Oscillations in insulin secretion, driven by islet Ca2+ waves, are crucial for glycemic control. Prior studies, performed with single-plane imaging, suggest that subpopulations of electrically coupled β-cells have privileged roles in leading and coordinating the propagation of Ca2+ waves. Here, we used 3D light-sheet imaging to analyze the location and Ca2+ activity of single β-cells within the entire islet at >2 Hz. In contrast with single-plane studies, 3D network analysis indicates that the most highly synchronized β-cells are located at the islet center, and remain regionally but not cellularly stable between oscillations. This subpopulation, which includes 'hub cells', is insensitive to changes in fuel metabolism induced by glucokinase and pyruvate kinase activation. β-cells that initiate the Ca2+ wave ('leaders') are located at the islet periphery, and strikingly, change their identity over time via rotations in the wave axis. Glucokinase activation, which increased oscillation period, reinforced leader cells and stabilized the wave axis. Pyruvate kinase activation, despite increasing oscillation frequency, had no effect on leader cells, indicating the wave origin is patterned by fuel input. These findings emphasize the stochastic nature of the β-cell subpopulations that control Ca2+ oscillations and identify a role for glucokinase in spatially patterning 'leader' β-cells.