La microbiologia predictiva és una de les parts més importants de la microbiologia dels aliments. En el creixement d'un cultiu bacterià es poden observar quatre fases: latència, exponencial, estacionària i mort. La fase de latència té un interès específic en microbiologia predictiva; al llarg de dècades ha estat abordada des de dues perspectives diferents: a nivell cel·lular i intracel·lular (escala microscòpica), i a nivell de població (escala macroscòpica). La primera estudia els processos que tenen lloc a l'interior dels bacteris durant la seva adaptació a les noves condicions del medi, com els canvis en l'expressió gènica i en el metabolisme. La segona descriu l'evolució de la població bacteriana per mitjà de models matemàtics continus i d'experiments que avaluen variables relacionades amb la densitat cel·lular. L'objectiu d'aquest treball és millorar la comprensió de la fase de latència dels cultius bacterians i dels fenòmens intrínsecs a la mateixa. Aquest objectiu s'ha abordat amb la metodologia Individual-based Modelling (IbM) amb el simulador INDISIM (INDividual DIScrete SIMulation), que ha calgut optimitzar. La IbM introdueix una perspectiva mecanicista a través de la modelització de les cèl·lules com a unitats bàsiques. Les simulacions IbM permeten estudiar el creixement d'entre 1 i 106 bacteris, així com els fenòmens que emergeixen de la interacció entre ells. Aquests fenòmens pertanyen al que anomenem escala mesoscòpica. Aquesta perspectiva és imprescindible per entendre l'efecte en la població dels processos d'adaptació individuals. Per tant, la metodologia IbM és un pont entre els individus i la població o, el que és el mateix, entre els models a escala microscòpica i a escala macroscòpica.En primer lloc hem estudiat dos dels diversos mecanismes que poden causar la fase de latència: inòculs amb massa mitjana petita, i canvis de medi.S'ha verificat també la relació de la durada de la latència amb variables com la temperatura o la grandària de l'inòcul. En aquest treball s'ha identificat la distribució de biomassa del cultiu com una variable cabdal per analitzar l'evolució del cultiu durant el cicle de creixement. S'han definit les funcions matemàtiques que anomenem distàncies per avaluar quantitativament l'evolució d'aquesta distribució.Hem abordat, també, la fase de latència des d'un punt de vista teòric. L'evolució de la velocitat de creixement al llarg del cicle ha permès distingir dues etapes en la fase de latència que anomenem inicial i de transició. L'etapa de transició s'ha descrit per mitjà d'un model matemàtic continu validat amb simulacions INDISIM. S'ha constatat que la fase de latència ha de ser vista com un procés dinàmic, i no com un simple període de temps descrit per un paràmetre. Les funcions distància també s'han utilitzat per avaluar les propietats del creixement balancejat.Alguns dels resultats de les simulacions amb INDISIM s'han corroborat experimentalment per mitjà de citometria de flux. S'ha comprovat, al llarg de les diverses fases del creixement, el comportament de la distribució de biomassa previst per simulació, així com l'evolució de les funcions distància. La coincidència entre els resultats experimentals i els de simulació no és trivial, ja que el sistema estudiat és molt complex. Per tant, aquests resultats permeten comprovar la bondat de la metodologia INDISIM.Finalment, hem avançat en l'optimització d'eines per parametritzar IbMs, un pas essencial per poder utilitzar les simulacions INDISIM de manera quantitativa. S'han adaptat i assajat els mètodes grid search, NMTA i NEWUOA. Aquest darrer mètode ha donat els millors resultats en termes de temps, mantenint una bona precisió en els valors òptims dels paràmetres. Per concloure, podem afirmar que INDISIM ha estat validat com una bona eina per abordar l'estudi dels estats transitoris com la fase de latència. / Predictive food microbiology has become an important