Two populations compete for the same resource at the same location. One population is slightly closer. How much does that matter?
Guha, Ryan, and Karamched (arXiv:2603.10911, March 2026) show that it matters exponentially. In a stochastic model of resource competition, the initial advantage is governed by extreme value statistics of first-passage times — who arrives first at the resource. A population with a linear spatial disadvantage (twice the distance) needs an exponentially larger population to have the same probability of arriving first. The fastest individual in a group of searchers determines when the group discovers the resource, and the fastest individual is drawn from the tail of the arrival time distribution. Tails amplify small advantages. Closeness doesn't just help. It dominates.
But discovery is not dominance. The population that arrives first monopolizes the resource temporarily. Can the second population displace them? Guha et al. prove that transient superiority alone — arriving first, occupying the site — cannot stabilize into permanent dominance. If the interactions between the populations are symmetric (each affects the other equally), fluctuations will eventually erase any lead. The system wanders. First-mover advantage, under symmetric competition, is temporary by mathematical necessity.
Permanent dominance requires a separate ingredient: non-reciprocal interaction bias. The occupying population must affect the challenger more than the challenger affects them. The asymmetry does not need to be large. But it must be present. Without it, no amount of head start produces a stable absorbing state. With it, the initial transient advantage locks in.
The structure is a two-phase process. Phase one is discovery, governed by extreme value statistics — exponentially sensitive to spatial position. Phase two is stabilization, governed by interaction symmetry — insensitive to the size of the initial advantage but absolutely dependent on whether the interactions are reciprocal. A large advantage in phase one (better position, larger population) cannot substitute for the necessary ingredient in phase two (non-reciprocal bias). The two phases test different properties of the system.
The practical implication: being first is easy to measure and hard to leverage. The question is not who arrived first but whether the rules of engagement are symmetric once they did.
Guha, Ryan, and Karamched, "Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition," arXiv:2603.10911 (March 2026).