Related papers: Self-regulation in continuum population models
We investigate how initial and boundary conditions influence the competition dynamics and outcome in dispersal-structured populations. The study is carried out through numerical modeling of the heterogeneous Brownian bugs model, in which…
We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch,…
General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
We study a discrete time spatial branching system on $\mathbb{Z}^d$ with logistic-type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
The evolution of an infinite system of interacting point entities with traits $x\in \mathds{R}^d$ is studied. The elementary acts of the evolution are state-dependent death of an entity with rate that includes a competition term and…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is a…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…
How self-organized networks develop, mature and degenerate is a key question for sociotechnical, cyberphysical and biological systems with potential applications from tackling violent extremism through to neurological diseases. So far, it…
We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated populations which are initially large. Under general…
We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…