Epithelial stem cells are routinely lost or damaged during adult life and must therefore be replaced to maintain homeostasis. Recent studies indicate that stem cell replacement occurs through neutral competition in many types of epithelial tissues, but little is known about the factors that determine competitive outcome. The epithelial follicle stem cells (FSCs) in the Drosophila ovary are regularly lost and replaced during normal homeostasis, and we show that FSC replacement conforms to a model of neutral competition. In addition, we found that FSCs mutant for the basolateral junction genes, lethal giant larvae (lgl) or discs large (dlg), undergo a biased competition for niche occupancy characterized by increased invasion of neighboring FSCs and reduced loss. Interestingly, FSCs mutant for a third basolateral junction gene, scribble (scrib), do not exhibit biased competition, suggesting that Lgl and Dlg regulate niche competition through a Scrib-independent process. Lastly, we found that FSCs have a unique cell polarity characterized by broadly distributed adherens junctions and the lack of a mature apical domain. Collectively, these observations indicate that Lgl and Dlg promote the differentiation of FSC progeny to a state in which they are less prone to invade the neighboring niche. In addition, we demonstrate that the neutral drift model can be adapted to quantify non-neutral behavior of mutant clones.