The document compares the performance of different population structures (ring, Watts-Strogatz, newscast) for a peer-to-peer evolutionary algorithm. It models a fine-grained parallel evolutionary algorithm using a peer-to-peer protocol as the underlying population structure. The experimental analysis tests these population structures on a 2-trap problem and finds that regular lattices require smaller population sizes but more evaluations to find a solution, while different small-world methods produce equivalent performance. Future work is proposed to validate the model on a real peer-to-peer infrastructure and explore other population structures and metaheuristics.