Many biological populations reside in increasingly fragmented landscapes, which arise from human activities and natural causes. Landscape characteristics may change abruptly in space and create sharp transitions (interfaces) in landscape quality. How patchy landscape affects ecosystem diversity and stability depends, among other things, on how individuals move through the landscape. Individuals adjust their movement behaviour to local habitat quality and show preferences for some habitat types over others. In this dissertation, we focus on how landscape composition and the movement behaviour at an interface between habitat patches of different quality affects the steady states of a single species and a predator-prey system. First, we consider a model for population dynamics in a habitat consisting of two homogeneous one-dimensional patches in a coupled ecological reaction-diffusion equation. Several recent publications by other authors explored how individual movement behaviour affects population-level dynamics in a framework of reaction-diffusion systems that are coupled through discontinuous boundary conditions. The movement between patches is incorporated into the interface conditions. While most of those works are based on linear analysis, we study positive steady states of the nonlinear equations. We establish the existence, uniqueness and global asymptotic stability of the steady state, and we classify their qualitative shape depending on movement behaviour. We clarify the role of nonrandom movement in this context, and we apply our analysis to a previous result where it was shown that a randomly diffusing population in a continuously varying habitat can exceed the carrying capacity at steady state. In particular, we apply our results to study the question of why and under which conditions the total population abundance at steady state may exceed the total carrying capacity of the landscape. Secondly, we model population dynamics with a predator-prey system in a coupled ecological reaction-diffusion equation in a heterogeneous landscape to study Turing patterns that emerge from diffusion-driven instability (DDI). We derive the DDI conditions, which consist of necessary and sufficient conditions for initiation of spatial patterns in a one-dimensional homogeneous landscape. We use a finite difference scheme method to numerically explore the general conditions using the May model, and we present numerical simulations to illustrate our results. Then we extend our studies on Turing-pattern formation by considering a predator-prey system on an infinite patchy periodic landscape. The movement between patches is incorporated into the interface conditions that link the reaction-diffusion equations between patches. We use a homogenization technique to obtain an analytically tractable approximate model and determine Turing-pattern formation conditions. We use numerical simulations to present our results from this approximation method for this model. With this tool, we then explore how differential movement and habitat preference of both species in this model (prey and predator) affect DDI.

L’os est un matériau vivant avec une structure hiérarchique complexe qui lui confère des propriétés mécaniques remarquables. L’os subit perpétuellement des contraintes mécaniques et physiologiques, ainsi sa qualité et sa résistance à la fracture évoluent constamment au cours du temps à travers le processus de remodelage osseux. La qualité osseuse est non seulement définie par la densité minérale osseuse mais également par les propriétés mécaniques ainsi que la microarchitecture. Dans le cadre de la présente thèse, on a développé une modélisation multiéchelle unifiée couplant à la fois les activités cellulaires au comportement mécanique de l'os tenant compte des différents niveaux hiérarchiques de l'os: de l’ultrastructure au remodelage osseux. Ce modèle permet d’étudier le comportement mécano-bibliologique de l’os et de prédire ses propriétés mécaniques apparentes à différentes échelles allant du nanoscopique au macroscopique en fonction des constituants élémentaires de l'os. Pour atteindre cet objectif, une démarche en quatre phases a été adoptée. La première phase consiste à décrire les constituants élémentaires de l’os. La deuxième phase avait pour objectif la modélisation multiéchelle de l'ultrastructure osseuse constituée de trois échelles nanoscopiques (microfibrille, fibrille et fibre) par la méthode des éléments finis et des réseaux de neurones. La troisième phase correspond à la modélisation des échelles micro-macroscopiques de l’os cortical (lamelle, ostéon, os cortical) en utilisant comme paramètres d’entrée les propriétés de la fibre déterminées dans la deuxième phase. Enfin, dans la dernière phase, on a développé un modèle mécano-biologique du remodelage osseux permettant de simuler le processus d'adaptation osseuse tenant compte explicitement des activités biologiques des cellules osseuses. Les propriétés mécaniques prédites par nos algorithmes multiéchelles ont servi pour alimenter le modèle de remodelage. Ce modèle a été implémenté au code de calcul d’éléments finis ABAQUS/Standard à travers sa routine utilisateur UMAT. Finalement, le modèle EF mécano-biologique multiéchelle du remodelage osseux a été appliqué pour simuler différents scénarii de remodelage sur des fémurs humains (2D et 3D). Différents facteurs ont été ainsi analysés tels que l'âge, le genre, l'amplitude des activités physiques, etc. Les résultats obtenus sont conformes (qualitativement) avec les observations cliniques et cohérents avec les différentes études expérimentales. En conclusion: (i) Les modèles unifiés ainsi développés (modèle multiéchelle, modèle mécano-biologique de remodelage osseux) contribuent à l'analyse fine du comportement de l'os humain. (ii) L'application des algorithmes a permis d'effectuer des essais virtuels pour analyser les effets combinés de nombreux facteurs caractérisant la qualité osseuse. / Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties. Bone undergoes permanent mechanical and physiological stresses, thus its quality and fracture toughness are constantly evolving over time through the process of bone remodeling. Bone quality is not only defined by bone mineral density but also by the mechanical properties and microarchitecture. The current thesis offers a multiscale modeling approach unifying the cell activity to the mechanical behavior, taking into consideration the hierarchical levels of bone, from the ultrastructure to bone remodeling. This model permits to study the mechanobiological behavior and to predict the mechanical properties of the bone at different scales from nano to macro depending on the elementary constituents of bone. To achieve the objective of the current work, an approach of four phases was adopted. The first phase is to describe the basic components of the bone. The second phase concerns the multiscale modeling of the three nanoscopic levels of bone ultrastructure (microfibril, fibril and fiber) by the finite element method and neural networks. The third phase aims to model the micro-macroscopic structures of cortical bone (lamella, osteon, cortical bone) using the fiber properties predicted from the second phase as input parameters. In the last phase, a mechano-biological model of bone remodeling was achieved to simulate the process of bone adaptation explicitly considering the biological activities of bone cells. Mechanical properties predicted by our multiscale algorithms were used to feed the remodeling model. This model has been implemented into the ABAQUS/Standard finite elements code as a user subroutine. Finally, the finite element mechano-biological multiscale model of bone remodeling was applied to simulate different scenarios on human femurs (2D and 3D). Hence, different factors such as: age, gender, physical activities, etc were analyzed. The obtained results are conformed (qualitatively) to clinical observations and consistent with the various experimental studies. In summary, (i) the models portrayed here (multiscale model, mechanical-biological model of bone remodeling) contribute by their unified approach to the realistic modeling of the response of human bone. (ii) The application of the algorithms permits to perform virtual experiments to scrutinize the combined effects of numerous factors dictating the bone quality.