Related papers: Spine for interacting populations and sampling

Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…

Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the…

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…

The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…

We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted…

The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.

The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…

This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

Complex time-varying systems are often studied by abstracting away from the dynamics of individual components to build a model of the population-level dynamics from the start. However, when building a population-level description, it can be…

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.…

To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…

Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population…

Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…

A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…

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 work focuses on clustering populations with a hierarchical dependency structure that can be described by a tree. A particular example that is the focus of our work is the phylogenetic tree, with nodes often representing biological…

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…