Clonal dominance arises when the descendants (clones) of one or a few founder cells contribute disproportionally to the final structure during collective growth [1-8]. In contexts such as bacterial growth, tumorigenesis, and stem cell reprogramming [2-4], this phenomenon is often attributed to pre-existing propensities for dominance, while in stem cell homeostasis, neutral drift dynamics are invoked [5,6]. The mechanistic origin of clonal dominance during development, where it is increasingly documented [1,6-8], is less understood. Here, we investigate this phenomenon in the follicle epithelium, a system in which the joint growth dynamics of cell lineage trees can be reconstructed. We demonstrate that clonal dominance can emerge spontaneously, in the absence of pre-existing biases, as a collective property of evolving excitable networks through coupling of divisions among connected cells. Similar mechanisms have been identified in forest fires and evolving opinion networks [9-11]; we show that the spatial coupling of excitable units explains a critical feature of the development of the organism, with implications for tissue organization and dynamics [1,12,13].