A central issue in biology concerns the presence, timing and nature of phylotypic periods of development, but whether, when and why species exhibit conserved morphologies remains unresolved. Here, we construct a developmental morphospace to show that amniote faces share a period of reduced shape variance and convergent growth trajectories from prominence formation through fusion, after which phenotypic diversity sharply increases. We predict in silico the phenotypic outcomes of unoccupied morphospaces and experimentally validate in vivo that observed convergence is not due to developmental limits on variation but instead from selection against novel trajectories that result in maladaptive facial clefts. These results illustrate how epigenetic factors such as organismal geometry and shape impact facial morphogenesis and alter the locus of adaptive selection to variation in later developmental events.