Heterogeneous animal group models and their group-level alignment dynamics: An equation-free approach

Moon, Sung Joon; Nabet, Benjamin; Leonard, Naomi Ehrich; Levin, Simon A.; Kevrekidis, I. G.

doi:10.1016/j.jtbi.2006.12.018

Cited by 14 publications

(11 citation statements)

References 42 publications

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“…Indeed some of the very same bifurcations proven in the present paper are recovered numerically in [19] suggesting a measure of robustness to the results here.…”

Section: Resultssupporting

confidence: 83%

Dynamics of Decision Making in Animal Group Motion

et al. 2009

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We present a continuous model of a multi-agent system motivated by simulation studies on dynamics of decision making in animal groups in motion. Each individual moves at constant speed in the plane and adjusts its heading in response to relative headings of others in the population. Two subgroups of the population are informed such that individuals in each subgroup have a preferred direction of motion. The model exhibits fast and slow time scales allowing for a reduction in the dimension of the problem. The stable solutions for the reduced model correspond to compromise by individuals with conflicting preferences. We study the global phase space for the proposed reduced model by computing equilibria and proving stability and bifurcations.

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“…Indeed some of the very same bifurcations proven in the present paper are recovered numerically in [19] suggesting a measure of robustness to the results here.…”

Section: Resultssupporting

confidence: 83%

Dynamics of Decision Making in Animal Group Motion

et al. 2009

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“…12 were shown to persist in the presence of randomness in the investigation of ref. 22. Simulations of the model presented here with some randomness suggest similarly that our results are robust (SI Text).…”

Section: Modelsupporting

confidence: 75%

Decision versus compromise for animal groups in motion

Leonard¹,

Tian²,

Nabet³

et al. 2011

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

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Previously, we showed using a computational agent-based model that a group of animals moving together can make a collective decision on direction of motion, even if there is a conflict between the directional preferences of two small subgroups of "informed" individuals and the remaining "uninformed" individuals have no directional preference. The model requires no explicit signaling or identification of informed individuals; individuals merely adjust their steering in response to socially acquired information on relative motion of neighbors. In this paper, we show how the dynamics of this system can be modeled analytically, and we derive a testable result that adding uninformed individuals improves stability of collective decision making. We first present a continuous-time dynamic model and prove a necessary and sufficient condition for stable convergence to a collective decision in this model. The stability of the decision, which corresponds to most of the group moving in one of two alternative preferred directions, depends explicitly on the magnitude of the difference in preferred directions; for a difference above a threshold the decision is stable and below that same threshold the decision is unstable. Given qualitative agreement with the results of the previous simulation study, we proceed to explore analytically the subtle but important role of the uninformed individuals in the continuous-time model. Significantly, we show that the likelihood of a collective decision increases with increasing numbers of uninformed individuals.collective behavior | Kuramoto | coordinated movement E xplaining the ability of animals that move together in a group to make collective decisions requires an understanding of the mechanisms of information transfer in spatially evolving distributions of individuals with limited sensing capability (1-6). In groups such as fish schools and large insect swarms, it is likely that individuals can sense only the relative motion of near neighbors and may not have the capacity to distinguish a wellinformed neighbor from the less well informed (2, 3). Further, it is increasingly becoming recognized that the emergent intelligence of a collective may be more reliable than the intelligence provided by a few leaders or well-informed individuals (7-11). This result suggests a subtle but important role in collective decision making for those individuals that have no particular information or preference.In this paper we define and analyze a continuous-time dynamical system model to examine collective decision making in moving groups of informed and uninformed individuals that are limited to sensing the relative motion of neighbors and adjusting their steering in response. Informed individuals have a preference for one of two alternative directions of motion, whereas uninformed individuals have no preference. The preferences are representative of knowledge of the direction to a food source or of a migration route, etc. In the discrete-time model of ref. 1 there is no signaling, no identification of t...

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“…The first efforts in this vein focused on testing the hypothesis in mobile animal groups, using strongly schooling golden shiner fish, and more generally on the nature of consensus within animal populations searching for targets, but where there is no variability in terms of how strongly opinions are held (111,(117)(118)(119). A major conclusion is that, although leaders obviously are important, the unopinionated are also crucial to the consensus in their ability to connect the population, and to shift momentum from one direction to the other.…”

Section: Collective Phenomena and Collective Decision-makingmentioning

confidence: 99%

Public goods in relation to competition, cooperation, and spite

Levin

2014

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

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104

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Public goods and common-pool resources are fundamental features of biological and social systems, and pose core challenges in achieving sustainability; for such situations, the immediate interests of individuals and the societies in which they are embedded are in potential conflict, involving game-theoretic considerations whose resolution need not serve the collective good. Evolution has often confronted such dilemmas-e.g., in bacterial biofilms-in the challenges of cancer, in nitrogen fixation and chelation, in the production of antibiotics, and in collective action problems across animal groups; there is much to learn from the Darwinian resolution of these situations for how to address problems our societies face today. Addressing these problems involves understanding the emergence of cooperative agreements, from reciprocal altruism and insurance arrangements to the social norms and more formal institutions that maintain societies. At the core are the issues of how individuals and societies discount the future and the interests of others, and the degree that individual decisions are influenced by regard for others. Ultimately, as Garrett Hardin suggested, the solution to problems of the commons is in "mutual coercion, mutually agreed upon," and hence in how groups of individuals form and how they arrive at decisions that ultimately benefit all.prosociality | collective phenomena | complex adaptive systems

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Heterogeneous animal group models and their group-level alignment dynamics: An equation-free approach

Cited by 14 publications

References 42 publications

Dynamics of Decision Making in Animal Group Motion

Dynamics of Decision Making in Animal Group Motion

Decision versus compromise for animal groups in motion

Public goods in relation to competition, cooperation, and spite

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