Compreender como as espécies interagem e como a topologia de redes ecológicas influencia a dinâmica de populações e comunidades tem sido um dos principais objetivos de estudos ecológicos há mais de um século. Apesar desta longa tradição, o estudo de redes ecológicas tem aumentado drasticamente nas últimas duas décadas. No entanto, só recentemente ecólogos começaram a ir além da descrição de padrões topológicos e passaram a integrar outros dados biológicos importantes, como características funcionais e filogenia. Esta tese teve principalmente dois objetivos: i) desenvolver novas abordagens analíticas capazes de integrar informações funcionais e filogenéticas, a fim de descrever padrões estruturais em redes ecológicas, e ii) compreender a influência de dinâmicas eco-evolutivas na robustez de redes mutualísticas. No Capítulo I, desenvolvi uma abordagem analítica integradora para particionar os efeitos da filogenia e de características funcionais sobre a estrutura de redes de interação biótica. O método combina Teoria de Conjuntos Difusos e correlação matricial. Eu também desenvolvi um estudo de simulação para testar a acurácia da metodologia proposta em termos de Erro Tipo I. As simulações demonstram que o método é acurado, ou seja, rejeita incorretamente uma hipótese nula verdadeira em ~ 5% dos casos. No Capítulo II, investiguei como diferentes cenários de extinção afetam a robustez de uma rede de dispersão de sementes do sul do Brasil, incluindo cenários onde as espécies são eliminadas com base em sua distinção evolutiva e funcional. Os resultados indicam que a perda de espécies generalistas e diversidade funcional faz com que rede seja mais propensa a colapsar. No Capítulo III, desenvolvi uma investigação teórica sobre a influencia de diferentes modos de evolução de atributos sobre a robustez de redes mutualísticas que estão sofrendo um ataque funcional. Os resultados mostram que, apesar da pequena faixa de variação na robustez das redes, o modo de evolução dos atributos, e a interação entre modos de evolução de cada conjunto de espécies que interagem, influenciam a robustez de redes ecológicas, especialmente em casos extremos, onde os atributos das espécies apresentam sinal filogenético muito baixo ou muito forte. / Understanding how species interact and how the topology of ecological networks influences the dynamics of populations and communities has been mindboggling ecologists for over a century now. Despite this long tradition, the study of complex ecological networks has increased dramatically in the past two decades. Nonetheless, only recently ecologists have started to move beyond the description of topological patterns and started to integrate other important biological data, such as functional traits and phylogenies. Therefore, the aim of this dissertation was mainly two-fold: develop new analytical approaches capable to integrate functional and phylogenetic information in order to describe structural patterns in ecological networks, and to understand the effects of ecoevolutionary dynamics on network robustness. In Chapter I, I developed a new and integrative analytical framework to partition the effects of phylogenies and functional traits on the structure of ecological networks. The method combines fuzzy set theory and matrix correlation. I also developed a simulation study to test the accuracy of the framework I proposed. My simulation study demonstrates that the method is accurate, i.e., incorrectly rejecting a true null hypothesis in ~ 5%. In Chapter II, I investigated how different extinction scenarios affect the robustness of a seed dispersal network, from southern Brazil, including scenarios where species are eliminated based on their evolutionary and functional distinctiveness. The results indicate that loss of generalist species and functional diversity makes the system more likely to collapse. In Chapter III, I developed a theoretical investigation of the role of distinct trait evolution modes on the robustness of mutualistic networks undergoing functional trait extinctions. My results show that, despite the small range of variation in network robustness, the mode of trait evolution alone and the interaction between modes of evolution of each set of interacting species matter for network robustness, especially in extreme cases, where species traits present either very low or very strong phylogenetic signal.

A homomorphism from a graph G to a graph H is a function from V (G) to V (H) that preserves edges. Many combinatorial structures that arise in mathematics and in computer science can be represented naturally as graph homomorphisms and as weighted sums of graph homomorphisms. In this thesis we study the complexity of various problems related to graph homomorphisms.

