Biological evolution is an inherently non-equilibrium process, by which a population acquires a new genetic composition, optimally suited to its present environment. Far from being the slow process it is traditionally viewed as, the rapid evolution of microbes is causing serious global concern in the acquisition of microbial resistance to antibiotics. Better understanding of the mechanisms that govern the evolution of microbes is therefore of paramount importance. In many traditional models, evolution occurs over the space of all possible genetic states (genotypes). These are assigned a quantity called fitness, which quantifies that genotype's suitability over others to thrive within its present environment. A population of replicating cells can evolve over this space under the competing influences of random variations of the genotype (i.e. mutations) and the increased likelihood of success for fitter genotypes (i.e. selection). Many of these models fail to account for the observation that biological diversity is rife, even amongst genetically identical cells that exist in the same environment. This diversity manifests itself as a difference in phenotype (the observable traits of an organism). It means that organisms with the same genotype, but a different phenotype, may have different fitnesses. Therefore, when phenotypic heterogeneity is apparent, evolution over genotype space should consider different fitness landscapes for each of the distinct phenotypic states that exist. Phenotypic heterogeneity has long been observed in populations of microbes. Often these can switch between different phenotypic states for a number of reasons. A common example of this is stochastic phenotype switching, in which cells randomly switch between two phenotypic states, without any inducing influence. This has been shown to benefit populations of cells that are subject to fluctuating environmental conditions, or by creating a division of labour in the population. In this work, I examine the possibility of another role for stochastic phenotype switching: as a mechanism that can accelerate evolution even in a static environment. During evolution, populations can spend large amounts of time trapped at local peaks on a fltness landscape. A cell that switches phenotype will change to a different fitness landscape, which may allow for faster genetic evolution. I begin this work in Chapters 3 and 4, where I present a model of an evolving population of haploid cells, trapped at a local peak on a 1D fitness landscape. These cells have access to a second phenotypic state, in which the fitness landscape is uniform. The focus of this study is to see the effect that stochastic phenotype switching to this secondary phenotype has on the populations evolution of a target state. In Chapter 3 I study this numerically and identify an optimal range for the rate of phenotype switching, within which the time taken for the process can be reduced by many orders of magnitude. I also find that if the frequency of switching is allowed to evolve, then the likely evolutionary trajectory taken by a population is one that first evolves a switching frequency to within the identified optimal range, before escaping from the local peak. In Chapter 4 I present an analytic study of the same model. The aim here is to recover the numerical results from Chapter 3. I employ numerous analytic techniques to show the existence of the optimal range, while developing an analytic approach that allows a study of the model at parameter values that are otherwise difficult to simulate. This same model is extended in Chapter 5 to consider evolution over a more complex genotype space: that of a hypercube. Here, genotypes correspond to particular binary sequences, which can be used as representations of many biological states of interest; for example, nucleotide sequences in DNA or the presence and absence of important mutations in specific genes. My focus here is again on the effect that stochastic phenotype switching has on how a population of cells evolves over genotype space. This is studied numerically for various kinds of randomly generated fitness landscapes. I find that in some instances phenotype switching can significantly benefit a population. However, in other instances it can significantly hinder the evolution, increasing the time taken for the process by many orders of magnitude. Finally, in Chapter 6 I present a model that explores how a population of the bacterium Escherichia coli (E. coli) evolves resistance to the antibiotic ciprofloxacin. This work is motivated by the observed rapid acquisition of resistance of E. coli when exposed to sub-lethal concentrations of the antibiotic. Upon damage to their DNA, cells can induce a switch to a secondary phenotypic state (as part of the SOS response), in which DNA repair and an increased rate of mutations occur. Using this model, with empirical data for the fitness and susceptibility of genotypes, I numerically explore the dependence of rapid evolution on the existence of this secondary phenotypic state. I find that the model predicts, over the short timescales considered, that the evolution of sufficient resistance requires the existence of the secondary phenotypic state. The findings of this work is that the phenotypic switching of cells can have a significant impact on how populations evolve in static environments. While stochastic phenotype switching can help populations escape from local peaks, it can also trap populations on sub-optimal landscapes if the frequency of switching is too low.

