How single cells in a mitotic tissue progressively acquire hallmarks of cancer is poorly understood. We exploited mitotic recombination in developing Drosophila imaginal tissues to analyze the behavior of cells devoid of the tumor suppressor PTEN, a negative regulator of PI3K signaling, under varying nutritional conditions. Cells lacking PTEN strongly overproliferated specifically in nutrient restricted larvae. Although the PTEN mutant cells were sensitive to starvation, they successfully competed with neighboring cells by autonomous and non-autonomous mechanisms distinct from cell competition. The overgrowth was strictly dependent on the activity of the downstream components Akt/PKB and TORC1, and a reduction in amino acid uptake by reducing the levels of the amino acid transporter Slimfast caused clones of PTEN mutant cells to collapse. Our findings demonstrate how limiting nutritional conditions impact on cells lacking the tumor suppressor PTEN to cause hyperplastic overgrowth. DOI:http://dx.doi.org/10.7554/eLife.00380.001.