  It is well-known that population structure is a catalyst for the evolution of
cooperation since individuals can reciprocate with their neighbors through
local interactions defined by network structures. Previous research typically
relies on the assumption that population size is fixed and the structure is
time-invariant, which is represented by a static network. However, real-world
populations are often evolving with the successive growth of nodes and links in
time, resulting in time-varying population structures. Here we model such
growing networked populations by sequential temporal networks with an
increasing number of nodes and edges and develop the theory of evolutionary
dynamics on sequential temporal networks. We derive explicit conditions under
which sequential temporal networks promote the evolution of cooperation
relative to their static counterparts. In particular, even if natural selection
disfavours cooperative behaviours on static networks, sequential temporal
networks can surprisingly rescue cooperation. Furthermore, we demonstrate
empirically that sequential temporal networks assembled from synthetic and
empirical datasets present such promotion in the evolution of cooperation. Our
results advance the study of evolutionary dynamics on temporal networks and
open the avenue for investigating the evolution of prosocial and other
behaviours.
