Individual-based models have been applied to study a broad spectrum of problems across multiple disciplines, such as the spread of epidemics or the outcome of social dilemma. They are used to investigate the macroscopic effects that arise from the microscopic dynamics of interacting individuals. Fixation describes the taking over of the population by a single type of individual or species. It is a prominent feature in the field of population genetics, which interprets many biological scenarios of evolution. Equilibration describes the process of reaching a heterogeneous steady state. In this thesis we analyse these macroscopic features through techniques derived from statistical physics and the theory of stochastic processes. Birth-death processes are used to describe the interaction of two types of individual in a population, such as competing strains of bacteria. These interactions are often specified using the framework of evolutionary game theory. The environment in which the population evolves can have a crucial impact on selection. In systems where the environment switches between multiple states we develop a general theory to calculate the fixation time statistics of a mutant individual in a population of wild-types, as well as the stationary distributions when mutations are present in the dynamics. In some birth--death processes, and in particular those described by evolutionary game theory, the mean fixation time contains only limited information. By diagonalising the master equation that describes the process, we are able to obtain closed-form expressions for the complete fixation time distributions. Individual-based models can also be used to describe the accumulation of mutations in a cell. This has important consequences for the initiation and progression of cancer. We find that such systems exhibit metastable states in the dynamics, and we can exploit the separation of timescales between relaxing to the quasi-stationary state and reaching fixation to characterise these phenomena. In this scenario we employ the WKB method to describe the population-level dynamics. Although this method has been used to describe numerous stochastic processes, a clear and coherent description is lacking in the literature. Through the use of multiple examples, including the aforementioned cancer initiation model, we carefully explain the multitude of constructs and equations that result from the application of this methodThe analytical characterisation of the evolutionary dynamics that are observed in these stochastic processes has resulted in a greater understanding of fixation and equilibration. This thesis promotes the benefits of analytical, or even semi-analytical methods, and on a more general level contributes toward a more complete understanding of evolutionary processes.

Les forces de sélection sont un des moteurs de l’évolution de la diversité phénotypique et de la diversité génétique neutre et des zones codantes du génome. Cette sélection peut s’appliquer sur des caractères transmis génétiquement ou culturellement. Le travail effectué s’intéresse à ces deux processus de sélection. Nous avons étudié dans un premier temps les effets de la transmission intergénérationnelle de la fécondité sur la diversité génétique neutre puis dans un deuxième temps l’impact de la sélection sur des phénotypes codés par des réseaux de gènes sur le polymorphisme de ces gènes.La transmission de la fécondité est un phénomène culturel ou génétique qui se caractérise par une corrélation positive entre la taille de fratrie d’un individu et la taille de fratrie de ses enfants. Il a été observé tant dans des populations humaines qu’animales. Nous montrons, par l’outil de la modélisation, que ses effets et la possibilité de le détecter dépendent autant du type de données étudiées (génétiques ou généalogiques), que des différents types de transmission (uniparentale, biparentale). Nous montrons que d’autres phénomènes, tels que l’hétérogénéité du succès reproducteur des individus, peuvent fortement moduler son impact. Nous développons un certain nombre d’outils permettant de détecter ce phénomène de transmission de la fécondité tant sur des données généalogiques que sur des données génétiques relevant de différents modèles mutationnels (microsatellite, séquences, SNPs) et de différents types de transmission (haploïde ou diploïde, lié au sexe ou non). Nous avons appliqué ces outils notamment à trois populations humaines du Cilento en Italie (généalogies et ADN mitochondrial), des données d’Asie Centrale (chromosome Y) et des données HapMap (autosomes).La seconde partie de la thèse porte sur la modélisation de l’action de la sélection naturelle sur des caractères codés par des réseaux de régulation et décrit l’impact de ce type de sélection sur l’évolution du phénotype et sur la diversité des gènes sous-jacents. Un phénotype est le résultat des interactions entre différents gènes et leurs produits. Nous montrons que la sélection sur ce phénotype va modifier l’organisation du réseau de gènes ainsi que le niveau de polymorphisme des gènes du réseau. Par exemple, lorsque le phénotype optimal correspond à une expression médiane des gènes, les gènes les plus régulateurs vont être soumis à une plus forte perte de diversité. En revanche, si le phénotype optimal