Related papers: A Non-Phenomenological Model to Explain Population…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment, focusing on whether a population already established in one patch either successfully invades an adjacent empty…
Human populations exhibit complex behaviors---characterized by long-range correlations and surges in activity---across a range of social, political, and technological contexts. Yet it remains unclear where these collective behaviors come…
Inspired by the work of [Kempe, Kleinberg, Oren, Slivkins, EC13] we introduce and analyze a model on opinion formation; the update rule of our dynamics is a simplified version of that of Kempe et. al. We assume that the population is…
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their…
We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power \alpha) and distance from city (to power -\beta) and…
Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
Predation driven Allee effects play an important role in the dynamics of small population, however, such predation-driven Allee effects cannot occur for the model with type I functional response. It generally occurs when a generalist…
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…
In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an…
The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits…
We consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and growth. The growth term may be of the Fisher-KPP type but may…
The dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and…
In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…