specific field in microbiology. Bacterial growth of a batch culture may show up to four phases: lag, exponential, stationary and death. The bacterial lag phase, which is of specific interest in the framework of predictive food microbiology, has generally been tackled with two generic approaches: at a cellular and intracellular level, which we call the microscopic scale, and at a population level, which we call the macroscopic scale. Studies at the microscopic level tackle the processes that take place inside the bacterium during its adaptation to the new conditions such as the changes in genetic expression and in metabolism. Studies at the macroscopic scale deal with the description of a population growth cycle by means of mathematical continuous modelling and experimental measurements of the variables related to cell density evolution.In this work we aimed to improve the understanding of the lag phase in bacterial cultures and the intrinsic phenomena behind it. This has been carried out from the perspective of Individual-based Modelling (IbM) with the simulator INDISIM (INDividual DIScrete SIMulation), which has been specifically improved for this purpose. IbM introduces a mechanistic approach by modelling the cell as an individual unit. IbM simulations deal with 1 to 106 cells, and allow specific study of the phenomena that emerge from the interaction among cells. These phenomena belong to the mesoscopic level.Mesoscopic approaches are essential if we are to understand the effects of cellular adaptations at an individual level in the evolution of a population.Thus, they are a bridge between individuals and population, or, to put it another way, between models at a microscopic scale and models at a macroscopic scale.First, we studied separately two of the several mechanisms that may cause a lag phase: the lag caused by the initial low mean mass of the inoculum, and the lag caused by a change in the nutrient source. The relationship among lag duration and several variables such as temperature and inoculum size were also checked. This analysis allowed identification of the biomass distribution as a very important variable to follow the evolution of the culture during the growth cycle. A mathematical tool was defined in order to assess its evolution during the different phases of growth: the distance functions.A theoretical approach to the culture lag phase through the dynamics of the growth rate allowed us to split this phase into two stages: initial and transition. A continuous mathematical model was built in order to shape the transition stage, and it was checked with INDISIM simulations. It was seen that the lag phase must be defined as a dynamic process rather than as a simple period of time. The distance functions were also used to discuss the balanced growth conditions.Some of the reported INDISIM simulation results were subjected to experimental corroboration by means of flow cytometry, which allow the assessment of size distributions of a culture through time. The dynamics of biomass distribution given by INDISIM simulations were checked, as well as the distance function evolution during the different phases of growth. The coincidence between simulations and experiments is not trivial: the system under study is complex; therefore, the coincidence in the dynamics of the different modelled parameters is a validation of both the model and the simulation methodology.Finally, we have made progress in IbM parameter estimation methods, which is essential to improve quantitative processing of INDISIM simulations.Classic grid search, NMTA and NEWUOA methods were adapted and tested, the latter providing better results with regard to time spent, which maintains satisfactory precision in the parameter estimation results.Above all, the validity of INDISIM as a useful tool to tackle transient processes such as the bacterial lag phase has been amply demonstrated.