correspond à une expression très forte, ce sont les gènes les plus régulés qui vont être les plus contraints. Cette analyse a permis de montrer la complexité des relations entre sélection, réseaux de régulation, phénotypes et environnement. / Selective forces are one of the major determinants of the evolution of phenotypic diversity and genetic diversity, in neutral and coding zones of the genome. Selection can occur on genetically - or culturally - transmitted traits. This thesis considers these two selective processes. First, we studied the effects of intergenerational fertility transmission on neutral genetic diversity. Second, we considered the impact of selection on phenotypes coded by a gene network and on the polymorphism of genes within the network.Fertility transmission is a cultural or genetic phenomenon, which is characterised by a positive correlation between the sibship size of an individual and that of its children. It was observed both in human and animal populations. Using a modelling approach, we show that its effects and the possibility to detect it depend both on the kind of studied data (genetic or genealogical data) and on the different kind of transmission (uniparental, biparental). We show that other phenomena, such as the heterogeneity of reproductive success between individuals, can affect its effects. We develop several tools allowing to infer this phenomenon of fertility transmission on genealogical data, as well as on genetic polymorphism data that follows different mutational models (microsatellites, sequences, SNPs) and different transmission modes (haploid or diploid, sex-linked or not). We applied in particular these tools to three human populations of the Cilento area in Italy (genealogical and mitochondrial DNA data), to Central Asian data (Y chromosome) and to HapMap data (autosomes).The second part of this thesis deals with the modelling of the action of natural selection on traits coded by regulation networks and describes the impact of such selection on the evolution of the phenotype and of the underlying genes. A given phenotype is the result of the interaction between different genes and their products. We show that phenotypic selection will modify the gene network organisation, as well as the level of polymorphism of the genes involved in the network. For example, when the optimal phenotype corresponds to an intermediate level of gene expression, the most regulatory genes will lose much of their diversity. Conversely, if the optimal phenotype corresponds to a very strong expression of the genes, it will be the most regulated genes that will be the most constrained. This analysis allowed us to show the complexity of the relations between selection, regulation networks, phenotypes and the environment.

No description available.

This dissertation examines aspects of the relationship between connectivity and the development of genetic structure in subdivided coral reef populations using both simulation and algebraic methods. The first chapter develops an object-oriented, individual based method of simulating the dynamics of genes in subdivided populations. The model is then used to investigate how changes to different components of population structure (e.g., connectivity, birth rate, population size) influence genetic structure through the use of autocorrelation analysis. The autocorrelograms also demonstrate how relationships between populations change at different spatial and temporal scales. The second chapter uses discrete multivariate distributions to model the relationship between connectivity, selection and resource use in subdivided populations. The equations provide a stochastic basis for multiple-niche polymorphism through differential resource use, and the role of scale in changing selective weightings is also considered. The third chapter uses matrix equations to study the expected development of genetic structure among Caribbean coral reefs. The results show an expected break between eastern and western portions of the Caribbean, as well as additional nested structure within the Bahamas, the central Caribbean (Jamaica and the reefs of the Nicaraguan Rise) and the Mesoamerican Barrier Reef. The matrix equations provide an efficient means of modeling the development of genetic structure in subdivided populations through time. The fourth chapter uses matrix equations to examine the expected development of genetic structure among Southeast Asian coral reefs. Projecting genetic structure reveals an expected unidirectional connection from the South China Sea into the Coral Triangle region via the Sulu Sea. Larvae appear to be restricted from moving back into the South China Sea by a cyclonic gyre in the Sulu Sea. Additional structure is also evident, including distinct clusters within the Philippines, in the vicinity of the Makassar Strait, in the Flores Sea, and near Halmahera and the Banda Sea. The ability to evaluate the expected development of genetic structure over time in subdivided populations offers a number of potential benefits, including the ability to ascertain the expected direction of gene flow, to delineate natural regions of exchange through clustering, or to identify critical areas for conservation or for managing the spread of invasive material via elasticity analysis.

