From Individuals to Aggregations: the Interplay between Behavior and Physics

Flierl, Glenn R.; Grünbaum, Daniel; Levin, Simon A.; Olson, Donald B.

doi:10.1006/jtbi.1998.0842

Cited by 346 publications

(265 citation statements)

References 0 publications

Supporting

Mentioning

259

Contrasting

Unclassified

Order By: Relevance

“…The Lagrangian approach treats each organism as a particle obeying a nonlinear difference or differential equation (Sakai, 1973;Suzuki and Sakai, 1973;Okubo et al, 1977;Vicsek et al, 1995;Levine et al, 2001;Schweitzer et al, 2001;Couzin et al, 2002;Erdmann et al, 2002;Parrish et al, 2003;Aldana and Huepe, 2003;Erdmann and Ebeling, 2003;Mogilner et al, 2003). Alternatively, the Eulerian approach describes the local flux of individuals with an advectiondiffusion equation for a continuum population density field (Kawasaki, 1978;Okubo, 1980;Mimura and Yamaguti, 1982;Passo and Demottoni, 1984;Ikeda, 1984;Alt, 1985;Ikeda, 1985;Satsuma and Mimura, 1985;Ikeda and Nagai, 1987;Hosono and Mimura, 1989;Grünbaum and Okubo, 1994;Edelstein-Keshet et al, 1998;Toner and Tu, 1998;Flierl et al, 1999;Mogilner and Edelstein-Keshet, 1999;Topaz and Bertozzi, 2004). A variety of methods can be used to connect the two formulations.…”

Section: Introductionmentioning

confidence: 99%

A Nonlocal Continuum Model for Biological Aggregation

Bertozzi²,

2006

View full text Add to dashboard Cite

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady state clumps are approached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit. The energy result holds in higher dimensions, as well, and is demonstrated via numerical simulations in two dimensions.

show abstract

Section: Introductionmentioning

confidence: 99%

A Nonlocal Continuum Model for Biological Aggregation

Bertozzi²,

2006

View full text Add to dashboard Cite

show abstract

“…Aggregation of organisms is one of the topics widely researched through this line (see Ref. [16] for a review). In some cases the nonlocality arises from the type of motion of the individuals, such as in Ref.…”

Section: Introductionmentioning

confidence: 99%

Clustering, advection, and patterns in a model of population dynamics with neighborhood-dependent rates

2004

View full text Add to dashboard Cite

We introduce a simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles arranged periodically in space. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model, such as the average number of individuals.

show abstract

“…Conservation biology has raised many new problems, including those associated with the design of nature reserves, and the fascinating subject of collective motion has attracted the attention of biologists, mathematicians and physicists alike [6,21]. Substantive mathematical problems remain, like the problem of scaling from the microscopic to the macroscopic, marrying the Lagrangian and Eulerian perspectives [8]. All of these issues are evident in the broad scope of the papers in this volume.…”

Section: Forewordmentioning

confidence: 99%

“…[4][5][6][7][8] considers how the properties of individual movement can be scaled up to the population level. It starts with a review of mathematical models of self-organized population patterning with an emphasis on interaction and communication between the individuals (Chap.…”

Section: Prefacementioning

confidence: 99%