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Variation et sélection sont au coeur de l'évolution Darwinienne. Cependant, ces deux mécanismes dépendent de processus eux-mêmes façonnés par l'évolution. Chez les micro-organismes, qui font face à des environnements souvent variables, ces propriétés adaptatives sont particulièrement bien exploitées, comme le démontrent de nombreuses expériences en laboratoire. Chez ses organismes, l'évolution semble donc avoir optimisé sa propre capacité à évoluer, un processus que nous nommons évolution de l'évolution (EvoEvo). La notion d'évolution de l'évolution englobe de nombreux concepts théoriques, tels que la variabilité, l'évolvabilité, la robustesse ou encore la capacité de l'évolution à innover (open-endedness). Ces propriétés évolutives des micro-organismes, et plus généralement de tous les organismes vivants, sont soupçonnées d'agir à tous les niveaux d'organisation biologique, en interaction ou en conflit, avec des conséquences souvent complexes et contre-intuitives. Ainsi, comprendre l'évolution de l'évolution implique l'étude de la trajectoire évolutive de micro-organismes — réels ou virtuels —, et ce à différents niveaux d'organisation (génome, interactome, population, …). L'objectif de ce travail de thèse a été de développer et d'étudier des modèles mathématiques et numériques afin de lever le voile sur certains aspects de l'évolution de l'évolution. Ce travail multidisciplinaire, car impliquant des collaborations avec des biologistes expérimentateur•rice•s, des bio-informaticien•ne•s et des mathématicien•ne•s, s'est divisé en deux parties distinctes, mais complémentaires par leurs approches : (i) l'extension d'un modèle historique en génétique des populations — le modèle géométrique de Fisher — afin d'étudier l'évolution du bruit phénotypique en sélection directionnelle, et (ii) le développement d'un modèle d'évolution in silico multi-échelles permettant une étude plus approfondie de l'évolution de l'évolution. Cette thèse a été financée par le projet européen EvoEvo (FP7-ICT-610427), grâce à la commission européenne. / Variation and selection are the two core processes of Darwinian Evolution. Yet, both are directly regulated by many processes that are themselves products of evolution. Microorganisms efficiently exploit this ability to dynamically adapt to new conditions. Thus, evolution seems to have optimized its own ability to evolve, as a primary means to react to environmental changes. We call this process evolution of evolution (EvoEvo). EvoEvo covers several aspects of evolution, encompassing major concepts such variability, evolvability, robustness, and open-endedness. Those phenomena are known to affect all levels of organization in bacterial populations. Indeed, understanding EvoEvo requires to study organisms experiencing evolution, and to decipher the evolutive interactions between all the components of the biological system of interest (genomes, biochemical networks, populations, ...). The objective of this thesis was to develop and exploit mathematical and numerical models to tackle different aspects of EvoEvo, in order to produce new knowledge on this topic, in collaboration with partners from diverse fields, including experimental biology, bioinformatics, mathematics and also theoretical and applied informatics. To this aim, we followed two complementary approaches: (i) a population genetics approach to study the evolution of phenotypic noise in directional selection, by extending Fisher's geometric model of adaptation, and (ii) a digital genetics approach to study multi-level evolution. This work was funded by the EvoEvo project, under the European Commission (FP7-ICT-610427).

This thesis is presented as a collection of five papers and one report, each of which has been either published after peer review or submitted for publication. It covers a broad range of applied statistical methods, from deterministic modelling to integrated Bayesian modelling using MCMC, via bootstrapping and stochastic simulation. It also covers a broad range of subjects, from analysis of recreational fishing diaries, to genetic mark recapture for wombats. However, it focuses on practical applications of statistics to the management of wild populations. The first chapter (Hoyle and Jellyman 2002, published in Marine and Freshwater Research) applies a simple deterministic yield per recruit model to a fishery management problem: possible overexploitation of the New Zealand longfin eel. The chapter has significant implications for longfin eel fishery management. The second chapter (Hoyle and Cameron 2003, published in Fisheries Management and Ecology) focuses on uncertainty in the classical paradigm, by investigating the best way to estimate bootstrap confidence limits on recreational harvest and catch rate using catch diary data. The third chapter (Hoyle et al., in press with Molecular Ecology Notes) takes a different path by looking at genetic mark-recapture in a fisheries management context. Genetic mark-recapture was developed for wildlife abundance estimation but has not previously been applied to fish harvest rate estimation. The fourth chapter (Hoyle and Banks, submitted) addresses genetic mark-recapture, but in the wildlife context for estimates of abundance rather than harvest rate. Our approach uses individual-based modeling and Bayesian analysis to investigate the effect of shadows on abundance estimates and confidence intervals, and to provide guidelines for developing sets of loci for populations of different sizes and levels of relatedness. The fifth chapter (Hoyle and Maunder 2004, Animal Biodiversity and Conservation) applies integrated analysis techniques developed in fisheries to the modeling of protected species population dynamics - specifically the north-eastern spotted dolphin, Stenella attenuata. It combines data from a number of different sources in a single statistical model, and estimates parameters using both maximum likelihood and Bayesian MCMC. The sixth chapter (Hoyle 2002, peer reviewed and published as Queensland Department of Primary Industries Information Series) results directly from a pressing management issue: developing new management procedures for the Queensland east coast Spanish mackerel fishery. It uses an existing stock assessment as a starting point for an integrated Bayesian management strategy evaluation. Possibilities for further research have been identified within the subject areas of each chapter, both within the chapters and in the final discussion chapter.

