethe roles of phenotypic plasticity in promoting speciation. The complexprocesses involved in speciation, however, are difficult to be evaluated byverbal accounts. I quantitatively test the proposed idea in a mechanisticmodel of ecological speciation in the presence and absence of plasticity. Ifind conditions under which plasticity can promote or hinder ecologicalspeciation. Plasticity facilitates speciation by producing a gap in thedistributions of expressed phenotypes, which serves as a barrier to gene flowin an assortatively mating population.Ecosystem ecology and evolutionary biology are the least integratedfields in ecology and evolution. Natural selection operating at the individuallevels on traits governing ecosystem functions may affect ecosystemproperties, which may feedback to individuals. I reviewed this idea anddemonstrate the feedback loop by using a simple consumer-resource model.

Dans une première partie, nous proposons un nouveau modèle de chemostat dans lequel la population bactérienne est représentée de manière individu-centrée, structurée en masse, et la dynamique du substrat est modélisée par une équation différentielle ordinaire. Nous obtenons un processus markovien que nous décrivons à l'aide de mesures aléatoires. Nous déterminons, sous une certaine renormalisation du processus, un résultat de convergence en loi de ce modèle individu-centré hybride vers la solution d'un système d'équations intégro-différentielles. Dans une seconde partie, nous nous intéressons à des modèles de dynamiques adaptatives du chemostat. Nous reprenons le modèle individu-centré étudié dans la première partie, auquel nous ajoutons un mécanisme de mutation. Sous des hypothèses de mutations rares et de grande population, les résultats asymptotiques obtenus dans la première partie nous permettent de réduire l'étude d'une population mutante à un modèle de croissance-fragmentation-soutirage en milieu constant. Nous étudions la probabilité d'extinction de cette population mutante. Nous décrivons également le modèle déterministe associé au modèle individu-centré hybride avec mutation et nous comparons les deux approches, stochastique et déterministe; notamment nous démontrons qu'elles mènent au même critère de possibilité d'invasion d'une population mutante dans une population résidente.Nous présentons des simulations numériques illustrant les résultats mathématiques obtenus. / In the first part, we propose a new chemostat model in which the bacterial population is mass structured and individual-based and the substrate dynamics are modelized by an ordinary differential equation. We obtain a Markovian process which we describe as random measures. We determine, under a certain normalization of the process, a result of convergence in distribution towards the solution of a system of integro-differential equations. In the second part, we are interested in adaptive dynamic models of the chemostat. We add a mutation mechanism to the individual-based model which was studied in the first part. Under rare mutations and large population size hypotheses, the asymptotical result of the first part allows us to reduce the study of the mutant population to a growth-fragmentation-washout model in a constant environment. We study the extinction probability of this mutant population. We also describe the deterministic model related to the hybrid individual-based model with mutations and we compare these two approaches (stochastic and deterministic). In particular we prove that the two approaches lead to the same invasion criteria of a mutant population in a resident population.We present numeric simulations in order to illustrate the mathematical results.

