Related papers: Large population limit of interacting population d…
We study the large scale behaviour of a population consisting of two types which evolve in dimension d = 1, 2 according to a spatial Lambda- Fleming-Viot process subject to random time-independent selection. If one of the two types is rare…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the…
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…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
Interacting particle systems provide a fundamental framework for modeling collective behavior in biological, social, and physical systems. In many applications, stochastic perturbations are essential for capturing environmental variability…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
Advection of entities induced by gradients in attractant concentration fields is observed via diffusiophoresis in colloids and via chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
The superior Fisher-Kopeliovich closure is applied to the hierarchy of master equations for spatial moments of population dynamics for the first time. As a consequence, the population density, pair and triplet distribution functions are…
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…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
This paper builds upon the methods developed in [22] and [15] to investigate the large population behavior of non exchangeable systems of N diffusive particles when the interaction matrix converges (in some sense) to a graphon. We first…
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…