Related papers: The Dynamics of Probabilistic Population Protocols
The transmission of monkeypox is studied using a stochastic model taking into account the biological aspects, the contact mechanisms and the demographic factors together with the intrinsic uncertainties. Our results provide insight into the…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
We consider several families of long jump random walks on groups of polynomial volume growth which are naturally expected to have a stable-like behavior. We then prove optimal pseudo-Poincar\'e inequalities for these walks. These…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
This tutorial article puts forth a framework to analyze the noncooperative strategic interactions among the members of a large population of bounded rationality agents. Our approach hinges on, unifies and generalizes existing methods and…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of…
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…
Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an…
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…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…