The proliferative and functional heterogeneity among seemingly uniform cells is a universal phenomenon. Identifying the underlying factors requires single-cell analysis of function and proliferation. Here we show that the pancreatic beta-cells in zebrafish exhibit different growth-promoting and functional properties, which in part reflect differences in the time elapsed since birth of the cells. Calcium imaging shows that the beta-cells in the embryonic islet become functional during early zebrafish development. At later stages, younger beta-cells join the islet following differentiation from post-embryonic progenitors. Notably, the older and younger beta-cells occupy different regions within the islet, which generates topological asymmetries in glucose responsiveness and proliferation. Specifically, the older beta-cells exhibit robust glucose responsiveness, whereas younger beta-cells are more proliferative but less functional. As the islet approaches its mature state, heterogeneity diminishes and beta-cells synchronize function and proliferation. Our work illustrates a dynamic model of heterogeneity based on evolving proliferative and functional beta-cell states.