The demand for information in a systematic way about ecology of target insect species of transgenic plants has increased in recent decades due to the growing interest in this new technology in pest management. Larval mobility in agricultural ecosystems when on occurrence of contamination of Bt crops, intentionally or unintentionally - has been subject of study by several researchers, however information about larval mobility in tropical conditions are still scarce. This scenario created opportunity for hypothesis testing on behavioural aspects of Spodoptera frugiperda (JE Smith) (Lepidoptera: Noctuidae) in landscapes with spatial-temporal co-occurence of Bt and non-Bt cotton plants. The main objective of the current research was to study the larval dispersal of the pest in field and laboratory conditions in order to insert computational modelling components to describe the evolution of resistance to Bt cotton. In the first chapter of this thesis, it is presented a general introduction. In the second one, we studied the feeding behaviour associated with larval dispersal of S. frugiperda genotypes and possible effects on spatial distribution of the resistant individuals in Bt and non-Bt cotton fields. We analyzed in the third chapter the consequences to resistance progress of the dispersal pattern of susceptible, Cry1F-resistant and heterozygous genotypes of S. frugiperda in pure and contaminated artificial landscapes. In the fourth chapter we assessed the impact of the dispersal by ballooning combined with walking dispersal on resistance evolution in conditions of plant mixture with non-Bt and Bt cotton plants in events with high and non-high dose. In the last chapter, we compared the movement dynamics of S. frugiperda genotypes between 28oC and 32oC, and with an individual-based model we analyzed the possibility if one of the genotypes could persist and would lead the other to the exclusion on refuge areas with non-Bt cotton plants. In a general way, faced on the larval dispersal of S. frugiperda genotypes, the results found here highlight the importance of implementation of strategies to avoid contamination through inadequate agronomic practices such as destruction of cotton plants after harvest, volunteer plant control, and seed saving after harvest. All information generated in this thesis could contribute in the optimization of regional resistance management within a concept of insect population control in wide areas. / A demanda por informações de forma sistematizada sobre ecologia de insetos-praga alvos de plantas transgênicas tem crescido nas últimas décadas devido ao proeminente interesse nesta tecnologia no manejo de pragas. A mobilidade larval em ecossistemas agrícolas quando na ocorrência de contaminação de plantas Bt, de forma intencional ou não intencional, tem sido assunto de estudo por diversos Pesquisadores, entretanto informações sobre a mobilidade larval em condições tropicais são ainda escassas. Este cenário criou oportunidades para testes de hipóteses em aspectos comportamentais de Spodoptera frugiperda (JE Smith) (Lepidoptera: Noctuidae) em paisagens com co-ocorrência espaço-temporal de plantas de algodão Bt e não Bt. O principal objetivo desta pesquisa foi estudar a dispersão larval da praga em condições de campo e de laboratório em ordem para inserir componentes de modelagem computacional para descrever a evolução da resistência ao algodão Bt. No primeiro capítulo desta tese, é apresentada uma introdução geral. No segundo capítulo, foi estudado o comportamento alimentar associado com a dispersão larval de genótipos de S. frugiperda e possíveis efeitos na distribuição espacial de indivíduos resistentes em campos de algodão Bt e não Bt. Foram analisadas no terceiro capítulo as consequências para o progresso da resistência do padrão de dispersão de genótipos suscetíveis, resistentes a Cry1F e heterozigotos de S. frugiperda em paisagens artificiais com pureza e com contaminação. No quarto capítulo, avaliou-se o impacto da dispersão por balonismo combinado dispersão por caminhamento na evolução da resistência em condições de mistura de plantas de algodão não Bt e algodão Bt em eventos com alta e baixa dose. No último capítulo, foi comparada a dinâmica de movimentação de genótipos de S. frugiperda entre as temperaturas de 28°C e 32°C, e com um modelo baseado no indivíduo analisou-se a possibilidade se um dos genótipos poderia persistir e levar o outro a exclusão em áreas de refúgio com plantas de algodão não Bt. Baseado na dispersão larval de genótipos de S. frugiperda, os resultados encontrados ressaltam a necessidade de implementação de estratégias para evitar contaminação por meio de práticas agronômicas inadequadas tais como destruição de plantas após a colheita, controle de plantas voluntárias, e o ato de se salvar as sementes após a colheita. Todas informações geradas nesta tese poderão contribuir para otimização de manejo da resistência regional dentro de um conceito de controle de insetos em grandes áreas.

This work uses mathematical models of evolutionary dynamics to address clinical questions about HIV treatment, public health questions about vaccination, and theoretical questions about evolution of high mutation rates.

