The Importance of Being Discrete (and Spatial)

Durrett, Rick; Levin, Simon A.

doi:10.1006/tpbi.1994.1032

Cited by 969 publications

(760 citation statements)

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“…To study how individual-level interaction affects spacing patterns, we need to take into account the discreteness of the population and the mediated interaction events (22). We do so with an individual-based simulation in continuous time and discrete space (2D lattice) with periodic boundary conditions (see SI Appendix for mode details).…”

Section: Model and Resultsmentioning

confidence: 99%

Stigmergy, collective actions, and animal social spacing

Giuggioli

Potts

Rubenstein

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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Significance Marking animals avoid locations recently visited by others. We conceptualized this time nonlocal avoidance behavior as stigmergy, a form of mediated interaction that gives rise to coordinated behavior from seemingly independent individuals. In so doing, the concept of stigmergy is used beyond the realm of eusocial insects. To link the population spatiotemporal patterns that emerge from the individual nonlocal rules of interaction, we construct a collective movement model whereby randomly moving animals have the tendency to avoid marks left by a conspecific, depending on the age of the mark. As a result, we are able to quantify animal decision-making processes in terms of current and past locations of other individuals, linking behavior to history-dependent actions.

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Section: Model and Resultsmentioning

confidence: 99%

Stigmergy, collective actions, and animal social spacing

Giuggioli

Potts

Rubenstein

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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“…Each cell directly interacts with its nearest neighbors, which corresponds to a plant's sphere of influence. Besides the full spatial model, two analytic approximations, a mean field (ignoring spatial interactions; Durret and Levin, 1994) and a pair approximation (Sato and Iwasa, 2000;van Baalen, 2000), leading to two systems of ordinary differential equations, were derived and analyzed for conditions leading to bistability. Comparing the results of the mean field and of the pair approximation models allows understanding the role of local interactions on the bistability of the system.…”

Section: Article In Pressmentioning

confidence: 99%

Local facilitation, bistability and transitions in arid ecosystems

Kéfi

Rietkerk

Baalen³

et al. 2007

Theoretical Population Biology

174

221

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Arid ecosystems are liable to undergo sudden discontinuous transitions from a vegetated to a desert state as a result of human pressure and climate change. A predictive framework about the conditions under which such transitions occur is lacking. Here, we derive and analyze a general model describing the spatial dynamics of vegetation in arid ecosystems considering local facilitation as an essential process. We investigate the conditions under which continuous or discontinuous transitions from a vegetated to a desert state are likely to occur. We focus on arid ecosystems but our approach is sufficiently general to be applied to other ecosystems with severe environmental conditions. The model exhibits bistability and vegetation patchiness. High local facilitation decreases the risk of discontinuous transitions. Moreover, for arid ecosystems where local facilitation is a driving process, vegetation patchiness indicates proximity to a transition point, but does not allow distinguishing between continuous and discontinuous transitions. r

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“…Moreover, there are reasons to mistrust the spatial homogeneity and well-mixed assumptions that underlie continuous models based on ordinary differential equations (ODEs) [10][11][12], despite the success of such models in immunology and virology [13][14][15][16][17][18][19][20][21]. Disease processes are spatially distributed and it is likely that this spatial distribution is critical in determining the course of infection, as has been argued by many, including [22,23].…”

Section: Introductionmentioning

confidence: 99%

A virtual look at Epstein–Barr virus infection: Simulation mechanism

Shapiro

Duca

Lee

et al. 2008

Journal of Theoretical Biology

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Epstein-Barr virus (EBV) is an important human pathogen that establishes a lifelong persistent infection and for which no precise animal model exists. In this paper we describe in detail an agentbased model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer's ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death.

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The Importance of Being Discrete (and Spatial)

Cited by 969 publications

References 0 publications

Stigmergy, collective actions, and animal social spacing

Stigmergy, collective actions, and animal social spacing

Local facilitation, bistability and transitions in arid ecosystems

A virtual look at Epstein–Barr virus infection: Simulation mechanism

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