The Earth harbors around 300 000 plant species. The rich and complex environment provided by plants is considered a key factor for the extraordinary diversity of the terrestrial fauna by, for example, providing food and shelter. This thesis contributes to the understanding of these questions by investigating how the interplay of physiology, demography, and evolution gives rise to variation and diversity in fundamental plant traits. This will help us answer questions such as: How has this amazing diversity of plant species emerged? Which mechanisms maintain diversity? How are plant strategies and plant diversity influenced by variations in the environment? A plant faces multiple problems to survive and reproduce successfully. These problems can be modeled by considering traits, trade-offs and a fitness measure. For example: How to maximize growth rate, while maximizing structural stability? I will investigate four plant models in order to understand the function of plants, and mechanisms promoting diversity.  Paper I: We study how annual plants with and without growth constraints should optimize their flowering time when productivity or season length changes. With a dynamic ontogenetic growth model and optimal control theory we prove that a bang-bang reproductive control is optimal under constrained growth and constant mortality rate. We find that growth constraints can flip the direction of optimal phenological response for increasing productivity. The reason is that the growth rate of vegetative mass saturates at high productivity and therefore it is better to flower earlier and take advantage of a longer reproductive period. If season length extends equally both in the beginning and the end of the season, growth constraints control the direction of the optimal response as well. Our theory can help explaining phenological patterns along productivity gradients, and can be linked to empirical observations made on a calendar scale. Paper II: We introduce a new measure of tree crown-rise efficiency based on the loss of biomass of the tree during growth. The more mass the tree looses during growth, the less crown-rise efficient it is. Top-heavy shapes loose more biomass than bottom-heavy shapes. Light-use efficiency is defined as the mean light assimilation of the leaves in the crown times the ratio of leaf mass and total mass. We then study the trade-off between light-use efficiency to crown-rise efficiency for tree crown shapes. We assume that the total tree mass is constant, and a constant vertical light gradient represent the shading from a surrounding forest. We find large differences in crown shapes at intermediate vertical light gradient, when both self-shading and mean-field shading are important, suggesting light-use vs crown-rise efficiency as a new trade-off that can explain tree diversity. Our crown-rise efficiency measure could easily be integrated into existing forest models. Paper III: We extend an evolutionary tree crown model, where trees with different heights compete for light, with drought-induced mortality rates depending on ground-water availability and the depth of an optional taproot. The model does not include competition for ground water. Our model explains how ground-water availability can shape plant communities, when taproot and non-taproot strategies can coexist, and when only one of these strategies can persist. We investigate how emerging plant diversity varies with water table depth, soil water gradient and drought-induced mortality rate. The taproot enables plants to reach deep water, thus reducing mortality, but also carries a construction cost, thus inducing a trade-off. We find that taproots maintain plant diversity under increasing drought mortality, and that taproots evolve when groundwater is accessible at low depths. There are no viable strategies at high drought mortality and deep water table. Red Queen evolutionary dynamics appear at intermediate drought mortality in mixed communities with and without taproots, as the community never reaches a final evolutionarily stable composition. Paper IV: We extend a size-structured plant model, with self-shading and two evolving traits, crown top-heaviness and crown width-to-height ratio. The model allows us to identify salient trade-offs for the crown shape. The most important trade-off for top-heaviness is light-use efficiency vs crownrise efficiency, and the most important trade-off for width-to-height ratio is self-shading vs branch costs. We find that when the two traits coevolve; the outcome is a single common evolutionarily stable strategy (ESS), far away from the highest net primary production (NPP). When only sun angle is decreasing with increasing latitude both the crown width-to-height ratio and crown top-heaviness decrease. However, when light response in addition to the sun angle decreases with increasing latitude, the crown width-to-height ratio is nearly invariant of latitude except at low site productivity when the ratio decreases with latitude. Top-heaviness is always decreasing with increasing latitude. Finally, we find that crown top-heaviness increases with the NPP or