Evolutionary dynamics arise from the interplay of mutation and selection. Fundamentally, these two processes operate at different levels: Mutations modify genetic information (the genotype), which is passed from parent to offspring. Selection is triggered by variation in reproductive success, which depends on the physical properties (the phenotype) of an organism and its environment. Thus the genotype-phenotype map determines if and how mutations can lead to selection. The aim of this dissertation is to incorporate this map explicitly into a theoretical description of evolutionary dynamics. The first part of the analysis presented here is concerned with the static properties of simple models of these maps, which are studied using exhaustive enumeration. The two most important observations are phenotypic bias – some phenotypes are realized by many more genotypes than most other phenotypes – and the existence of neutral spaces – genotypes with the same phenotype can often be reached from each other by single mutational steps. The remainder of the dissertation provides a theoretical description of evolutionary dynamics on and across neutral spaces. Two different mean-field approximations lead to simple analytic results for the first discovery of alternative phenotypes, highlighting the importance of phenotypic bias: Rare phenotypes are hard to find by evolutionary search. These results are used to discuss the relationship of robustness, the ability to withstand mutational change, and evolvability, the ability to create variation through mutation. Several types of fluctuations beyond the mean-field limit are studied, both theoretically and in simulations. The discrete structure of genotype spaces can lead to strong correlations in the spectra of phenotypes produced, increasing the probability that a particular phenotype is fixed in the population quickly after its discovery. Structural correlations between genotypes can increase the effect of phenotypic bias, while the qualitative features of the mean-field description remain valid. All these results highlight that neutral spaces impact evolutionary dynamics in many non-trivial ways, in particular by favouring phenotypes of high accessibly, but comparably low fitness over those phenotypes that are highly fit, but very hard to discover.

When provided with spatial niches by growth in static nutrient medium, Pseudomonas fluorescens diversifies through adaptive radiation into several well-defined phenotype classes. One of these classes, named wrinkly spreader (WS) for its morphology on agar medium, forms a biofilm at the air-liquid interface through mutations in one of several loci including the genes wspF and awsX. These genes code for negative regulators of di-guanylate cyclases (DGCs). These DGCs catalyse synthesis of cyclic-di-GMP, a second messenger, overproduction of which effects physiological changes leading to overproduction of a cellulose polymer and the WS phenotype. Intriguingly, a diverse range of wspF mutations leads to diversity both in colony morphology and strain fitness.In this study, I investigate genetic and fitness diversity in wrinkly spreaders with the aim of identifying the causal factors that link genetic diversity and physiological factors with diversity in fitness. I approach the subject from several directions, examining the historical context of genetic diversity in wspF and awsX, distribution of control over output in the Wsp pathway and overall fitness effects of different causal factors. I investigate the genetic basis of wrinkly spreader evolution through generation of a large number of novel WS strains and exploration of the distribution of mutations in the wspF and awsX genes. In combination with this I calculate estimates of the past rates of mutation in these genes, derived from a phylogenetic investigation of a group of orthologues. I examine the response of the Wsp pathway to change in WspF function through a novel computational analysis that is capable of revealing valuable information on control in a biological system based purely on model structure. In addition I show how this analysis can be refined through specification of broad estimates of system parameters, thereby avoiding issues related to over-reliance on specific parameter values. Finally, I investigate the fitness implications of these factors, as well as a variety of others, through assays of fitness in a group of WS strains combined with machine learning analyses of predictive relationships between protein and mutation characteristics and experimentally measured strain fitness, and consider the implications of this analysis in the context of intermediate physiological effects.I find that mutations in the WspF protein that lead to the WS phenotype tend to be located in regions of historically strong conservation, the first time that any such pattern to WS mutations has been identified. Mutations in AwsX, on the other hand, do not fit such a pattern. Computational analysis of the Wsp pathway shows that, regardless of model parameters, pathway output is always more sensitive to changes in methylesterase activity by WspF than to changes in phosphorylation of WspF, which may explain the greater frequency of mutations fixed in vivo seen in the methylesterase domain. Despite these patterns, none of a wide range of mutation and sequence-based biochemical characteristics, including local rates of past evolution and size and position of mutations, exhibited any predictive power over WS fitness. Overall, the findings in this study point towards an essential role for complex pleiotropic effects in strongly modulating the fitness effect of different mutations in wspF.

