  We explore the evolution of cooperation in the framework of the evolutionary
game theory using the prisoner's dilemma as metaphor of the problem. We present
a minimal model taking into account the growing process of the systems and
individuals with imitation capacity. We consider the topological structure and
the evolution of strategies decoupled instead of a coevolutionary dynamic. We
show conditions to build up a cooperative system with real topological
structures for any natural selection intensity. When the system starts to grow,
cooperation is unstable but becomes stable as soon as the system reaches a
small core of cooperators whose size increase when the intensity of natural
selection decreases. Thus, we reduce the emergence of cooperative systems with
cultural reproduction to justify a small initial cooperative structure that we
call cooperative seed. Otherwise, given that the system grows principally as
cooperator whose cooperators inhabit the most linked parts of the system, the
benefit-cost ratio required for cooperation evolve is drastically reduced
compared to the found in static networks. In this way, we show that in systems
whose individuals have imitation capacity the growing process is essential for
the evolution of cooperation.