The general aim of my dissertation was to investigate the role of plant interactions in driving population dynamics. Both theoretical and empirical approaches were employed. All my studies were conducted on the basis of metabolic scaling theory (MST), because the complex, spatially and temporally varying structures and dynamics of ecological systems are considered to be largely consequences of biological metabolism. However, MST did not consider the important role of plant interactions and was found to be invalid in some environmental conditions. Integrating the effects of plant interactions and environmental conditions into MST may be essential for reconciling MST with observed variations in nature. Such integration will improve the development of theory, and will help us to understand the relationship between individual level process and system level dynamics. As a first step, I derived a general ontogenetic growth model for plants which is based on energy conservation and physiological processes of individual plant. Taking the mechanistic growth model as basis, I developed three individual-based models (IBMs) to investigate different topics related to plant population dynamics: 1. I investigated the role of different modes of competition in altering the prediction of MST on plant self-thinning trajectories. A spatially-explicit individual-based zone-of-influence (ZOI) model was developed to investigate the hypothesis that MST may be compatible with the observed variation in plant self-thinning trajectories if different modes of competition and different resource availabilities are considered. The simulation results supported my hypothesis that (i) symmetric competition (e.g. belowground competition) will lead to significantly shallower self-thinning trajectories than asymmetric competition as predicted by MST; and (ii) individual-level metabolic processes can predict population-level patterns when surviving plants are barely affected by local competition, which is more likely to be in the case of asymmetric competition. 2. Recent studies implied that not only plant interactions but also the plastic biomass allocation to roots or shoots of plants may affect mass-density relationship. To investigate the relative roles of competition and plastic biomass allocation in altering the mass-density relationship of plant population, a two-layer ZOI model was used which considers allometric biomass allocation to shoots or roots and represents both above- and belowground competition simultaneously via independent ZOIs. In addition, I also performed greenhouse experiment to evaluate the model predictions. Both theoretical model and experiment demonstrated that: plants are able to adjust their biomass allocation in response to environmental factors, and such adaptive behaviours of individual plants, however, can alter the relative importance of above- or belowground competition, thereby affecting plant mass-density relationships at the population level. Invalid predictions of MST are likely to occur where competition occurs belowground (symmetric) rather than aboveground (asymmetric). 3. I introduced the new concept of modes of facilitation, i.e. symmetric versus asymmetric facilitation, and developed an individual-based model to explore how the interplay between different modes of competition and facilitation changes spatial pattern formation in plant populations. The study shows that facilitation by itself can play an important role in promoting plant aggregation independent of other ecological factors (e.g. seed dispersal, recruitment, and environmental heterogeneity). In the last part of my study, I went from population level to community level and explored the possibility of combining MST and unified neutral theory of biodiversity (UNT). The analysis of extensive data confirms that most plant populations examined are nearly neutral in the sense of demographic trade-offs, which can mostly be explained by a simple allometric scaling rule based on MST. This demographic equivalence regarding birth-death trade-offs between different species and functional groups is consistent with the assumptions of neutral theory but allows functional differences between species. My initial study reconciles the debate about whether niche or neutral mechanisms structure natural communities: the real question should be when and why one of these factors dominates. A synthesis of existing theories will strengthen future ecology in theory and application. All the studies presented in my dissertation showed that the approaches of individual-based and pattern-oriented modelling are promising to achieve the synthesis.