The ability to link a particular phenotype to its causative genotype is one of the most challenging objectives for biological research. Although the genetic code provides an explicit formula for determining the sequence of amino acid phenotypes produced by a given nucleotide sequence, identifying specific residues that are functionally important remains problematic. Many computational approaches have been developed that use patterns observed in DNA sequences to identify these critical sites. However, very few research studies have used empirical data to test whether these approaches are truly able to identify sites of interest.In most empirical studies, the actual protein function and selective pressures are unknown; thus it is difficult to assess whether computational approaches are correctly identifying critical sites. Here I present two studies that utilize well-characterized empirical systems to evaluate and compare the performance of several computational approaches. In both cases, the proteins under study have specific amino acid substitutions that are confirmed to alter protein function and expected to be constrained by natural selection. In chapter 2, I examine functional variants in angiopoietin-like protein 4 (ANGPTL4), a protein involved in regulating plasma triglyceride levels; loss-of-function variants in this gene are believed to decrease the risk of cardiovascular disease. I apply several computational approaches to identify functional variants, including phylogenetic approaches for detecting positive selection. In chapter 3, I investigate the emergence of drug-resistance in HIV-1 during the course of antiretroviral drug therapy. I compare the performance of eight selection detection methods in identifying drug-resistant mutations in 109 intrapatient datasets with HIV-1 sequences isolated at multiple timepoints throughout drug treatment.It is critical that we develop methods to detect positively selected sites. The ability to detect these sites in silico, without the need for expensive and time consuming assays, would be invaluable to researchers in evolutionary biology, human genetics, and medicine. Through the research presented in this thesis, I hope to provide insight into the strengths and weaknesses of current approaches, thereby facilitating future research towards the development and improvement of evolutionary models.

O presente trabalho tem por objetivo o desenvolvimento de políticas de administração do saldo de caixa. Este problema de finanças abordado inicialmente por Baumol (1952) e Tobin (1956) teve sua origem na aplicação de modelos determinísticos de controle de inventário ao caixa existente nas empresas. Desta forma, os autores traçaram um paralelo entre o saldo de caixa e os estoques de ativos, de maneira a minimizar os custos relativos ao caixa. Posteriormente Miller e Orr (1966) aperfeiçoaram a abordagem ao introduzirem um modelo estocástico que não mais definia o ponto ideal do saldo de caixa, mas uma faixa de oscilação. Apesar disso, os modelos apresentavam apenas uma única opção de investimento em detrimento ao caixa. Mais recentemente uma série de trabalhos resgatou o problema com novas metodologias, diversificando os custos de transferência e manutenção do caixa e aplicando, principalmente, modelos estocásticos em sua resolução, melhorando seu desempenho. Este trabalho aplica uma modelagem para gerenciamento do saldo ideal de caixa, considerando para isso os custos de manutenção, custos de transferência, diversificação em mais de dois ativos, liquidez associada aos investimentos, além da ruptura de caixa. Para isso, são utilizados modelos computacionais de meta-heurística, com a utilização de algoritmos genéticos (AG), particle swarm optimization (PSO) e simulated annealing (SA). Assim, a partir da simulação de fluxos líquidos de caixa, de acordo com as premissas apresentadas na literatura, considerando as distribuições Normal, de Poisson, Triangular e Movimento Browniano (processo de Wiener) foram realizadas experimentações computacionais a fim de desenvolver uma política de gerenciamento de caixa multiobjetivo capaz de minimizar o custo do saldo de caixa ao mesmo tempo em que minimiza o risco associado ao caixa. Os resultados demonstram que os modelos empregados são válidos para o desenvolvimento das políticas de gerenciamento de caixa, com a prevalência do PSO em problemas mais simples e do AG em problemas mais complexos, com grandes perspectivas para uso prático na definição de políticas de gerenciamento do saldo de caixa. / The present work aims at the development of cash balance management policies. This financial problem initially by Baumol (1952) and Tobin (1956) had its origin in the application of deterministic models for inventory control to the existing cash in companies. These authors drew a parallel between the cash balance and asset inventories in order to minimize the cost of the cash balance. Later, Miller and Orr (1966) refined the approach by introducing a stochastic model that no longer defined the ideal point of cash balance, but an oscillation range. Nevertheless, the models had only one investment option over the cash. More recently a series of studies rescued the problem with new methods, diversifying the transfer and cash maintenance costs, applying stochastic models in its resolution and improving their performance. This work applies a modeling for managing the ideal cash balance, considering maintenance costs, transfer costs, diversification of financial investment in more than two assets, the liquidity associated with investments and penalty costs for the lack of cash. For this, meta-heuristics computer models are used for, with the use of genetic algorithms (GA), particle swarm optimization (PSO) and simulated annealing (SA). Thus, based on the simulation of net cash flows in accordance with the assumptions presented in the literature, considering the distributions Normal, Poisson, Triangular and Brownian motion (Wiener process) computational experiments were performed to develop a multi-objective cash balance management policy able to minimize the cost of the cash balance at the same time then minimizes the risk associated with cash. The results demonstrate that the models used are valid for the development of cash management policies, with better results for the PSO in simple problems and GA on more complex problems, with great perspective for practical use in policy management for cash balance.