leaf-area index (LAI) at ESS, but crown width-to-height ratio is maximal at an intermediate NPP or LAI. / Artikel I: Arters reproduktionsframgång (fitness), till exempel antal avkommor eller frön som produceras under livet, är ofta avgörande för huruvida de är evolutionärt framgångsrika eller inte. Här undersöker vi hur ettåriga växter med eller utan tillväxtbegränsningar ska optimera sin blomningstid när produktivitet eller säsongslängd ändras. Det är optimalt att gå direkt från tillväxt till blomning när tillväxten är begränsad och dödligheten är konstant. Vid ökad produktivitet sker blomningen tidigare med tillväxtbegränsningar men senare utan tillväxtbegränsningar, vilket beror på att med tillväxtbegränsningar ökar den vegetativa massan långsamt. Därför är det bättre att blomma tidigare och ta tillvara på en längre reproduktionsperiod. Vi får samma resultat om säsongslängden ökar lika mycket i början och slutet av säsongen. Vår teori kan bidra till att förutsäga blomningstider vid produktivitetsförändringar och säsongsförändringar. Artikel II: Tillväxten hos träd kan begränsas av brist på ljus, vatten, och näring, men också genom förlust av grenar. Vi introducerar ett nytt mått på tillväxteffektiviteten hos trädkronor baserat på förlust av biomassa under trädets tillväxt. Ju mer massa trädet förlorar under tillväxt, desto mindre tillväxteffektiva är de. Topptunga former förlorar mer biomassa än bottentunga former. Vi studerar avvägningar mellan ljuseffektivitet och tillväxteffektivitet för trädformer, där ljuseffektiviteten definieras som medelljusupptaget för löven i kronan. Vi antar en konstant totalmassa, och en statisk vertikal skuggning som representerar skuggningen från en omgivande skog. Vi hittar stora skillnader i kronformer vid en medelhög skuggning, då både självskuggningen och medelskuggningen har betydelse. Vårt mått för tillväxteffektivitet kan enkelt integreras i existerande skogsmodeller. Studien visar att avvägningar mellan tillväxteffektivitet och ljuseffektivitetet kan vara viktig för mångfalden av trädformer i en skog. En överraskande upptäckt är att konformade eller sfäriska trädkronor aldrig är effektiva, men däremot timglasformade kronor. Artikel III: Växter kan försvara sig på olika sätt mot torka, till exempel genom att rulla ihop bladen eller genom att reproducera tidigare och därigenom undvika uttdragen torka. Här undersöker vi fördelarna med en pålrot vid torka. En pålrot är en rot som växer nedåt för att nå djupliggande grundvatten. Vi utvidgar en evolutionär modell av trädkronor med grundvatten och en pålrot, där träd med olika höjd konkurrerar om ljus. Det finns ingen konkurrens om vatten. Vi undersöker hur mångfalden hos träden beror på vattendjup, vattengradient och dödlighet orsakad av torka. Med hjälp av pålroten kan träden nå djupt vatten och därigenom minska dödligheten, men den medför också en kostnad, så en avvägning måste göras. Vi ser att pålrötter upprätthåller mångfalden hos växterna vid ökad mortalitet, och att pålrötter uppstår när grundvattnet är grunt. Det finns inga strategier som kan överleva om grundvattnet är djupt och dödligheten är hög. Vår modell kan förklara hur grundvatten kan förändra sammansättningen på trädsamhällen, när träd med och utan pålrot kan samexistera, och under vilka förutsättningar endast en av strategierna förväntas dominera. Artikel IV: Träd som växer upp i en skog måste konkurrera med andra träd om ljus, framförallt större träd. Detta ger upphov till en asymmetrisk ljuskonkurrens, där de små träden hämmas av större träd. Små träd har därmed små chanser att överleva utom då skogen nyligen störts och det öppnas upp en glänta. Vid denna ljuskonkurrens kan man anta att trädkronans form har stor betydelse för trädets framgång. Frågan är hur de evolutionärt fördelaktiga kronformerna beror på latituden och produktiviteten. Vi antar att latituden påverkar solens genomsnittliga vinkel och ljusrespons. Vi utvidgar en storleksstrukturerad trädmodell med självskuggning där två evolverande egenskaper beskriver kronans topptyngd och bredd. Med modellen kan vi undersöka vilka strategiska avvägningar som bestämmer om kronans form blir konkurrenskraftig. En topptung krona har högt ljusupptag eftersom det finns mest ljus högt upp i grenverket. Å andra sidan har den en låg tillväxteffektivitet eftersom topptunga kronor måste tappa mycket grenar för att behålla sin form. En bred krona har en låg självskuggning eftersom bladen är utspridda. Å andra sidan har den höga kostnader för de långa grenar som krävs. Vi finner att när dessa egenskaper evolverar tillsammans så finns endast en evolutionärt stabil strategi (ESS), långt från den högsta nettoproduktionen. När endast solvinkeln minskar med ökande latitud minskar både kronans bredd och topptyngd, men när både solvinkel och ljusrespons minskar med ökande latitud så är bredden nästan oförändrad utom vid låg produktivitet då den minskar med latituden. Kronans topptyngd minskar alltid med latituden. Slutligen ser vi hur kronans topptyngd alltid ökar med nettoproduktionen vid ESS, medan kronans bredd har ett maxium för ett mellanvärde hos nettoproduktionen vid ESS.

Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T01:49:08Z (GMT). No. of bitstreams: 1 Araujo_SabrinaBorgesLino_D.pdf: 18627531 bytes, checksum: aed18ab505ee489e8cde08b6d2850bba (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estudamos a dinâmica espaço-temporal de cadeias alimentares compostas por duas e três espécies. Utilizamos uma modelagem baseada nos indivíduos, que consiste em tratar cada membro da população de forma explícita. Um dos ingredientes do modelo é a possibilidade de restringir a área de forrageio dos predadores à uma região circular, de raio R, em torno da sua residência. O tamanho desta região é tratado como uma característica adaptativa, sujeita à pequenas variações aleatórias ao longo das gerações. Observamos que existe um raio de predação ótimo R', para o qual os predadores evoluem. Desenvolvemos cálculos analíticos utilizando aproximações de Campo Médio com correlações de pares e verificamos que a estratégia de predação é um mecanismo crucial para a ocorrência do raio ótimo. Observamos também que a distribuição da abundância de indivíduos por região espacial pode exibir um comportamento invariante de escala, indicando que o sistema é criticamente auto-organizado, e que a ocorrência de surtos populacionais locais é uma característica intrínseca do sistema / Abstract: In this work we study the spatial dynamics of two and three species food chains. We use an individual based model, which treats each member of the population explicitly. One of the model ingredients is the possibility to control the size of the predators foraging area, defined as a circular neighborhood, of radius R, around their home position. This home range size is treated as an adaptive, subject to small random variations along generations. We find that the predators evolve to a optimum predation radius R'. We develop analytical approximations using mean field and pair correlation techniques that indicate that the predation strategy is crucial for existence of this optimum radius. We also find that the population abundance distributions display a scale invariant power law tail, indicating self-organized criticality and that the occurrence of local outbreaks is an intrinsic characteristic of the system / Doutorado / Ciências Exatas e da Terra / Doutora em Ciências

Les plantes, comme tous les êtres vivants, entretiennent un rapport double à leur environnement. L’environnement sélectionne quelles stratégies peuvent s’établir, et les stratégies ainsi sélectionnées façonnent en retour cet environnement. Cette boucle de rétroaction environnementale, lorsqu’elle est alimentée par une variabilité de formes, est le moteur de l’évolution, de l’assemblage des communautés et du développement écosystémique, et détermine en fin de compte les propriétés émergentes des écosystèmes.Les approches issues de l’écologie théorique reconnaissent depuis longtemps cette dualité, comme en témoignent les concepts de "niche de besoin" et "niche d’impact" au cœur de la théorie contemporaine de la niche. Similairement, les approches type « théorie des jeux » comme la dynamique adaptative reconnaissent le rôle central joué par la boucle de rétroaction environnementale en tant que moteur des dynamiques éco-évolutives.Dans cette thèse, j'unifie ces deux perspectives théoriques et les applique à des problèmes écologiques variés, dans le but de comprendre comment les interactions réciproques entre les plantes et leur environnement déterminent les traits adaptatifs des plantes et les propriétés émergentes des écosystèmes.Dans un premier temps, je propose un cadre mathématique général et rigoureux à la théorie contemporaine de la niche et la méthode graphique qui lui est associée. Après avoir étendu ce cadre à la prise en compte d’un continuum de stratégies en interaction à l’aide d’enveloppes géométriques, je montre comment appliquer la théorie contemporaine de la niche à deux perspectives, à savoir les dynamiques éco-évolutives et l’assemblage de communautés par remplacements successifs de stratégies.Dans un second temps, j’applique cette approche à l’étude de l’évolution des défenses des plantes contre les herbivores le long de gradients de nutriments, en considérant l’évolution des traits d’acquisition de la ressource, de tolérance et de résistance aux herbivores. Je montre que la prise en compte des transferts trophiques conduit à la sélection de stratégies compétitives mais sans défense dans les environnements pauvres, alors que ce sont toujours des stratégies défendues (résistantes, tolérantes, ou la coexistence des deux) qui dominent dans les environnements riches en nutriments. Mes résultats mettent en évidence le rôle central joué par la rétroaction plante-herbivores dans la détermination des patrons de défense des plantes.Dans un troisième temps, je montre comment la théorie contemporaine de la niche peut être étendue pour prendre en compte la facilitation. J’utilise ensuite cette approche pour montrer comment la colonisation d’un substrat nu par une communauté de plantes fixatrices d’azote couplée au recyclage des nutriments peut donner naissance à de la succession