<p>We develop an evolutionary model to study the emergence of natural property rights (NPR) in a structured population with an endogenously evolving connection network. We propose a novel network-rewiring rule that governs how agents adjust their social connections. The rule is compatible with economic rationality and generates a mechanism of selfish punishment that stabilizes an equilibrium in which property rights are respected. Crucially, this punishment does not rely on third-party enforcement, altruistic behavior, or exogenous asymmetries between owners and intruders, and can therefore arise spontaneously among selfish agents. We compare our network-based model with the canonical endowment-effect model and show that their distinct driving forces generate fundamentally different convergence paths toward NPR and opposite welfare dynamics. While the endowment-effect model relies on defensive fighting to sustain convergence, our model allows NPR to emerge peacefully through endogenous partner selection. Along this process, individual incentives are aligned with aggregate population welfare. From this perspective, our framework offers a novel and historically plausible explanation for the emergence of natural property rights.</p>