La malària és encara avui en dia una malaltia que causa aproximadament un milió de morts a l'any a tot el món. La seva eradicació suposa un gran repte per a la humanitat i per a la comunitat científica, en particular. El cultiu in vitro del paràsit és essencial per al desenvolupament de nous medicaments. Els mètodes de cultiu actuals es basen en l'heurística i requereixen millores.En aquesta tesi es presenta una aproximació teòrica al procés d'infecció a eritròcits en cultius in vitro amb Plasmodium falciparum, un dels protozous paràsits causants de la malària. El treball està centrat en la construcció i avaluació de models d'una complexitat adequada per tractar els problemes específics detectats pels experts en l'àmbit, i inclou també la formulació d'algorismes de simulació i el disseny de protocols experimentals.Aquest tipus de treball requereix de la col·laboració multidisciplinària. La visió dels experts en malària es complementa amb la modelització i simulació, que permet la comprovació dels supòsits preestablerts, la comprensió de fenòmens observats i la millora dels mètodes de cultiu actuals. Així doncs, cal establir i desenvolupar eines que permetin crear, analitzar i compartir models amb grups que estudien la malària des d'altres perspectives. En aquesta tesi, s'ha optat per la modelització basada en l'individu (IbM) i orientada a la reproducció de múltiples patrons (PoM). El model s'ha formulat seguint l'ODD, un protocol estàndard en el camp de l'ecologia teòrica, que s'ha adaptat a la representació de comunitats microbianes.Els models basats en l'individu (IbMs) defineixen un conjunt de normes que regeixen el comportament de cada cèl·lula i les seves interaccions amb les altres cèl·lules i amb el seu entorn immediat. A partir d'aquestes regles, i tenint en compte una certa diversitat dins de la població i un cert grau d'aleatorietat en els processos individuals, els IbMs mostren explícitament el comportament emergent del sistema en conjunt. Complementàriament, s'han aplicat conceptes propis de la termodinàmica per tal d'entendrel'aparició de patrons macroscòpics a partir de l'estructura de la població (per exemple de la distribució de les fases d'infecció entre els glòbuls vermells infectats).Aquesta recerca ha comportat la la creació i aplicació del model i simulador INDISIM-RBC, que ha demostrat ser una bona eina per millorar la comprensió dels cultius estudiats. Es tracta d'un model mecanicista, basat en l'individu, que reprodueix quantitativament els patrons observats en cultius reals a diferents nivells de descripció, i que en prediu el comportament sota determinades condicions.Hem demostrat que INDISIM-RBC pot ser emprat per a estudiar en detall alguns aspectes del cultiu del paràsit causant de la malària que calia aclarir. Permet realitzar experiments virtuals i així impulsar noves línies de recerca i explorar noves tècniques de cultiu. En particular, INDISIM-RBC s'ha utilitzat per millorar els protocols experimentals actuals del cultius estàtics, definint la geometria òptima de l'hematòcrit i els protocols de subcultiu més adequats per als cultius continus.El treball realitzat en malària s'ha comparat amb la investigació duta a terme pel grup de recerca em relació amb d'altres comunitats microbianes. D'aquesta manera, podem estudiar les propietats emergents dels sistemes microbians en general en relació als efectes de la individualitat de la cèl·lula, la diversitat de les poblacions, l'heterogeneïtat en el medi, o el caràcter local de les interaccions, entre d'altres. Aquesta visió general proporciona eines conceptuals que poden ser emprades per refinar l'anàlisi dels processos d'infecció sota estudi. / Malaria is still a major burden that causes approximately one million deaths annually worldwide. Its eradication supposes a great challenge to the humanity and to the scientific community, in particular. In vitro cultivation of the parasite is essential for the development of new drugs. Current culture methods are based on heuristics and demand for specific improvements.The present thesis is a theoretical approach to in vitro cultivation of the protozoan parasite Plasmodium falciparum infecting human red blood cells. It mainly focuses on the process of building a model of appropriate complexity to deal with the specific demands above mentioned, but it also includes the formulation and implementation of algorithms, and the design and execution of experimental trials.This kind of work requires multidisciplinary collaboration: the insight of the experts in malaria research is complemented with modeling and simulation, which allows for checking settled assumptions, increasing the understanding on the system and improving the current culturing methods.The use of tools for building, analyzing and sharing models is an imperative to this end. In this thesis, Pattern-oriented Modeling (PoM) has been adopted as the most appropriate way for raising of models and the ODD protocol (Objectives, Design Concepts and Details) has been proposed as the standard tool for communicating them.Individual-based Modeling (IbM) has been used to tackle malaria culture systems. IbMs define a set of rules governing each cell, its interactions with others and with its immediate surroundings. From this set of rules, and taking into account diversity within the population and a certain degree of randomness in the individual processes, IbMs explicitly show the emerging behavior of the system as a whole. Methods from statistical thermodynamics have been applied to understand the emergence of macroscopic patterns from the population structure (e.g. distribution of infection stages among infected red blood cells).The research resulted in the development of the model and simulator INDISIM-RBC, which has proved to be a good tool to improve understanding of the cultures under study. It is a mechanistically rich individual-based model and it quantitatively reproduces and predicts several patterns observed in real cultures at different levels of description.We demonstrated that INDISIM-RBC can be used to study in detail several aspects of malaria cultivation that remained unclear, as well as to perform virtual experiments. Consequently, it can be used to open novel lines of research and to examine potential experimental techniques. INDISIM-RBC has also been used to improve the current experimental culturing protocols in static cultivation by obtaining the optimal geometry of the hematocrit layer and subcultivation periods in the continuous cultures.This study on malaria has been compared to the research carried out by the group regarding other microbial communities. Thereby studying general emerging properties of microbial systems in general, with regard to the effect of cell individuality, heterogeneity and diversity, the local nature of interactions; and biological and spatial complexity. In doing so, the acquired holistic view has been used to develop tools that allow for a better characterization and study of the infection process, in particular.

No description available.

O objetivo geral desta tese foi investigar como a distribuição espacial dos indivíduos influencia a organização dos sistemas de acasalamento e a intensidade da seleção sexual. A tese contém dois capítulos em que analisamos dados empíricos e dois capítulo em que abordamos questões mais teóricas mais gerais. No primeiro capítulo, avaliamos como a distribuição espacial de haréns defendidos por machos territoriais influencia a rede de competição espermática que existe entre machos do opilião Serracutisoma proximum. No segundo capítulo, propusemos um modelo probabilístico de escolha de parceiros que leva em consideração o fato de que as fêmeas estão restritas a amostrar apenas alguns machos da população, e que essa restrição é imposta principalmente pela distribuição espacial dos indivíduos. Nosso modelo foi mais acurado do que modelos alternativos que ignoram o espaço. No terceiro capítulo, investigamos os movimentos de busca de parceiros do besouro Leptinotarsa undecimlineata. Encontramos que tanto machos quanto fêmeas se movimentam estrategicamente, saindo de onde estão quando não obtém cópulas buscando áreas próximas e com muitos parceiros em potencial. Finalmente, no quarto capítulo, voltamos a explorar o efeito de restrições espaciais sobre a escolha de parceiros. Usamos simulações baseadas em indivíduos para investigar como a restrição espacial influencia a seleção sexual e a evolução de ornamentos sexualmente selecionados. Encontramos que quanto maior o número de parceiros que as fêmeas podem amostrar durante a escolha, mais intensa é a seleção sexual, o que permite a evolução de ornamentos mais exagerados nos machos. Além disso, analisamos um conjunto de dados publicados sobre a intensidade de seleção sexual e observamos que estes se ajustam às previsões do modelo teórico. Concluímos que o espaço é muito mais importante para a organização de sistemas de acasalamento e para a intensidade da seleção sexual do que se acreditava previamente. Esperamos que as idéias propostas aqui encontrem terreno fértil na mente do leitor e que gerem novos e estimulantes desdobramentos no campo teórico e empírico / The main goal of this thesis was to investigate how the spatial distribution of individuals influences the organization of the mating systems and the intensity of sexual selection. The thesis contains two empirical chapters and two chapters with a theoretical scope. In the first chapter, we investigate how the spatial distribution of harems defended by territorial males influences the sperm competition network among males of the harvestman Serracutisoma proximum. In the second chapter, we proposed a probabilistic model of mate choice that includes the spatial constraint in the analyses of mate choice. This model takes into account the fact that females are restricted to sample only some males available in the population, and that this restriction is imposed primarily by the spatial distribution of individuals. In the third chapter, we investigate the mate searching movements of the leaf beetle Leptinotarsa undecimlineata. We