par facilitation. Contrairement aux modèles habituels de succession, je montre que la succession par facilitation donne lieu à un développement autogène de l’écosystème ainsi qu’un régime de bistabilité entre la végétation et le substrat nu en fin de succession. Enfin, je propose une nouvelle théorie de la succession basée sur les ratios de ressources.Pris dans leur ensemble, ces nouveaux développements démontrent que la théorie de la niche peut être adaptée à l’étude d’un large champ de situations écologiques, de la facilitation aux dynamiques éco-évolutives et à l’assemblage des communautés. Dans ce cadre conceptuel, mon approche basée sur les enveloppes s’avère être un outil efficace pour passer de l’échelle individuelle à l’échelle de l’écosystème, en assimilant le remplacement adaptatif d’espèces à une plasticité des propriétés écosystémiques. Cette approche permet alors de décrire l’émergence des boucles de régulation qui contrôlent le fonctionnement des écosystèmes, comme l’illustrent mes résultats le long de gradients de nutriments sur la transition entre régimes de succession ou encore l’émergence de culs-de-sac trophiques. / As living organisms, plants present a dual relationship with their biotic and abiotic environment. The environment selects plant strategies that can establish, and selected strategies in turn impact and shape the environment as they spread. When fueled by variation ,this environmental feedback loop drives evolution, community assembly and ecosystem development, and eventually determines the emergent properties of ecosystems.Theoretical ecology approaches have long recognized this duality, as it is at the core of contemporary niche theory through the concepts of requirement and impact niche. Similarly, game-theoretical approaches such as adaptive dynamics have emphasized the role played by the environmental feedback loop in driving eco-evolutionary dynamics. However, niche theory could benefit from a more individualistic, selection based perspective, while adaptive dynamics could benefit from niche theory’s duality and graphical approach.In my dissertation, I unify these theoretical perspectives and apply them to various ecological situations in an attempt to understand how the reciprocal interaction between plants and their environment determines plant adaptive traits and emergent ecosystem functions.First, I introduce a general and rigorous mathematical framework to contemporary niche theory and the associated graphical approach. By extending these ideas to a continuum of interacting strategies using geometrical envelopes, I show how contemporary niche theory enables the study of both eco-evolutionary dynamics and community assembly through species sorting. I show how these two perspectives only differ by the range of invaders considered, from infinitesimally similar mutants to any strategy from the species pool. My results also emphasize the fact that selection only acts on the requirement niche, evolution of the impact niche being just an indirect consequence of the former.Second, I use this approach to study the evolution of plant defenses against herbivores along a nutrient gradient, by considering the joint evolution of resource acquisition, tolerance and resistance to herbivores. I show that trophic transfers lead to the selection of very competitive, undefended strategies in nutrient-poor environments, while defended strategies -- either resistant, tolerant or the coexistence of both -- always dominate in nutrient-rich environments. My results highlight the central, and often underestimated, role played by plant-environment feedbacks in shaping plant defense patterns.Third, I extend contemporary niche theory to facilitation originating from positive environmental feedback loops. I use these new tools to show how colonization of a bare substrate by a community of nitrogen-fixing plants coupled with nutrient recycling can lead to facilitative succession. Contrarily to previous competition-based succession models, I point out that facilitative succession leads to autogenic ecosystem development, relatively ordered trajectories and late succession bistability between the vegetated ecosystem and the bare substrate. By showing how facilitative succession can turn into competition-based succession along an increasing nitrogen gradient, I derive a new resource-ratio theory of succession.Overall, these new theoretical developments demonstrate that niche theory can be adapted to study a broad range of ecological situations, from facilitation to eco-evolutionary dynamics and community assembly. Within this framework, my envelope-based approach provides a powerful tool to scale from the individual level to the ecosystem level, lumping selection-driven species turnover into plastic ecosystem properties. This, is turn, helps describing the emergence at the ecosystem scale of regulation feedback loops that drive ecosystem dynamics and functioning, as exemplified by my results along increasing resource gradients showing a transition from facilitation- to competition-based succession or the emergence of trophic dead-ends.

