The role of punishment and its effects in a spatial structured population in promoting cooperation are relevant issues. In the Snowdrift Game (SG) incorporating a Punisher agent (P), Chan et al. (2013) studied the effects of a population linked by a spatial network. Punishers, which carry a cooperative character (C), are willing to pay a cost alpha in order to punish a defector (D), i.e., a non-cooperative opponent, in a beta cost. Depending on the values assigned to alpha, beta, the ratio of cost-benefit r, and the initial distribution of the frequency of the strategies, the system displays an evolutionary behavior that can be homogeneous, with only a single strategy perpetuating in the long run, or non-homogeneous, with over a strategy corresponding to the asymptotic equilibrium. The spatial structure imposes a geometric constraint on the competitive environment. In this work, we extended the model proposed by Chan et al. (2013) for two populations with spatial arrangement. The results of numerical simulations are presented. The dynamic observed in the Agent Based Simulation approach in two spatial networks is discussed. In contrast to a single structured population, punishing strategy (P) survive in only one of the cases we shown. In the evolutionary equilibrium long-term, the competitive dynamics set in two spatial populations differs from that one presented by Chan et al. (2013). In this sense, we can observe the formation of entire populations of cooperators and defectors or the coexistence of C and P in each of the two populations for the case that the cost to benefit of cooperation is extremely low.