L’identification de l’information génétique comme support de l’hérédité a accordé aux gènes une importance majeure dans l’étude de l’évolution et des mécanismes permettant la mise en place des caractères. Cependant, les processus permettant à une variation génétique de se traduire en variation phénotypique sont complexes et leur identification est centrale pour la compréhension de l’évolution.On parle de relation génotype-phénotype pour désigner la fonction qui relie l’espace des gènes à celui des caractères. Étudier les propriétés de cette relation permet d’identifier des mécanismes pouvant altérer les trajectoires évolutives et améliorer notre compréhension de l’évolution de systèmes vivants. Je défends notamment l’intérêt d’étudier mécanistiquement les processus par lesquels une variation génétique donne naissance à une variation phénotypique, et emploie, pour ce faire, un modèle de réseau de régulation transcriptionnelle.Ici, j’étudie les effets d’une information environnementale sur la relation génotype-phénotype et ses propriétés (notamment sa canalisation, sa robustesse à des perturbations génétiques ou environnementales). Pour ce faire, l’évolution de réseaux de régulation simulés est étudiée en présence d’un gène senseur de l’environnement ou d’une forme d’hérédité non génétique.Ce manuscrit débute par une discussion générale de l’intérêt des approches par modélisation, notamment pour l’étude de phénomènes complexes. Enfin, les résultats obtenus sont présentés en regard des discussions sur la nécessité d’une « synthèse évolutive étendue » pour décrire le processus évolutif d’une manière difficilement accessible par une approche gène-centrée. / The identification of genetic information as the as a physical basis for heredity put genes in the spotlight for the study of evolution and of the mechanisms shaping characters. However, the processes allowing genetic variation to translate into phenotypic variation are complex and their identification is crucial for the study of evolution.Genotype-phenotype relationship designates the function connecting the genotype and the phenotype spaces. Studying its properties will shed the light on mechanisms able to alter evolutionary trajectories and improve our understanding of the evolutionary process. I defend the importance of a mechanistic study of the processes translating genetic variation into a phenotypic one and use a model of transcriptional regulation networks to do so.This study tackles the topic of the effects of an environmental information on the genotype-phenotype relationship and its properties (especially canalization, the robustness of a phenotype to genetic or environmental disturbances). To do so, I studied the evolution of simulated regulatory networks in presence of a gene acting as an environmental sensor as well as in presence of non genetic inheritance.This document begins with a general discussion on the purpose of modelling approaches and the insights they bring on the study of complex phenomena. The results are discussed in the light of the debates on the necessity of an « evolutionary extended synthesis » to describe the evolutionary processes in a way hardly available with the gene-centered approach

The evolutionary options of a population are strongly influenced by the avail- ability of adaptive mutants. In this thesis, I use the concept of neutral networks to show that neutral drift can actually increase the accessibility of adaptive mu- tants, and therefore facilitate adaptive evolutionary change. Neutral networks are groups of unique genotypes which all code for the same phenotype, and are connected by simple point mutations. I calculate the size and shape of the networks in a small but exhaustively enumerated space of RNA genotypes by mapping the sequences to RNA secondary structure phenotypes. The qual- itative results are similar to those seen in many other genotype–phenotype map models, despite some significant methodological differences. I show that the boundary of each network has single point–mutation connections to many more phenotypes than the average individual genotype within that network. This means that paths involving a series of neutral point–mutation steps across a network can allow evolution to adaptive phenotypes which would otherwise be extremely unlikely to arise spontaneously. This can be likened to walking along a flat ridge in an adaptive landscape, rather than traversing or jumping across a lower fitness valley. Within this model, when a genotype is made up of just 10 bases, the mean neutral path length is 1.88 point mutations. Furthermore, the map includes some networks that are so convoluted that the path through the network is longer than the direct route between two sequences. A minimum length adaptive walk across the genotype space usually takes as many neutral steps as adaptive ones on its way to the optimum phenotype. Finally I show that the shape of a network can have a very important affect on the number of generations it takes a population to drift across it, and that the more routes between two sequences, the fewer generations required for a population to find an advantageous sequence. My conclusion is that, within the RNA map at least, the size, shape and connectivity of neutral networks all have a profound effect on the way that sequences change and populations evolve, and by not considering them, we risk missing an important evolutionary mechanism.