Tropical mountains are hot spots of biodiversity and endemism, but the evolutionary origins of their unique biotas are poorly understood. In varying degrees, local and regional extinction, long-distance colonization, and local recruitment may all contribute to the exceptional character of these communities. Also, it is debated whether mountain endemics mostly originate from local lowland taxa, or from lineages that reach the mountain by long-range dispersal from cool localities elsewhere. Here we investigate the evolutionary routes to endemism by sampling an entire tropical mountain biota on the 4,095-metre-high Mount Kinabalu in Sabah, East Malaysia. We discover that most of its unique biodiversity is younger than the mountain itself (6 million years), and comprises a mix of immigrant pre-adapted lineages and descendants from local lowland ancestors, although substantial shifts from lower to higher vegetation zones in this latter group were rare. These insights could improve forecasts of the likelihood of extinction and 'evolutionary rescue' in montane biodiversity hot spots under climate change scenarios.