相关论文: A spatially explicit Markovian individual-based mo…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
In this work, we investigate an individual-based model (IBM) for self-propelled agents interacting locally on a plane. Agents are characterized by their position, the angle determining their direction of motion, and their angular velocity.…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
A major challenge for community ecology is using spatio-temporal data to infer parameters of dynamical models without conducting laborious experiments. We present a novel framework from statistical physics -- Maximum Caliber -- to…
We propose a flexible stochastic framework for modeling the market share dynamics over time in a multiple markets setting, where firms interact within and between markets. Firms undergo stochastic idiosyncratic shocks, which contract their…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of…
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable,…
We propose and analyze an implicit mass-matrix penalization (IMMP) technique which enables efficient and exact sampling of the (Boltzmann/Gibbs) canonical distribution associated to Hamiltonian systems with fast degrees of freedom (fDOFs).…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
A complex two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. Monte-Carlo type computer simulations are performed on the model, investigating species…
Understanding how multicellular organisms reliably orchestrate cell-fate decisions is a central challenge in developmental biology. This is particularly intriguing in early mammalian development, where early cell-lineage differentiation…
We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with space-mean dependence. Such systems are proposed as models for population growth in a random environment. We obtain sufficient and…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space…