found that both males and females move strategically, leaving the host plant when they do not obtain copulations and seeking neighboring areas with many potential mates. Finally, in the fourth chapter, we explore the effect of spatial restrictions on mate choice. We used individual based simulations to investigate how spatial restrictions influence sexual selection and the evolution of sexually selected ornaments. We found that the higher the number of potential partners female can sample during mate choice, the more intense is sexual selection, which leads to the evolution of more exaggerated male ornaments. In addition, we analyzed a published dataset of intensity of sexual selection and found that the data adjust to the predictions made by our simulations. We conclude that the space is much more important than previously thought to mating systems organization and the intensity of sexual selection. We hope the ideas proposed here can flourish in the minds of the readers, stimulating both empirical and theoretical follow ups

Cette thèse s'inscrit dans le cadre de la modélisation de systèmes biologiques complexes. En premier lieu (travail en collaboration avec l'équipe de biologistes de Louis Casteilla), nous introduisons un modèle individus-centré pour étudier l'émergence de structures cellulaires de forme lobulaire dans un réseau organisé de fibres. Une étude paramétrique sur les résultats numériques ainsi que des méthodes de traitement d'images sur les données biologiques nous permettent de montrer que l'émergence de structures biologiquement cohérentes peut être reproduite par un modèle basé essentiellement sur des règles mécaniques entre les cellules et le réseau de fibres. L'originalité de ce modèle réside dans la modélisation de structures géométriques complexes (réseaux de fibres) par un ensemble d'unités élémentaires connectées interagissant à l'aide de fonctionnelles simples. Cette nouveauté a donné lieu à d'autres types de travaux en cours présentés comme perspectives directes de ce travail. Les deuxième et troisième parties portent sur la dérivation d'un modèle cinétique puis macroscopique pour étudier la matrice extra-cellulaire dans sa globalité. L'originalité de notre résultat réside dans l'obtention d'un système d'équations fermé décrivant l'évolution de la distribution des fibres individuelles et des liens de fibres. La limite hydrodynamique de l'équation cinétique est obtenue à l'aide de techniques non conventionnelles dû au un manque d'équation de conservation pour le système étudié. Dans le cas d'une densité homogène de fibres, nous prouvons l'existence de solutions au modèle macroscopique, et les simulations numériques montrent une bonne correspondance entre le modèle macroscopique et son homologue microscopique. Finalement (travail en collaboration avec S. Motsch), nous nous intéressons à l'influence d’interactions de type répulsion cellules-cellules dans un modèle de croissance tumorale. Nous montrons que le modèle macroscopique dérivé des équations microscopiques fait apparaître une instabilité et proposons une version modifiée de l'équation macroscopique que nous sommes capables de relier à la dynamique cellulaire. Les simulations numériques montrent la bonne correspondance entre les deux modèles. / In a first part (work in collaboration with the team of biologists of L. Casteilla) we propose an Individual based model for studying the emergence of lobule-like structures of cells in an organized fiber network. A parametric analysis on the numerical results as well as image processing methods on the biological images enable us to show that biologically-relevant structures can be reproduced by a model mostly based on cell-fiber mechanical interactions. The originality of this model mainly relies in the modelling of complex geometrical structures such as fiber networks as sets of connected elementary units interacting through simple functionals. This novelty has been used to build other types of models presented as direct perspective of this work. The second and third parts lie in the derivation of kinetic and macroscopic models for an interconnected fiber network, closely linked to the microscopic one. The originality of this work lies in the obtained closed system of two evolution equations: one for the distribution of individual fibers and one for the fiber links. In the case of homogeneous fiber density, we show existence of stationary solutions to the macroscopic equation, and numerical simulations show the good correspondence between the microscopic and macroscopic models. Finally (work in collaboration with S. Motsch), we are interested in the role of cell-cell interactions in the invasion properties (speed, geometry...) of a growing mass of cells. We show that the macroscopic model derived from the microscopic one features instabilities, and we propose a modified macroscopic model that we are able to link to the particle dynamics. The numerical simulations show the relevance of the macroscopic model to describe the microscopic dynamics at large scale.