There is growing concern that the worldwide loss in biodiversity will harm the stability of the ecosystems, and thereby, the carrying capacity and critical ecosystem services the biosphere provides. Phytoplankton (microalgae) in lakes and oceans are arguably the most important primary producers. They are responsible for approximately half of the earth's primary production. However, there is little research into what influences the biodiversity of phytoplankton communities and of those studies the mechanisms for coexistence of phytoplankton have so far almost exclusively been studied on ecological time scales. We, therefore, explored how biodiversity and biomass (a proxy to primary production) of phytoplankton communities respond to co-varied environmental drivers over evolutionary time scales. We model adaptive evolution of phytoplankton' resource use, with a non-dimensionalized model of negatively buoyant phytoplankton inhabiting a partially mixed one-dimensional water column using reaction-advection-diffusion equations. We show that a number of environmental drivers have novel effects on biodiversity and biomass on evolutionary timescales. In contrast with previous non-evolutionary work, we found that decreasing light attenuation or increasing resource use efficiency can result in decreased biomass of plankton communities and nutrient-poor environments. One novel driver of species diversity was the combination of low rates of diffusion with relatively intermediate rates of sinking promote species diversity. Furthermore, we show that the phytoplankton turnover rate affects environmental heterogeneity and is, therefore, a contributing driver to species diversity.The evolution of half saturation constants can produce a variety of biodiversity-ecosystem function patterns as two positive, one unimodal, and one negative association were found when comparing biodiversity-ecosystem function. Collectively, our analyses suggest that environmental drivers can have substantially different effects over evolutionary timescales than those effects ecological modeling has previously shown.

Die vorliegende Arbeit behandelt das biologische Phänomen der Dormanz mit Hilfe mathematischer Modellierung. Dormanz beschreibt dabei einen reversiblen Zustand von Individuen, in dem die metabolische Aktivität reduziert wird und die Resistenz gegen Natureinflüsse erhöht ist. Der erste Teil der Arbeit widmet sich den ökologischen Eigenschaften. Hier wird zunächst ein Moranmodell vorgestellt, welches verschiedene Modellierungsarten von Dormanz aus der Populationsgenetik vereint und unter verschiedenen Skalierungen den schwachen seed-bank Koaleszenten und den starken seed-bank Koaleszenten als anzestralen Prozess innehat. Dadurch werden die Parameter der Koaleszenten vergleichbar. Als Anwendung betrachten wir die sogenannte species abundance distribution, welche mithilfe von Koaleszenten beschrieben werden kann. Der zweite Teil beschäftigt sich mit den Auswirkungen von Dormanz auf evolutionäre Eigenschaften und beginnt mit einer Einführung in die Theorie von adaptive dynamics. Dort werden auch verschiedene Möglichkeiten der Modellierung von Dormanz in individuenbasierten Modellen besprochen. Danach befassen wir uns mit der Erweiterung eines Modells für sympatrische Speziation um den Aspekt der Dormanz. Die canonical equation of adaptive dynamics wird - motiviert durch ein Modell mit Dormanz - für schnellere Mutationsraten aus dem sogenannten power-law Mutationsregime für einen Grenzfall hergeleitet. Die Arbeit schließt mit dem dritten Teil, in welchem ein individuenbasiertes Modell für die Entwicklung von Krebs unter dem Einfluss von Chemotherapie und unter Berücksichtigung von Dormanz vorgestellt wird. In Simulationsstudien wird untersucht, inwiefern Dormanz zu Misserfolg einer Therapie beiträgt. Ein weiteres Ziel ist die Analyse von Kombinationsbehandlung mit einem Medikament welches mit dormanten Zellen interagieren kann insbesondere unter Betrachtung verschiedener Therapieansätze zur Behandlung von dormanten Krebszellen. / The present thesis uses mathematical modelling to investigate the consequences of dormancy. Dormancy describes a reversible and protected state of reduced metabolic activity which enhances an individual's resilience to hazardous conditions. In this sense, dormancy acts as a protection mechanism against habitats with unfavourable environments. The thesis considers the impact of dormancy on ecological, evolutionary and in its broadest sense pathogenic properties of microbial populations. The first part is concerned with studying the impact of dormancy on ecology. For this, a Moran model is presented which unifies different models of dormancy from population genetics and exhibits the weak seed-bank coalescent and the strong seed-bank coalescent as the scaling limit of the ancestral process. As an application we consider the species abundance distribution which can be described using coalescent theory. In the second part we consider the influence of dormancy on evolutionary properties. The modelling framework for this is the theory of adaptive dynamics. We then show that competition-induced dormancy may favour sympatric speciation. A key aspect in the derivation of this result is the canonical equation of adaptive dynamics. We extend this equation - motivated by a model including dormancy - to power-law mutations in a limiting case. We conclude the thesis with the third part where we provide an individual-based model for the treatment of cancer with chemotherapy under consideration of dormant cancer cells. Using simulation studies, we investigate how dormancy may contribute to treatment failure. Another goal of this chapter is to analyse combination treatment with a drug which directly targets dormant cancer cells and to formulate general observations regarding various strategies to counter cancer cell dormancy.