A phylogenetic tree is a tree to represent an evolutionary history between species or other entities. Phylogenomics is a new field intersecting phylogenetics and genomics and it is well-known that we need statistical learning methods to handle and analyze a large amount of data which can be generated relatively cheaply with new technologies. Based on the existing Markov models, we introduce a new method, CURatio, to identify outliers in a given gene data set. This method, intrinsically an unsupervised method, can find outliers from thousands or even more genes. This ability to analyze large amounts of genes (even with missing information) makes it unique in many parametric methods. At the same time, the exploration of statistical analysis in high-dimensional space of phylogenetic trees has never stopped, many tree metrics are proposed to statistical methodology. Tropical metric is one of them. We implement a MCMC sampling method to estimate the principal components in a tree space with the tropical metric for achieving dimension reduction and visualizing the result in a 2-D tropical triangle.

octor of Philosophy(PhD) / Molecular Evolution is the key to explain the divergence of species and the origin of life on earth. The main task in the study of molecular evolution is the reconstruction of evolutionary trees from sequences data of the current species. This thesis introduces a novel algorithm for inferring evolutionary trees from genetic data using quartet-based approach. The new method recursively merges sub-trees based on a global statistical provided by the global quartet weight matrix. The quarte weights can be computed using several methods. Since the quartet weights computation is the most expensive procedure in this approach, the new method enables the parallel inference of large evolutionary trees. Several techniques developed to deal with quartets inaccuracies. In addition, the new method we developed is flexible in such a way that can combine morphological and molecular phylogenetic analyses to yield more accurate trees. Also, we introduce the concept of critical point where more than one possible merges are possible for the same sub-tree. The critical point concept can provide information about the relationships between species in more details and show how close they are. This enables us to detect other reasonable trees. We evaluated the algorithm on both synthetic and real data sets. Experimental results showed that the new method achieved significantly better accuracy in comparison with existing methods.

octor of Philosophy(PhD) / Molecular Evolution is the key to explain the divergence of species and the origin of life on earth. The main task in the study of molecular evolution is the reconstruction of evolutionary trees from sequences data of the current species. This thesis introduces a novel algorithm for inferring evolutionary trees from genetic data using quartet-based approach. The new method recursively merges sub-trees based on a global statistical provided by the global quartet weight matrix. The quarte weights can be computed using several methods. Since the quartet weights computation is the most expensive procedure in this approach, the new method enables the parallel inference of large evolutionary trees. Several techniques developed to deal with quartets inaccuracies. In addition, the new method we developed is flexible in such a way that can combine morphological and molecular phylogenetic analyses to yield more accurate trees. Also, we introduce the concept of critical point where more than one possible merges are possible for the same sub-tree. The critical point concept can provide information about the relationships between species in more details and show how close they are. This enables us to detect other reasonable trees. We evaluated the algorithm on both synthetic and real data sets. Experimental results showed that the new method achieved significantly better accuracy in comparison with existing methods.

