Related papers: Long-time behavior and darwinian optimality for an…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
We propose and analyze a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by potential applications in viral marketing and cancer treatment. We show that the optimal exponential…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
The complexity of gene regulatory networks in multicellular organisms makes interpretable low-dimensional models highly desirable. An attractive geometric picture, attributed to Waddington, visualizes the differentiation of a cell into…
We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…
We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…
We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations…
One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbr\"uck. Here, individual resistant mutants emerge…
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action…