Les communautés végétales constituent des systèmes complexes au sein desquels de nombreuses espèces, pouvant présenter une large variété de traits fonctionnels, interagissent entre elles et avec leur environnement. En raison de la quantité et de la diversité de ces interactions les mécanismes qui gouvernent les dynamiques des ces communautés sont encore mal connus. Les approches basées sur la modélisation permettent de relier de manière mécaniste les processus gouvernant les dynamiques des individus ou des populations aux dynamiques des communautés qu'ils forment. L'objectif de cette thèse était de développer de telles approches et de les mettre en oeuvre pour étudier les mécanismes sous-jacents aux dynamiques des communautés. Nous avons ainsi développés deux approches de modélisation. La première s'appuie sur un cadre de modélisation stochastique permettant de relier les dynamiques de populations aux dynamiques des communautés en tenant compte des interactions intra- et interspécifiques et de l'impact des variations environnementale et démographique. Cette approche peut-être aisément appliquée à des systèmes réels et permet de caractériser les populations végétales à l'aide d'un petit nombre de paramètres démographiques. Cependant nos travaux suggèrent qu'il n'existe pas de relation simple entre ces paramètres et les traits fonctionnels des espèces, qui gouvernent pourtant leur réponse aux facteurs externes. La seconde approche a été développée pour dépasser cette limite et s'appuie sur le modèle individu-centré Nemossos qui représente de manière explicite le lien entre le fonctionnement des individus et les dynamiques de la communauté qu'ils forment. Afin d'assurer un grand potentiel d'application à Nemossos, nous avons apportés une grande attention au compromis entre réalisme et coût de paramétrisation. Nemossos a ainsi pu être entièrement paramétré à partir de valeur de traits issues de la littérature , son réalisme a été démontré, et il a été utilisé pour mener des expériences de simulations numériques sur l'importance de la variabilité temporelle des conditions environnementales pour la coexistence d'espèces fonctionnellement différentes. La complémentarité des deux approches nous a permis de proposer des éléments de réponse à divers questions fondamentales de l'écologie des communautés incluant le rôle de la compétition dans les dynamiques des communautés, l'effet du filtrage environnementale sur leur composition fonctionnel ou encore les mécanismes favorisant la coexistence des espèces végétales. Ici ces approches ont été utilisées séparément mais leur couplage peut offrir des perspectives intéressantes telles que l'étude du lien entre le fonctionnement des plantes et les dynamiques des populations. Par ailleurs chacune des approches peut être utilisée dans une grande variété d'expériences de simulation susceptible d'améliorer notre compréhension des mécanismes gouvernant les communautés végétales. / Plant communities are complex systems in which multiple species differing by their functional attributes interact with their environment and with each other. Because of the number and the diversity of these interactions the mechanisms that drive the dynamics of theses communities are still poorly understood. Modelling approaches enable to link in a mechanistic fashion the process driving individual plant or population dynamics to the resulting community dynamics. This PhD thesis aims at developing such approaches and to use them to investigate the mechanisms underlying community dynamics. We therefore developed two modelling approaches. The first one is based on a stochastic modelling framework allowing to link the population dynamics to the community dynamics whilst taking account of intra- and interspecific interactions as well as environmental and demographic variations. This approach is easily applicable to real systems and enables to describe the properties of plant population through a small number of demographic parameters. However our work suggests that there is no simple relationship between these parameters and plant functional traits, while they are known to drive their response to extrinsic factors. The second approach has been developed to overcome this limitation and rely on the individual-based model Nemossos that explicitly describes the link between plant functioning and community dynamics. In order to ensure that Nemossos has a large application potential, a strong emphasis has been placed on the tradeoff between realism and parametrization cost. Nemossos has then been successfully parameterized from trait values found in the literature, its realism has been demonstrated and it has been used to investigate the importance of temporal environmental variability for the coexistence of functionally differing species. The complementarity of the two approaches allows us to explore various fundamental questions of community ecology including the impact of competitive interactions on community dynamics, the effect of environmental filtering on their functional composition, or the mechanisms favoring the coexistence of plant species. In this work, the two approaches have been used separately but their coupling might offer interesting perspectives such as the investigation of the relationships between plant functioning and population dynamics. Moreover each of the approaches might be used to run various simulation experiments likely to improve our understanding of mechanisms underlying community dynamics.

The general aim of my dissertation was to investigate the role of plant interactions in driving population dynamics. Both theoretical and empirical approaches were employed. All my studies were conducted on the basis of metabolic scaling theory (MST), because the complex, spatially and temporally varying structures and dynamics of ecological systems are considered to be largely consequences of biological metabolism. However, MST did not consider the important role of plant interactions and was found to be invalid in some environmental conditions. Integrating the effects of plant interactions and environmental conditions into MST may be essential for reconciling MST with observed variations in nature. Such integration will improve the development of theory, and will help us to understand the relationship between individual level process and system level dynamics. As a first step, I derived a general ontogenetic growth model for plants which is based on energy conservation and physiological processes of individual plant. Taking the mechanistic growth model as basis, I developed three individual-based models (IBMs) to investigate different topics related to plant population dynamics: 1. I investigated the role of different modes of competition in altering the prediction of MST on plant self-thinning trajectories. A spatially-explicit individual-based zone-of-influence (ZOI) model was developed to investigate the hypothesis that MST may be compatible with the observed variation in plant self-thinning trajectories if different modes of competition and different resource availabilities are considered. The simulation results supported my hypothesis that (i) symmetric competition (e.g. belowground competition) will lead to significantly shallower self-thinning trajectories than asymmetric competition as predicted by MST; and (ii) individual-level metabolic processes can predict population-level patterns when surviving plants are barely affected by local competition, which is more likely to be in the case of asymmetric competition. 2. Recent studies implied that not only plant interactions but also the plastic biomass allocation to roots or shoots of plants may affect mass-density relationship. To investigate the relative roles of competition and plastic biomass allocation in altering the mass-density relationship of plant population, a two-layer ZOI model was used which considers allometric biomass allocation to shoots or roots and represents both above- and belowground competition simultaneously via independent ZOIs. In addition, I also performed greenhouse experiment to evaluate the model predictions. Both theoretical model and experiment demonstrated that: plants are able to adjust their biomass allocation in response to environmental factors, and such adaptive behaviours of individual plants, however, can alter the relative importance of above- or belowground competition, thereby affecting plant mass-density relationships at the population level. Invalid predictions of MST are likely to occur where competition occurs belowground (symmetric) rather than aboveground (asymmetric). 3. I introduced the new concept of modes of facilitation, i.e. symmetric versus asymmetric facilitation, and developed an individual-based model to explore how the interplay between different modes of competition and facilitation changes spatial pattern formation in plant populations. The study shows that facilitation by itself can play an important role in promoting plant aggregation independent of other ecological factors (e.g. seed dispersal, recruitment, and environmental heterogeneity). In the last part of my study, I went from population level to community level and explored the possibility of combining MST and unified neutral theory of biodiversity (UNT). The analysis of extensive data confirms that most plant populations examined are nearly neutral in the sense of demographic trade-offs, which can mostly be explained by a simple allometric scaling rule based on MST. This demographic equivalence regarding birth-death trade-offs between different species and functional groups is consistent with the assumptions of neutral theory but allows functional differences between species. My initial study reconciles the debate about whether niche or neutral mechanisms structure natural communities: the real question should be when and why one of these factors dominates. A synthesis of existing theories will strengthen future ecology in theory and application. All the studies presented in my dissertation showed that the approaches of individual-based and pattern-oriented modelling are promising to achieve the synthesis.