In Evolutionary Dynamics the understanding of cooperative phenomena in natural and human social systems has been the subject of intense research for decades. I'll focus attention on the "Lattice Reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the Prisoner's Dilemma game when a population of Darwinian replicators interact through a fixed network of social contacts. Exact results on a Dipole Model Network will be presented, along with different types of mean-field analysis as well as extensive numerical Monte Carlo simulations. The theoretical framework used is that of Standard Statistical Mechanics of macroscopic systems, but with fitness (instead of energy) considerations.