Modern-day management of infectious diseases is critically linked to the use of mathematical models to understand and predict dynamics at many levels, from the mechanisms of pathogenesis to the patterns of population-wide transmission and evolution. This thesis describes the development and application of mathematical techniques for HIV infection and dynamics on social networks. Treatment of HIV infection has improved dramatically in the past few decades but is still limited by the development of drug resistance and the inability of current therapies to completely eradicate the virus from an individual. We begin with a synthesis of the important evolutionary principles governing the HIV epidemic, emphasizing the role of modeling. We then describe a modeling framework to study the emergence of drug-resistant HIV within a patient. Our model integrates laboratory data and patient behavior, with the goal of predicting outcomes of clinical trials. Current results demonstrate how pharmacologic properties of antiretroviral drugs affect selection for drug resistance, and can explain drug-class-specific resistance risks. Thirdly, we describe models for a new class of drugs that aim to eliminate cells with latent viral infection. We provide estimates for the required efficacy of these drugs and describe the potential challenges of future clinical trials. Finally, models and mechanisms for understanding viral dynamics are increasingly finding applications outside traditional virology. They can be used to study the dynamics of behaviors, to help predict and intervene in their spread. We describe techniques for applying infectious disease models to social contagion, drawing on techniques for network epidemiology. We use this framework to interpret data on the interpersonal spread of health-related behaviors.

Compreender como as espécies interagem e como a topologia de redes ecológicas influencia a dinâmica de populações e comunidades tem sido um dos principais objetivos de estudos ecológicos há mais de um século. Apesar desta longa tradição, o estudo de redes ecológicas tem aumentado drasticamente nas últimas duas décadas. No entanto, só recentemente ecólogos começaram a ir além da descrição de padrões topológicos e passaram a integrar outros dados biológicos importantes, como características funcionais e filogenia. Esta tese teve principalmente dois objetivos: i) desenvolver novas abordagens analíticas capazes de integrar informações funcionais e filogenéticas, a fim de descrever padrões estruturais em redes ecológicas, e ii) compreender a influência de dinâmicas eco-evolutivas na robustez de redes mutualísticas. No Capítulo I, desenvolvi uma abordagem analítica integradora para particionar os efeitos da filogenia e de características funcionais sobre a estrutura de redes de interação biótica. O método combina Teoria de Conjuntos Difusos e correlação matricial. Eu também desenvolvi um estudo de simulação para testar a acurácia da metodologia proposta em termos de Erro Tipo I. As simulações demonstram que o método é acurado, ou seja, rejeita incorretamente uma hipótese nula verdadeira em ~ 5% dos casos. No Capítulo II, investiguei como diferentes cenários de extinção afetam a robustez de uma rede de dispersão de sementes do sul do Brasil, incluindo cenários onde as espécies são eliminadas com base em sua distinção evolutiva e funcional. Os resultados indicam que a perda de espécies generalistas e diversidade funcional faz com que rede seja mais propensa a colapsar. No Capítulo III, desenvolvi uma investigação teórica sobre a influencia de diferentes modos de evolução de atributos sobre a robustez de redes mutualísticas que estão sofrendo um ataque funcional. Os resultados mostram que, apesar da pequena faixa de variação na robustez das redes, o modo de evolução dos atributos, e a interação entre modos de evolução de cada conjunto de espécies que interagem, influenciam a robustez de redes ecológicas, especialmente em casos extremos, onde os atributos das espécies apresentam sinal filogenético muito baixo ou muito forte. / Understanding how species interact and how the topology of ecological networks influences the dynamics of populations and communities has been mindboggling ecologists for over a century now. Despite this long tradition, the study of complex ecological networks has increased dramatically in the past two decades. Nonetheless, only recently ecologists have started to move beyond the description of topological patterns and started to integrate other important biological data, such as functional traits and phylogenies. Therefore, the aim of this dissertation was mainly two-fold: develop new analytical approaches capable to integrate functional and phylogenetic information in order to describe structural patterns in ecological networks, and to understand the effects of ecoevolutionary dynamics on network robustness. In Chapter I, I developed a new and integrative analytical framework to partition the effects of phylogenies and functional traits on the structure of ecological networks. The method combines fuzzy set theory and matrix correlation. I also developed a simulation study to test the accuracy of the framework I proposed. My simulation study demonstrates that the method is accurate, i.e., incorrectly rejecting a true null hypothesis in ~ 5%. In Chapter II, I investigated how different extinction scenarios affect the robustness of a seed dispersal network, from southern Brazil, including scenarios where species are eliminated based on their evolutionary and functional distinctiveness. The results indicate that loss of generalist species and functional diversity makes the system more likely to collapse. In Chapter III, I developed a theoretical investigation of the role of distinct trait evolution modes on the robustness of mutualistic networks undergoing functional trait extinctions. My results show that, despite the small range of variation in network robustness, the mode of trait evolution alone and the interaction between modes of evolution of each set of interacting species matter for network robustness, especially in extreme cases, where species traits present either very low or very strong phylogenetic signal.

