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Spatial structure can play an important role in the evolution of cooperative behavior and the achievement of collective success of a population. In this paper, we explore the role of random and directed motion on spatial pattern formation…

Populations and Evolution · Quantitative Biology 2025-09-26 Tianyong Yao , Chenning Xu , Daniel B. Cooney

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource…

Populations and Evolution · Quantitative Biology 2026-03-24 Yuxuan Zhao , Kaisheng Zhu , Yefei Zhang , Daniel B. Cooney

Populations of globally coupled identical maps subject to additive, independent noise are studied in the regimes of strong coupling. Contrary to each noisy population element, the mean field dynamics undergoes qualitative changes when the…

Statistical Mechanics · Physics 2007-05-23 Silvia De Monte , Francesco d'Ovidio , Erik Mosekilde

We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability…

Dynamical Systems · Mathematics 2020-04-24 Irina Vortkamp , Sebastian J. Schreiber , Alan Hastings , Frank M. Hilker

We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schr\"{o}dinger equation for a quantum particle subjected to a uniform…

Adaptation and Self-Organizing Systems · Physics 2008-11-17 Niraj Kumar , V. M. Kenkre

Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…

Populations and Evolution · Quantitative Biology 2024-12-30 Alia Abbara , Anne-Florence Bitbol

This paper is devoted to a nonlocal reaction-diffusion-advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamic…

Analysis of PDEs · Mathematics 2024-05-14 Yaobin Tang , Binxiang Dai

This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…

Analysis of PDEs · Mathematics 2016-03-29 Ling Jin , Qi Wang , Zengyan Zhang

In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals…

Analysis of PDEs · Mathematics 2023-01-04 Rui Peng , Zhi-an Wang , Guanghui Zhang , Maolin Zhou

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…

Classical Analysis and ODEs · Mathematics 2010-03-02 Yun Kang , Nicolas Lanchier

The spatial structure of populations may promote the emergence and maintenance of cooperation. Cooperation in the prisoner's dilemma is favored under specific update rules in evolutionary graph theory models with one individual per node of…

Populations and Evolution · Quantitative Biology 2026-01-29 Damien Ribière , Alia Abbara , Anne-Florence Bitbol

Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…

Dynamical Systems · Mathematics 2015-10-01 Stefan C. Mancas , Roy S. Choudhury

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…

Condensed Matter · Physics 2007-05-23 Irene Giardina , Jean-Philippe Bouchaud , Marc Mezard

This paper investigates a class of reaction-diffusion population models defined on a bounded domain, characterized by a general time-delayed per capita growth rate and a general advection term. Notably, the growth rate encompasses both…

Dynamical Systems · Mathematics 2025-12-04 Jingxiao Song , Chengwei Ren , Shaofen Zou

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

Quantitative Methods · Quantitative Biology 2015-10-05 Christian A. Yates , Mark B. Flegg

We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a…

Populations and Evolution · Quantitative Biology 2023-05-04 J. Menezes , E. Rangel

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…

patt-sol · Physics 2016-09-08 Xiao-Biao Lin

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…

Machine Learning · Computer Science 2025-11-05 Qingyue Long , Can Rong , Tong Li , Yong Li

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…

Analysis of PDEs · Mathematics 2019-09-10 Yan Wang , Junping Shi

We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…

Probability · Mathematics 2011-12-05 Nicolas Champagnat , Amaury Lambert