Related papers: Long-time behavior and darwinian optimality for an…

Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…

A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…

We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation.…

This paper concentrates on the limit behavior of discrete-time branching process with circular mechanism. Three types of limit behaviour of discrete-time branching process with circular mechanism are given explicitly under various moment…

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

Decision-making by imitating the highest earners has been observed in experimental studies. In two-strategy decision-making problems, this behavior may result in perpetual fluctuations in the population proportions of the two strategies.…

We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct…

We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…

We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process…

We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…

The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…

Asymmetric segregation of key proteins at cell division -- be it a beneficial or deleterious protein -- is ubiquitous in unicellular organisms and often considered as an evolved trait to increase fitness in a stressed environment. Here, we…

Cell movement, for example during embryogenesis or tumor metastasis, is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating…

A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…

The mean size of exponentially dividing E. coli cells cultured in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time and individual growth rate…

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…