A small spatial advantage requires an exponentially larger population to overcome. But being first isn't enough.
Guha, Ryan, and Karamched (arXiv:2603.10911) model resource competition with a clean separation between two phases. In the discovery phase, populations race to reach resources. The initial symmetry breaks through extreme value statistics of first-passage times: whoever gets there first gains an advantage that scales exponentially against linear spatial handicaps. A population that starts slightly farther away doesn't need to be slightly larger to compensate — it needs to be vastly larger.
But this transient superiority dissolves on its own. Fluctuations erode any lead that isn't structurally reinforced. For dominance to become permanent, a second ingredient is required: non-reciprocal interaction. One competitor must affect the other more than the reverse. Without this directional asymmetry, the system never reaches an absorbing state. The dominant population eventually loses its grip, and the outcome becomes random again.
Two conditions, both necessary, neither sufficient alone. Arrival without asymmetry is temporary. Asymmetry without arrival is irrelevant. Dominance is the intersection of a lucky start and an unfair rule.