Compreender como as espécies interagem e como a topologia de redes ecológicas influencia a dinâmica de populações e comunidades tem sido um dos principais objetivos de estudos ecológicos há mais de um século. Apesar desta longa tradição, o estudo de redes ecológicas tem aumentado drasticamente nas últimas duas décadas. No entanto, só recentemente ecólogos começaram a ir além da descrição de padrões topológicos e passaram a integrar outros dados biológicos importantes, como características funcionais e filogenia. Esta tese teve principalmente dois objetivos: i) desenvolver novas abordagens analíticas capazes de integrar informações funcionais e filogenéticas, a fim de descrever padrões estruturais em redes ecológicas, e ii) compreender a influência de dinâmicas eco-evolutivas na robustez de redes mutualísticas. No Capítulo I, desenvolvi uma abordagem analítica integradora para particionar os efeitos da filogenia e de características funcionais sobre a estrutura de redes de interação biótica. O método combina Teoria de Conjuntos Difusos e correlação matricial. Eu também desenvolvi um estudo de simulação para testar a acurácia da metodologia proposta em termos de Erro Tipo I. As simulações demonstram que o método é acurado, ou seja, rejeita incorretamente uma hipótese nula verdadeira em ~ 5% dos casos. No Capítulo II, investiguei como diferentes cenários de extinção afetam a robustez de uma rede de dispersão de sementes do sul do Brasil, incluindo cenários onde as espécies são eliminadas com base em sua distinção evolutiva e funcional. Os resultados indicam que a perda de espécies generalistas e diversidade funcional faz com que rede seja mais propensa a colapsar. No Capítulo III, desenvolvi uma investigação teórica sobre a influencia de diferentes modos de evolução de atributos sobre a robustez de redes mutualísticas que estão sofrendo um ataque funcional. Os resultados mostram que, apesar da pequena faixa de variação na robustez das redes, o modo de evolução dos atributos, e a interação entre modos de evolução de cada conjunto de espécies que interagem, influenciam a robustez de redes ecológicas, especialmente em casos extremos, onde os atributos das espécies apresentam sinal filogenético muito baixo ou muito forte. / Understanding how species interact and how the topology of ecological networks influences the dynamics of populations and communities has been mindboggling ecologists for over a century now. Despite this long tradition, the study of complex ecological networks has increased dramatically in the past two decades. Nonetheless, only recently ecologists have started to move beyond the description of topological patterns and started to integrate other important biological data, such as functional traits and phylogenies. Therefore, the aim of this dissertation was mainly two-fold: develop new analytical approaches capable to integrate functional and phylogenetic information in order to describe structural patterns in ecological networks, and to understand the effects of ecoevolutionary dynamics on network robustness. In Chapter I, I developed a new and integrative analytical framework to partition the effects of phylogenies and functional traits on the structure of ecological networks. The method combines fuzzy set theory and matrix correlation. I also developed a simulation study to test the accuracy of the framework I proposed. My simulation study demonstrates that the method is accurate, i.e., incorrectly rejecting a true null hypothesis in ~ 5%. In Chapter II, I investigated how different extinction scenarios affect the robustness of a seed dispersal network, from southern Brazil, including scenarios where species are eliminated based on their evolutionary and functional distinctiveness. The results indicate that loss of generalist species and functional diversity makes the system more likely to collapse. In Chapter III, I developed a theoretical investigation of the role of distinct trait evolution modes on the robustness of mutualistic networks undergoing functional trait extinctions. My results show that, despite the small range of variation in network robustness, the mode of trait evolution alone and the interaction between modes of evolution of each set of interacting species matter for network robustness, especially in extreme cases, where species traits present either very low or very strong phylogenetic signal.

