Related papers: Adaptation in a heterogeneous environment. I: Pers…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
We study a stochastic epidemic model with multiple patches (locations), where individuals in each patch are categorized into three compartments, Susceptible, Infected and Recovered/Removed, and may migrate from one patch to another in any…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in continuous homogeneous environments through isolation by distance. When the environment is not homogeneous, natural…
Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this work, we study a one-dimensional…
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc.…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
Biological systems must be robust for stable function against perturbations, but robustness alone is not sufficient. The ability to switch between appropriate states (phenotypes) in response to different conditions is essential for…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
How adaptive evolution to one environmental stress improves or suppresses adaptation to another is an important problem in evolutionary biology. For instance, in microbiology, the evolution of bacteria to be resistant to different…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology, i.e. in cancer evolution. These dynamics play an important…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist…
A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a…
Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring…