<p>Wrinkled patterns in biofilms arise from buckling instabilities triggered by stresses that accumulate as growth is constrained by a stationary substrate. While nutrient availability, friction, and adhesion each influence wrinkling, their combined effects remain poorly understood. Here, we address this gap using a lattice-network model of biofilm morphogenesis. Under constant nutrient supply, wrinkles initiate at the center, where stresses are highest and isotropic, regardless of the level of friction or adhesion. Stronger adhesion delays wrinkling and decouples the length scale governing the buckling instability from the overall biofilm size. Heterogeneous adhesion lowers the critical stress by triggering wrinkles in weakly adhered regions, with the effect modulated by friction and the average adhesion. Under nonuniform nutrient supply, our model predicts that wrinkle initiation shifts from the center to the edge as initial nutrient availability decreases, a transition we experimentally validate using <i>E. coli</i> biofilms.</p>