  Cooperation is ubiquitous in every level of living organisms. It is known
that spatial (network) structure is a viable mechanism for cooperation to
evolve. Until recently, it has been difficult to predict whether cooperation
can evolve at a network (population) level. To address this problem, Pinheiro
et al. proposed a numerical metric, called Average Gradient of Selection (AGoS)
in 2012. AGoS can characterize and forecast the evolutionary fate of
cooperation at a population level. However, stochastic mutation of strategies
was not considered in the analysis of AGoS. Here we analyzed the evolution of
cooperation using AGoS where mutation may occur to strategies of individuals in
networks. Our analyses revealed that mutation always has a negative effect on
the evolution of cooperation regardless of the fraction of cooperators and
network structures. Moreover, we found that mutation affects the fitness of
cooperation differently on different social network structures.
