TY - JOUR
T1 - Superdiffusion and encounter rates in diluted, low dimensional worlds
AU - Bartumeus, F.
AU - Fernández, P.
AU - da Luz, M. G.E.
AU - Catalan, J.
AU - Solé, R. V.
AU - Levin, S. A.
N1 - Funding Information:
FB and SAL dedicate the present work to the memory of Prof. R. Margalef. FB also thanks D. Alonso and S. Bernal for contributing in the development of previous stages of the work. This study was supported by funds provided by DARPA (HR0011-05-1-0057) and the Andrew W. Mellon Foundation. FB’s work was also supported by a postdoctoral fellowhip from the Spanish Government (EX-2005-1011) and the National Science Foundation (DEB-0083566).
PY - 2008/4
Y1 - 2008/4
N2 - Rate limitation due to encounters is fundamental to many ecologicalinteractions. Since encounter rate governs reaction rates, and thus, dynamics of systems, it deserves systematic study. In classicalpopulation biology, ecological dynamics rely on the assumption ofperfectly mixed interacting entities (e.g., individuals, populations,etc.) in a spaceless world. The so-called mean field assumptionassumes that encounter rates are driven exclusively by changes in thedensity of the interacting entities and not on how they aredistributed or move in space. Therefore, the mean field assumptiondoes not give any insight into relevant spatiotemporal statisticalproperties produced by the trajectories of moving entities throughspace. In the present study, we develop spatially explicitsimulations of random walking particles (i.e., Lévy walkers) toevaluate encounter rate constraints beyond the mean fieldassumption. We show that encounter rate fluctuations are driven notonly by physical aspects such as the size or the velocity of theinteracting particles, but also by different motion patterns. Inparticular, superdiffusion phenomena might be relevant at lowdensities and/or low spatial dimensionality. Finally, we discusspotential adaptive responses of living organisms that may allowindividuals to control how they diffuse through space and/or thespatial dimensions employed in the exploration process.
AB - Rate limitation due to encounters is fundamental to many ecologicalinteractions. Since encounter rate governs reaction rates, and thus, dynamics of systems, it deserves systematic study. In classicalpopulation biology, ecological dynamics rely on the assumption ofperfectly mixed interacting entities (e.g., individuals, populations,etc.) in a spaceless world. The so-called mean field assumptionassumes that encounter rates are driven exclusively by changes in thedensity of the interacting entities and not on how they aredistributed or move in space. Therefore, the mean field assumptiondoes not give any insight into relevant spatiotemporal statisticalproperties produced by the trajectories of moving entities throughspace. In the present study, we develop spatially explicitsimulations of random walking particles (i.e., Lévy walkers) toevaluate encounter rate constraints beyond the mean fieldassumption. We show that encounter rate fluctuations are driven notonly by physical aspects such as the size or the velocity of theinteracting particles, but also by different motion patterns. Inparticular, superdiffusion phenomena might be relevant at lowdensities and/or low spatial dimensionality. Finally, we discusspotential adaptive responses of living organisms that may allowindividuals to control how they diffuse through space and/or thespatial dimensions employed in the exploration process.
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U2 - 10.1140/epjst/e2008-00638-6
DO - 10.1140/epjst/e2008-00638-6
M3 - Article
AN - SCOPUS:42649120111
SN - 1951-6355
VL - 157
SP - 157
EP - 166
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 1
ER -