Trees compete for space in the canopy, but where and how individuals or their component parts win or lose is poorly understood. We developed a stochastic model of three-dimensional dynamics in canopies using a hierarchical Bayesian framework, and analysed 267 533 positive height changes from 1.25 m pixels using data from airborne LiDAR within 43 ha on the windward flank of Mauna Kea. Model selection indicates a strong resident's advantage, with 97.9% of positions in the canopy retained by their occupants over 2 years. The remaining 2.1% were lost to a neighbouring contender. Absolute height was a poor predictor of success, but short stature greatly raised the risk of being overtopped. Growth in the canopy was exponentially distributed with a scaling parameter of 0.518. These findings show how size and spatial proximity influence the outcome of competition for space, and provide a general framework for the analysis of canopy dynamics.