O presente trabalho tem por objetivo o desenvolvimento de políticas de administração do saldo de caixa. Este problema de finanças abordado inicialmente por Baumol (1952) e Tobin (1956) teve sua origem na aplicação de modelos determinísticos de controle de inventário ao caixa existente nas empresas. Desta forma, os autores traçaram um paralelo entre o saldo de caixa e os estoques de ativos, de maneira a minimizar os custos relativos ao caixa. Posteriormente Miller e Orr (1966) aperfeiçoaram a abordagem ao introduzirem um modelo estocástico que não mais definia o ponto ideal do saldo de caixa, mas uma faixa de oscilação. Apesar disso, os modelos apresentavam apenas uma única opção de investimento em detrimento ao caixa. Mais recentemente uma série de trabalhos resgatou o problema com novas metodologias, diversificando os custos de transferência e manutenção do caixa e aplicando, principalmente, modelos estocásticos em sua resolução, melhorando seu desempenho. Este trabalho aplica uma modelagem para gerenciamento do saldo ideal de caixa, considerando para isso os custos de manutenção, custos de transferência, diversificação em mais de dois ativos, liquidez associada aos investimentos, além da ruptura de caixa. Para isso, são utilizados modelos computacionais de meta-heurística, com a utilização de algoritmos genéticos (AG), particle swarm optimization (PSO) e simulated annealing (SA). Assim, a partir da simulação de fluxos líquidos de caixa, de acordo com as premissas apresentadas na literatura, considerando as distribuições Normal, de Poisson, Triangular e Movimento Browniano (processo de Wiener) foram realizadas experimentações computacionais a fim de desenvolver uma política de gerenciamento de caixa multiobjetivo capaz de minimizar o custo do saldo de caixa ao mesmo tempo em que minimiza o risco associado ao caixa. Os resultados demonstram que os modelos empregados são válidos para o desenvolvimento das políticas de gerenciamento de caixa, com a prevalência do PSO em problemas mais simples e do AG em problemas mais complexos, com grandes perspectivas para uso prático na definição de políticas de gerenciamento do saldo de caixa. / The present work aims at the development of cash balance management policies. This financial problem initially by Baumol (1952) and Tobin (1956) had its origin in the application of deterministic models for inventory control to the existing cash in companies. These authors drew a parallel between the cash balance and asset inventories in order to minimize the cost of the cash balance. Later, Miller and Orr (1966) refined the approach by introducing a stochastic model that no longer defined the ideal point of cash balance, but an oscillation range. Nevertheless, the models had only one investment option over the cash. More recently a series of studies rescued the problem with new methods, diversifying the transfer and cash maintenance costs, applying stochastic models in its resolution and improving their performance. This work applies a modeling for managing the ideal cash balance, considering maintenance costs, transfer costs, diversification of financial investment in more than two assets, the liquidity associated with investments and penalty costs for the lack of cash. For this, meta-heuristics computer models are used for, with the use of genetic algorithms (GA), particle swarm optimization (PSO) and simulated annealing (SA). Thus, based on the simulation of net cash flows in accordance with the assumptions presented in the literature, considering the distributions Normal, Poisson, Triangular and Brownian motion (Wiener process) computational experiments were performed to develop a multi-objective cash balance management policy able to minimize the cost of the cash balance at the same time then minimizes the risk associated with cash. The results demonstrate that the models used are valid for the development of cash management policies, with better results for the PSO in simple problems and GA on more complex problems, with great perspective for practical use in policy management for cash balance.

