A new mathematical study of competing populations suggests that winning the evolutionary race is not determined by reproductive fitness alone. When populations expand across space, their success can also depend on how quickly they advance and where their ancestors happen to be located along a constantly changing growth front. The findings, reported in the Journal of Statistical Mechanics: Theory and Experiment, offer a possible explanation for the striking patterns seen when mixed bacterial colonies separate into distinct sectors. They also make a testable prediction: spatial structure may leave a measurable signature in the way fitness is distributed across an expanding population.
The study was conducted by Sergio Eraso, an MIT PhD student, and physicist Mehran Kardar. Their work was inspired by earlier experiments in which bacterial populations began mixed together but gradually formed visible wedges and sectors as the colonies spread. These boundaries did not behave like ordinary random interfaces. Instead, they fluctuated and advanced according to scaling laws associated with the Kardar-Parisi-Zhang, or KPZ, equation, a landmark model of rough growth developed in 1986 by Kardar, Giorgio Parisi and Yi-Cheng Zhang.
The KPZ equation describes how an irregular surface changes as it grows. A familiar analogy is the edge of a flame moving across a sheet of paper. Although the fire advances overall, its boundary develops bumps, valleys and local protrusions rather than remaining perfectly straight. Expanding microbial colonies can behave in a similar way. Individual cells reproduce at different times and locations, producing a rough front whose geometry influences which cells reach new territory first. That unevenness can also redirect the boundaries separating competing populations.
To investigate this process, Eraso and Kardar combined the KPZ equation with the Fisher equation, a classic model from mathematical biology. The Fisher equation describes how a population with a selective advantage spreads through space, balancing reproduction against the movement or dispersal of individuals. In the new framework, the researchers treated competitive ability and expansion speed as related but distinct properties. A population could be better at replacing a local competitor while still advancing more slowly across the colony’s outer edge.
That distinction produced unexpectedly varied outcomes. Depending on the relationship between fitness and propagation speed, the boundary between two populations could form a rounded bulge, a composite bulge with sloping sides, or a V-shaped indentation. The V-shaped pattern is especially revealing. In that case, the population with greater competitive fitness continues to invade its rival from the sides, where local competition favors it. Yet at the center of the front, it falls behind because its overall expansion speed is lower. The result is a population that is stronger in direct competition but occupies less territory at the leading edge.
The model therefore challenges the intuitive idea that the fastest population should automatically dominate an expanding environment. Speed helps a population reach fresh territory, but speed alone does not determine what happens after populations meet. A slower population with a stronger local competitive advantage may overtake its neighbor once contact occurs, while a faster population may preserve a lead simply by remaining ahead of the competition. The final pattern emerges from the interaction between these effects and the constantly shifting geometry of the growth front.
Position can be just as important. According to the simulations, a population that would disappear on a flat front may survive for a long time if it begins in a favorable location, such as a peak or protruding region. These features can act as temporary spatial niches. Descendants of cells positioned at the front of a protrusion may gain repeated access to unoccupied territory, allowing them to persist despite having lower fitness than surrounding populations. On a less favorable section of the front, the same population could be eliminated.
This possibility gives evolutionary history a strong geographical component. The descendants of a population may succeed not only because they possess advantageous traits, but also because their ancestors occupied the right place at the right moment. In a growing colony, chance differences in position can become amplified over generations. A small initial lead may expose one lineage to more resources and space, while a neighboring lineage becomes trapped behind it. Such effects could help explain why populations with similar genetic properties sometimes produce dramatically different spatial patterns.
Although the model is deliberately simplified, its predicted shapes resemble bulges and dents observed in previous experiments on microbial colonies. The agreement does not prove that the same mechanism controls every real biological system, since actual colonies involve additional factors such as nutrient depletion, cell movement, chemical signaling and changes in growth conditions. It does show, however, that a relatively small set of ingredients—rough-front growth, differences in competitive ability and differences in expansion speed—can reproduce the broad geometry of the observed patterns.
The researchers’ most distinctive prediction concerns the distribution of fitness itself. In a spatially expanding population, fitness may not appear as a uniform or randomly arranged property. Instead, the roughness of the front and the positions of lineages could leave a detectable fingerprint in where highly fit and less fit individuals are found. New experiments could test this idea by tracking genetic lineages, measuring their growth rates and mapping their positions across expanding colonies over time. If the predicted relationship is observed, it would demonstrate that spatial structure is not merely a backdrop for evolution but an active force shaping which traits survive and spread.
Subject of Research: Spatial competition, population expansion, evolutionary fitness, and rough growth fronts in microbial colonies.
Article Title: Competition at the front of expanding populations
Article Publication Date: 3-Aug-2026
Keywords: Expanding populations, bacterial colonies, microbial evolution, fitness, expansion speed, spatial competition, KPZ equation, Fisher equation, mathematical biology, statistical physics, population dynamics, growth fronts, evolutionary modeling