O objetivo geral desta tese foi investigar como a distribuição espacial dos indivíduos influencia a organização dos sistemas de acasalamento e a intensidade da seleção sexual. A tese contém dois capítulos em que analisamos dados empíricos e dois capítulo em que abordamos questões mais teóricas mais gerais. No primeiro capítulo, avaliamos como a distribuição espacial de haréns defendidos por machos territoriais influencia a rede de competição espermática que existe entre machos do opilião Serracutisoma proximum. No segundo capítulo, propusemos um modelo probabilístico de escolha de parceiros que leva em consideração o fato de que as fêmeas estão restritas a amostrar apenas alguns machos da população, e que essa restrição é imposta principalmente pela distribuição espacial dos indivíduos. Nosso modelo foi mais acurado do que modelos alternativos que ignoram o espaço. No terceiro capítulo, investigamos os movimentos de busca de parceiros do besouro Leptinotarsa undecimlineata. Encontramos que tanto machos quanto fêmeas se movimentam estrategicamente, saindo de onde estão quando não obtém cópulas buscando áreas próximas e com muitos parceiros em potencial. Finalmente, no quarto capítulo, voltamos a explorar o efeito de restrições espaciais sobre a escolha de parceiros. Usamos simulações baseadas em indivíduos para investigar como a restrição espacial influencia a seleção sexual e a evolução de ornamentos sexualmente selecionados. Encontramos que quanto maior o número de parceiros que as fêmeas podem amostrar durante a escolha, mais intensa é a seleção sexual, o que permite a evolução de ornamentos mais exagerados nos machos. Além disso, analisamos um conjunto de dados publicados sobre a intensidade de seleção sexual e observamos que estes se ajustam às previsões do modelo teórico. Concluímos que o espaço é muito mais importante para a organização de sistemas de acasalamento e para a intensidade da seleção sexual do que se acreditava previamente. Esperamos que as idéias propostas aqui encontrem terreno fértil na mente do leitor e que gerem novos e estimulantes desdobramentos no campo teórico e empírico / The main goal of this thesis was to investigate how the spatial distribution of individuals influences the organization of the mating systems and the intensity of sexual selection. The thesis contains two empirical chapters and two chapters with a theoretical scope. In the first chapter, we investigate how the spatial distribution of harems defended by territorial males influences the sperm competition network among males of the harvestman Serracutisoma proximum. In the second chapter, we proposed a probabilistic model of mate choice that includes the spatial constraint in the analyses of mate choice. This model takes into account the fact that females are restricted to sample only some males available in the population, and that this restriction is imposed primarily by the spatial distribution of individuals. In the third chapter, we investigate the mate searching movements of the leaf beetle Leptinotarsa undecimlineata. We found that both males and females move strategically, leaving the host plant when they do not obtain copulations and seeking neighboring areas with many potential mates. Finally, in the fourth chapter, we explore the effect of spatial restrictions on mate choice. We used individual based simulations to investigate how spatial restrictions influence sexual selection and the evolution of sexually selected ornaments. We found that the higher the number of potential partners female can sample during mate choice, the more intense is sexual selection, which leads to the evolution of more exaggerated male ornaments. In addition, we analyzed a published dataset of intensity of sexual selection and found that the data adjust to the predictions made by our simulations. We conclude that the space is much more important than previously thought to mating systems organization and the intensity of sexual selection. We hope the ideas proposed here can flourish in the minds of the readers, stimulating both empirical and theoretical follow ups

An object-oriented framework is presented for developing and simulating individual-based models of cell populations. The framework supplies classes to define objects called simulation channels that encapsulate the algorithms that make up a simulation model. These may govern state-updating events at the individual level, perform global state changes, or trigger cell division. Simulation engines control the scheduling and execution of collections of simulation channels, while a simulation manager coordinates the engines according to one of two scheduling protocols. When the ensemble of cells being simulated reaches a specified maximum size, a procedure is introduced whereby random cells are ejected from the simulation and replaced by newborn cells to keep the sample population size constant but representative in composition. The framework permits recording of population snapshot data and/or cell lineage histories. Use of the framework is demonstrated through validation benchmarks and two case studies based on experiments from the literature.