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Molecular evolution aims to characterize the mechanisms at work in the evolution of sequences, governed by a stochastic process whose main components are mutation, selection and genetic drift. In the long term, this stochastic process results in a history of substitution events along species trees, inducing complex patterns of molecular divergence between species. By analysing them, phylogenetic codon models aim at capturing the intrinsic parameters of evolution. In this context, this thesis has been focused on phylogenetic codon models, and on modelling the interplay between mutation, selection and drift shaping protein-coding DNA sequences. Because the composition of protein-coding DNA sequences does not reflect the underlying mutational process, but its filtering by selection at the level of amino acids, a careful modelling is necessary to tease apart mutation and selection. Therefore, I first developed a phylogenetic codon model of inference in which different rates of evolution give an accurate representation of how mutation and selection oppose each other at equilibrium. Between the opposing forces of mutation and selection, the balance is arbitrated by genetic drift, which in turn is modulated by effective population size. As a consequence, variation of effective population size along of a phylogeny can theoretically be inferred from the trails of substitutions along the lineages. I thus developed a second model of inference, reconstructing altogether site-specific fitness landscape, long-term trends in effective population size and in the changes in the mutation rate along the phylogeny. This Bayesian framework was tested against simulated data and then applied to empirical data. Estimates of the variation of effective population size corresponds to the expected direction of correlation with life-history traits or ecological variables. However, the magnitude of inferred variation is narrower than expected based on independent estimates. In order to understand this narrow variation in the estimated effective population size, I finally developed a theoretical model describing how changes in both effective population size or expression level of protein translate into a change in substitution rate. This response of the change in substitution rate is obtained under the assumption that proteins are under directional selection to maximize their conformational stability, and related the molecular parameters of protein biophysics. Results of this work imply a weak response of the substitution rate to changes in expression level or effective population size, which are interchangeable. This thesis demonstrates that the assumptions made on the structure of the fitness landscape have a critical importance on the sensitivity of changes in substitution rates to changes in ecological or molecular variables. Conversely, empirical observations of the patterns of substitutions in response to changes in molecular or ecological variables inform us about the underlying structure of the fitness landscape. Being based on the mutation-selection balance and by explicitly integrating effective population size, this work also presents a conceptual framework allowing to relate phylogenetics and population genetics, of which certain unification paths are envisaged; L'évolution moléculaire vise à caractériser les mécanismes à l'œuvre dans l'évolution des séquences, régie par un processus stochastique dont les principaux composants sont la mutation, la sélection et la dérive génétique. À long terme, ce processus stochastique se traduit par une histoire d'événements de substitutions le long des arbres d'espèces, induisant des motifs complexes de divergence moléculaire entre les espèces. En analysant ces divergences, les modèles de codons phylogénétiques visent à capturer les paramètres intrinsèques de l'évolution. Dans ce contexte, cette thèse s'est concentrée sur les modèles à codons phylogénétiques et sur la modélisation de l'interaction entre la mutation, la sélection et la dérive génétique dans les séquences d'ADN codant pour des protéines. Parce que la composition de ces séquences ne reflète pas le processus de mutation sous-jacent, mais son filtrage par sélection au niveau des acides aminés, une modélisation minutieuse est nécessaire pour démêler la mutation et la sélection. Ainsi, j'ai développé un modèle d'inférence phylogénétique dans lequel différents taux d'évolution donnent une représentation précise de la manière dont la mutation et la sélection s'opposent à l’équilibre. Deuxièmement, l'équilibre entre mutation et sélection est arbitré par la dérive génétique, qui est médiée par la taille efficace de la population, et ses changements le long d'une phylogénie peuvent être déduits des motifs de substitutions le long des lignées. J'ai ainsi développé un deuxième modèle d'inférence, reconstituant à la fois le paysage de fitness en chaque site, les tendances à long terme de taille efficace de population et les changements de taux de mutation le long de la phylogénie. Ce cadre bayésien a été testé sur des données simulées puis appliqué à des données empiriques. Les estimations de la variation de taille efficace de population correspondent à la direction attendue de la corrélation avec les traits d’histoire de vie ou les variables écologiques, bien que l'ampleur de la variation de la taille efficace de population estimée soit étroite. Afin de comprendre cette variation étroite de la taille efficace de population estimée, j'ai finalement développé un modèle théorique décrivant comment les changements à la fois de taille efficace de population ou du niveau d'expression ou la protéine se traduisent par un changement du taux de substitution, sous l'hypothèse que les protéines sont sous sélection directionnelle pour maximiser leur stabilité conformationnelle. Cette réponse est déterminée en fonction des paramètres moléculaires de la biophysique des protéines, et implique une faible réponse du taux de substitution aux changements de niveau d'expression ou de taille efficace de population dans ce contexte. Ce travail démontre que les hypothèses faites sur la structure du paysage de fitness ont une importance critique sur la sensibilité des changements vitesse d'évolution à des changements de variables écologiques ou moléculaires. Réciproquement, les observations empiriques des motifs de substitutions en réponse à des changements de variables moléculaires ou écologiques nous informent sur la structure sous-jacente du paysage de fitness. En se basant sur l'équilibre mutation-sélection et en intégrant explicitement la taille efficace de population, ce travail présente aussi un cadre conceptuel permettant de relier phylogénie et génétique des populations, dont certaines pistes d'unifications sont envisagées

Codon Usage Preferences (CUPrefs) describe the unequal usage of synonymous codons at the gene, chromosome, or genome levels. Numerous indices have been developed to evaluate CUPrefs, either in absolute terms or with respect to a reference. We introduce the normalized index COUSIN (for COdon Usage Similarity INdex), that compares the CUPrefs of a query against those of a reference and normalizes the output over a Null Hypothesis of random codon usage. The added value of COUSIN is to be easily interpreted, both quantitatively and qualitatively. An eponymous software written in Python3 is available for local or online use (http://cousin.ird.fr). This software allows for an easy and complete analysis of CUPrefs via COUSIN, includes seven other indices, and provides additional features such as statistical analyses, clustering, and CUPrefs optimization for gene expression. We illustrate the flexibility of COUSIN and highlight its advantages by analyzing the complete coding sequences of eight divergent genomes. Strikingly, COUSIN captures a bimodal distribution in the CUPrefs of human and chicken genes hitherto unreported with such precision. COUSIN opens new perspectives to uncover CUPrefs specificities in genomes in a practical, informative, and user-friendly way.

Genetic data are often used to infer history, demographic changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposeda prioriknown, the evolution of the genetic composition of a population does not affect demography nor population structure, and there is no selection nor interaction between and within genetic strains. In this paper, we present a stochastic birth-death model with competitive interaction to describe an asexual population, and we develop an inferential procedure for ecological, demographic and genetic parameters. We first show how genetic diversity and genealogies are related to birth and death rates, and to how individuals compete within and between strains. This leads us to propose an original model of phylogenies, with trait structure and interactions, that allows multiple merging. Second, we develop an Approximate Bayesian Computation framework to use our model for analyzing genetic data. We apply our procedure to simulated and real data. We show that the procedure give accurate estimate of the parameters of the model. We finally carry an illustration on real data and analyze the genetic diversity of microsatellites on Y-chromosomes sampled from Central Asia populations in order to test whether different social organizations show significantly different fertility.

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep., 29 pages

International audience; We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump process that generalizes the Trait Substitution Sequence process describing Adaptive Dynamics for populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N to infinity (where N is the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible N by N matrices and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types., Comment: 31 pages, 2 figures. Thorough revision, additional material included. J. Math. Biol., in press