Les communautés écologiques présentent une diversité importante d'organismes et d'interactions. Comprendre le fonctionnement de ces différents types d'interactions constitue l'un des enjeux majeurs de l'écologie des communautés. Cependant, une large majorité des travaux s'intéressant à ces questions s'est focalisée sur les différents types d'interactions séparément. Cette thèse cherche à comprendre comment le couplage entre différents types d'interactions affecte la dynamique des communautés naturelles. Au travers d'une approche théorique, des modèles simples de communautés comprenant deux types d'interactions sont construits. Ces communautés sont constituées de trois espèces : une espèce basale, plante, interagissant avec un antagoniste, herbivore et un mutualiste, pollinisateur. Nous décrivons comment l'effet indirect entre interactions antagonistes et mutualistes affecte les dynamiques écologiques et évolutives des communautés face à une perturbation. Nous montrons que la relation entre pollinisateurs et herbivores à des conséquences importantes pour le maintien éco-Évolutif de la communauté et pour sa stabilité. Nous étudions ensuite la dynamique évolutive de traits particuliers, qui sont impliqués dans chaque type d'interactions. Certains traits attractifs ou de défense des plantes, affectent à la fois les interactions avec les pollinisateurs et les herbivores. Nous montrons comment les pressions de sélection opposées dues à la pollinisation et à l'herbivorie modifient l'évolution de ces traits et peuvent amener à la diversification des plantes. / Ecological communities involve an amazing diversity of organisms and interactions. Understanding how this diversity of interaction types (competition, mutualism or predation) affects the ecological and evolutionary dynamics of natural systems is an important challenge of community ecology. However, a large majority of works in community ecology theory considers interaction types separately. This thesis focus on the interplay between antagonism and mutualism. With a theoretical approach, small community models, including antagonistic and mutualistic interactions are built. These communities contain three species : one basal species (a plant) with an antagonist (herbivore) and a mutualistic species (pollinator). First, we study how the indirect effect between the two interaction types affects the ecological and evolutionary dynamics of communities in the currency of a disturbance. Second, we study the evolutionary dynamics of special traits, that are involved in each interaction type. Attractive traits or defensive traits of plants affect both interaction with pollinators and herbivores. We depict how the opposite selective pressures due to pollination and herbivory modify the evolution of these traits and show that they can lead to evolutionary diversification of plants. Following this diversification, the coevolutionary emergence of complex interaction networks is studied.

Topological evolution is a new dynamical systems model of biological evolution occurring within a genomic state space. It can be modeled equivalently as a stochastic dynamical system, a stochastic differential equation, or a partial differential equation drift-diffusion model. An application of this approach is a model of disease evolution tracing diseases in ways similar to standard functional traits (e.g., organ evolution). Genetically embedded diseases become evolving functional components of species-level genomes. The competition between species-level evolution (which tends to maintain diseases) and individual evolution (which acts to eliminate them), yields a novel structural topology for the stochastic dynamics involved. In particular, an unlimited set of dynamical time scales emerges as a means of timing different levels of evolution: from individual to group to species and larger units. These scales exhibit a dynamical tension between individual and group evolutions, which are modeled on very different (fast and slow, respectively) time scales. This is analyzed in the context of a potentially major constraint on evolution: the species-level enforcement of lifespan via (topological) barriers to genomic longevity. This species-enforced behavior is analogous to certain types of evolutionary altruism, but it is denoted here as extreme altruism based on its potential shaping through mass extinctions. We give examples of biological mechanisms implementing some of the topological barriers discussed and provide mathematical models for them. This picture also introduces an explicit basis for lifespan-limiting evolutionary pressures. This involves a species-level need to maintain flux in its genome via a paced turnover of its biomass. This is necessitated by the need for phenomic characteristics to keep pace with genomic changes through evolution. Put briefly, the phenome must keep up with the genome, which occurs with an optimized limited lifespan. An important consequence of this model is a new role for diseases in evolution. Rather than their commonly recognized role as accidental side-effects, they play a central functional role in the shaping of an optimal lifespan for a species implemented through the topology of their embedding into the genome state space. This includes cancers, which are known to be embedded into the genome in complex and sometimes hair-triggered ways arising from DNA damage. Such cancers are known also to act in engineered and teleological ways that have been difficult to explain using currently very popular theories of intra-organismic cancer evolution. This alternative inter-organismic picture presents cancer evolution as occurring over much longer (evolutionary) time scales rather than very shortened organic evolutions that occur in individual cancers. This in turn may explain some evolved, intricate, and seemingly engineered properties of cancer. This dynamical evolutionary model is framed in a multiscaled picture in which different time scales are almost independently active in the evolutionary process acting on semi-independent parts of the genome. We additionally move from natural evolution to artificial implementations of evolutionary algorithms. We study genetic programming for the structured construction of machine learning features in a new structural risk minimization environment. While genetic programming in feature engineering is not new, we propose a Lagrangian optimization criterion for defining new feature sets inspired by structural risk minimization in statistical learning. We bifurcate the optimization of this Lagrangian into two exhaustive categories involving local and global search. The former is accomplished through local descent with given basins of attraction while the latter is done through a combinatorial search for new basins via an evolution algorithm.

The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1