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We propose a model to describe the adaptation of a phenotypically structured population in a $H$-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous…
We investigate a model for a mosquito-borne epidemic in which human hosts may adopt protective behaviour against vector bites in response to information on both past and current disease prevalence. Assuming that mosquitoes can also feed on…
The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses such as HIV can cause chronic infections by evolving as quickly as the adaptive immune system, forming an…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a…
Modern ecology has re-emphasized the need for a quantitative understanding of the original 'survival of the fittest theme' based on analyzis of the intricate trade-offs between competing evolutionary strategies that characterize the…
Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence system are overwhelming against advanced propagation of the disease. News are becoming more effortlessly…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple…
We investigate the adaptive Ambush strategy in cyclic models following the rules of the spatial rock-paper-scissors game. In our model, individuals of one species possess cognitive abilities to perceive environmental cues and assess the…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To…
Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur,…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We discuss the feasibility of predicting, managing and subsequently manipulating, the future evolution of a Complex Adaptive System. Our archetypal system mimics a population of adaptive, interacting objects, such as those arising in the…
We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…
In past decades, Gaussian processes has been widely applied in studying trait evolution using phylogenetic comparative analysis. In particular, two members of Gaussian processes: Brownian motion and Ornstein-Uhlenbeck process, have been…