Related papers: Giant fluctuations in logistic growth

Theoretically, communities at or near their equilibrium species number resist entry of new species. Such 'biotic resistance' recently has been questioned because of successful entry of alien species into diverse natural communities. Data on…

We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…

We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…

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…

The degree to which population fluctuations arise from variable adult survival relative to variable recruitment has been debated widely for marine organisms. Disentangling these effects remains challenging because data generally are not…

This paper considers a multi-patch model, where each patch follows a logistic law, and patches are coupled by asymmetrical migration terms. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total…

The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…

Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…

Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist…

Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…

Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and…

Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…

We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the…

Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two…

The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…

At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…

We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population…

We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…

We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…