Natural Selection of cooperation and degree hierarchy in heterogeneous populations
J. Poncela, J. Gómez-Gardeñes, L.M. Floría, Y. MorenoJOURNAL OF THEORETICAL BIOLOGY 253, 296 (2008)
Times cited: 37
Abstract
One of the current theoretical challenges to the explanatory powers of
Evolutionary Theory is the
understanding of the observed evolutionary survival of cooperative
behavior when selfish actions
provide higher fitness (reproductive success). In unstructured
populations natural selection drives
cooperation to extinction. However, when individuals are allowed to
interact only with their neighbors,
specified by a graph of social contacts, cooperation-promoting
mechanisms (known as lattice
reciprocity) offer to cooperation the opportunity of evolutionary
survival. Recent numerical works on
the evolution of Prisoner’s Dilemma in complex network settings have
revealed that graph
heterogeneity dramatically enhances the lattice reciprocity. Here we
show that in highly heterogeneous
populations, under the graph analog of replicator dynamics, the fixation
of a strategy in the whole
population is in general an impossible event, for there is an asymptotic
partition of the population in
three subsets, two in which fixation of cooperation or defection has
been reached and a third one which
experiences cycles of invasion by the competing strategies. We show how
the dynamical partition
correlates with connectivity classes and characterize the temporal
fluctuations of the fluctuating set,
unveiling the mechanisms stabilizing cooperation in macroscopic
scale-free structures.