MIT model finds fitness, speed, and front position jointly shape expanding populations

A study in the Journal of Statistical Mechanics: Theory and Experiment uses mathematical models, inspired by bacterial colony experiments, to explain how competing populations expand. MIT doctoral student Sergio Eraso and MIT physicist Mehran Kardar argue that fitness, defined as a reproductive advantage, is not the only factor and is not necessarily decisive. Expansion speed and position along the growth front also matter, Phys.org reports. Sector boundaries in earlier colony work moved faster than ordinary diffusion would predict, following scaling from the KPZ equation introduced in 1986 by Kardar, Giorgio Parisi and Yi-Cheng Zhang. The new model combines that KPZ front dynamics with the Fisher equation from evolutionary biology. Fitness and expansion speed can diverge: a population may win local competition while advancing more slowly. The model yields three front shapes, including a V-shaped dent in which a competitively stronger population invades from the sides but lags at the center. Greater expansion speed does not necessarily bring greater success colonizing new territory, Eraso said. A less fit population that would vanish on a flat front can persist in a favorable peak or protrusion, creating long-lived niches. The work predicts that spatial structure leaves a measurable fingerprint on how fitness is distributed, which future experiments could test. Kardar received the 2025 Boltzmann Medal for nonequilibrium statistical physics contributions including KPZ.