Biodiversity conservation requires a framework for prioritising limited resources to the many endangered species. One such framework that has seen much attention and is considered extensively in this thesis, is the Noah's Ark Problem (NAP). The NAP combines a biodiversity measure (Phylogenetic Diversity; PD) with species survival probabilities and conservation costs. The aim of the NAP is to allocate the limited conservation resources such that the future expected PD is maximised. Obtaining optimal solutions to the NAP is a computationally complex problem to which several efficient algorithms are provided here. An extension to the NAP is also developed which allows uncertainty about the survival probability estimates to be included. Using this extension we show that the NAP is robust to uncertainty in these parameters and that even very poor estimates are beneficial. To justify using or promoting PD, it must produce a significant increase in the amount of biodiversity that is preserved. We show that the increase attainable from the NAP is typically around 20% but may be as high as 150%. An alternative approach to PD and the NAP is to prioritise species using simple species specific indices. The benefit of these indices is that they are easy to calculate, explain and integrate into existing management frameworks. Here we investigate the use of such indices and show that they provide between 60% and 80% of the gains obtainable using PD. To explore the expected behaviours of conservation methods (such as the NAP) a distribution of phylogenetics trees is required. Evolutionary models describe the diversification process by which a single species gives rise to multiple species. Such models induce a probability distribution on trees and can therefore be used to investigate the expected behaviour of conservation methods. Even simple and widely used models, such as the Yule model, remain poorly understood. In this thesis we present some new analytic results and methods for sampling trees from a broad range of evolutionary models. Lastly we introduce a new model that provides a simple biological explanation for a long standing discrepancy between models and trees derived from real data -- the tree balance distribution.

Biodiversity conservation requires a framework for prioritising limited resources to the many endangered species. One such framework that has seen much attention and is considered extensively in this thesis, is the Noah's Ark Problem (NAP). The NAP combines a biodiversity measure (Phylogenetic Diversity; PD) with species survival probabilities and conservation costs. The aim of the NAP is to allocate the limited conservation resources such that the future expected PD is maximised. Obtaining optimal solutions to the NAP is a computationally complex problem to which several efficient algorithms are provided here. An extension to the NAP is also developed which allows uncertainty about the survival probability estimates to be included. Using this extension we show that the NAP is robust to uncertainty in these parameters and that even very poor estimates are beneficial. To justify using or promoting PD, it must produce a significant increase in the amount of biodiversity that is preserved. We show that the increase attainable from the NAP is typically around 20% but may be as high as 150%. An alternative approach to PD and the NAP is to prioritise species using simple species specific indices. The benefit of these indices is that they are easy to calculate, explain and integrate into existing management frameworks. Here we investigate the use of such indices and show that they provide between 60% and 80% of the gains obtainable using PD. To explore the expected behaviours of conservation methods (such as the NAP) a distribution of phylogenetics trees is required. Evolutionary models describe the diversification process by which a single species gives rise to multiple species. Such models induce a probability distribution on trees and can therefore be used to investigate the expected behaviour of conservation methods. Even simple and widely used models, such as the Yule model, remain poorly understood. In this thesis we present some new analytic results and methods for sampling trees from a broad range of evolutionary models. Lastly we introduce a new model that provides a simple biological explanation for a long standing discrepancy between models and trees derived from real data -- the tree balance distribution.

Le but de cette thèse est d'étudier la distribution des tailles des répétitions au sein d'un même génome, ainsi que la distribution des tailles des appariements obtenus en comparant différents génomes. Ces distributions présentent d'importantes déviations par rapport aux prédictions des modèles probabilistes existants. Étonnamment, les déviations observées sont distribuées selon une loi de puissance. Afin d'étudier ce phénomène, nous avons développé des modèles mathématiques prenant en compte des mécanismes évolutifs plus complexes, et qui expliquent les distributions observées. Nous avons aussi implémenté des modèles d'évolution de séquences in silico générant des séquences ayant les mêmes propriétés que les génomes étudiés. Enfin, nous avons montré que nos modèles permettent de tester la qualité des génomes récemment séquencés, et de mettre en évidence la prévalence de certains mécanismes évolutifs dans les génomes eucaryotes. / In this thesis, we study the length distribution of maximal exact matches within and between eukaryotic genomes. These distributions strongly deviate from what one could expect from simple probabilistic models and, surprisingly, present a power-law behavior. To analyze these deviations, we develop mathematical frameworks taking into account complex mechanisms and that reproduce the observed deviations. We also implemented in silico sequence evolution models that reproduce these behaviors. Finally, we show that we can use our framework to assess the quality of sequences of recently sequenced genomes and to highlight the importance of unexpected biological mechanisms in eukaryotic genomes.