Cette thèse est divisée en deux parties reliées par un même fil conducteur. Elle porte sur l'étude théorique et l'application de modèles mathématiques décrivant des dynamiques de population où les individus se reproduisent et meurent à des taux dépendant de leur âge et d'un trait phénotypique. Le trait est fixé durant la vie de l'individu. Il est modifié au fil des générations par des mutations apparaissant lors de la reproduction. On modélise la sélection naturelle en introduisant un taux de mortalité densité-dépendant décrivant la compétition pour les ressources.Dans une première partie, nous nous intéressons au comportement en temps long d'une équation aux dérivées partielles de sélection-mutation structurée en âge décrivant une grande population d'individus. En étudiant les propriétés spectrales d'une famille d'opérateurs positifs sur un espace de mesures, nous montrons l'existence de mesures stationnaires pouvant admettre des masses de Dirac en les traits maximisant la fitness. Lorsque ces mesures admettent une densité continue, nous montrons la convergence des solutions vers cet (unique) état stationnaire.La seconde partie de cette thèse est motivée par un problème issu de la biologie du vieillissement. Nous voulons comprendre l'apparition et le maintien au cours de l'évolution d'un marqueur de sénescence observé chez l'espèce Drosophila melanogaster. Pour cela, nous introduisons un modèle individu-centré décrivant la dynamique d'une population structurée par l'âge et par le trait d'histoire de vie suivant : l'âge de fin de reproduction et celui où la mortalité devient non-nulle. Nous modélisons également l'effet Lansing, qui est l’effet suivant lequel « la descendance de parent jeune vit plus longtemps que celle de parents vieux » . Nous montrons, sous des hypothèses de grande population et de mutations rares, que l'évolution amène ces deux traits à coïncider. Pour cela, nous sommes amenés à étendre l'équation canonique de la dynamique adaptative à une situation où le gradient de fitness n'admet pas des propriétés de régularité suffisantes. L'évolution du trait n'est plus décrite par la trajectoire (unique) d'une équation différentielle ordinaire mais par un ensemble de trajectoires solutions d'une inclusion différentielle. / This thesis is divided into two parts connected by the same thread. It concerns the theoretical study and the application of mathematical models describing population dynamics. The individuals reproduce and die at rates which depend on age a and phenotypic trait. The trait is fixed duringthe life of the individual. It is modified over generations by mutations appearing during reproduction. Natural selection is modeled by introducing a density-dependent mortality rate describing competition for resources.In the first part, we study the long-term behavior of a selection-mutation partial differential equation with age structure describing such a large population. By studying the spectral properties of a family of positive operators on a measures space, we show the existence of stationary measures that can admit Dirac masses in traits maximizing fitness. When these measures admit a continuous density, we show the convergence of the solutions towards this (unique) stationary state.The second part of this thesis is motivated by a problem from the biology of aging. We want to understand the appearance and maintenance during evolution of a senescence marker observed in the species Drosophila melanogaster. For this, we introduce an individual-based model describing the dynamics of a population structured by age and by the following life history trait: the age of reproduction ending and the one where the mortality becomes non-zero. We also model the Lansing effect, which is the effect through which the “progeny of old parents do not live as long as those of young parents”. We show, under large population and rare mutation assumptions, that the evolution brings these two traits to coincide. For this, we are led to extend the canonical equation of adaptive dynamics to a situation where the fitness gradient does not admit sufficient regularity properties. The evolution of the trait is no longer described by the (unique) trajectory of an ordinary differential equation but by a set of trajectories solutions of a differential inclusion.