PMID: 22587213May 17, 2012Paper

Percolation threshold determines the optimal population density for public cooperation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Zhen WangMatjaz Perc

Abstract

While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact of population density on the evolution of public cooperation in structured populations and find that the optimal density is uniquely related to the percolation threshold of the host graph irrespective of its topological details. We explain our observations by showing that spatial reciprocity peaks in the vicinity of the percolation threshold, when the emergence of a giant cooperative cluster is hindered neither by vacancy nor by invading defectors, thus discovering an intuitive yet universal law that links the population density with social prosperity.

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Citations

Jun 4, 2014·PloS One·Pierre Buesser, Marco Tomassini
Mar 15, 2013·Journal of Theoretical Biology·Attila Szolnoki, Matjaž Perc
May 26, 2015·Journal of Theoretical Biology·Xiaofeng WangLong Wang
May 17, 2015·Physics of Life Reviews·Zhen WangJun Tanimoto
Feb 11, 2014·Journal of Theoretical Biology·Zhen WangMatjaž Perc
Apr 19, 2015·Journal of Theoretical Biology·Aming Li, Long Wang
Aug 27, 2013·Scientific Reports·Genki IchinoseDavid Sloan Wilson
Aug 21, 2013·Scientific Reports·Zhen WangMatjaž Perc
Aug 22, 2013·Scientific Reports·Luo-Luo Jiang, Matjaž Perc
Jun 10, 2014·Scientific Reports·Haibin Duan, Changhao Sun
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xiaojie ChenMatjaž Perc
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Keizo ShigakiNaoki Ikegaya
Jan 11, 2013·Journal of the Royal Society, Interface·Matjaz PercYamir Moreno
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Anatolij GelimsonErwin Frey
Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Genki IchinoseToshihiro Tanizawa
Oct 16, 2016·Physical Review. E·Alex StivalaMichael Kirley
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Woosik ChoiYup Kim
Oct 22, 2019·Journal of Molecular Biology·J CremerE Frey
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mendeli H VainsteinJeferson J Arenzon
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kohei MiyajiNaoki Ikegaya
Nov 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre BuesserAlberto Antonioni

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