In normal development and tumor metastasis, epithelial cells can acquire migratory and invasive properties. Border cells in the Drosophila ovary provide a genetic model for such behaviors. Earlier work has shown that JAK/STAT signaling is critical to specify the migratory population and sustain their motility. In a genetic screen for new mutations that affect border cell motility, we identified the gene apontic. Apontic, a nuclear protein, converts an initially graded pattern of STAT activity into an all-or-nothing response. This defines and limits the invasive border cell population. Apt functions as a feedback inhibitor of STAT, providing a molecular mechanism to explain a classic problem in embryology: how a graded signal can generate discrete cellular responses. This work, which includes a mathematical model, elucidates one mechanism to limit cell invasion in vivo.