Combining two classic equations, MIT physicists show that position along a growth front can matter as much as reproductive advantage.

Evolutionary reasoning usually treats the outcome of competition as a question about fitness: the variant that reproduces faster takes over. A paper in the Journal of Statistical Mechanics: Theory and Experiment argues that in a population spreading into new territory, this is not enough to predict the winner, and that where a lineage sits on the expanding edge can decide the contest.

The work is by Sergio Eraso, a PhD student at MIT, and the MIT physicist Mehran Kardar, and it began with an observation from the laboratory rather than from theory.

“The work was inspired by experiments on expanding bacterial colonies, in which populations that were initially mixed eventually separated into distinct sectors,” Eraso said.

Two equations, joined

That sectoring is a familiar sight on an agar plate. A colony seeded with two strains does not stay blended as it grows; it fragments into wedges radiating from the centre, because only cells at the advancing edge get to reproduce into empty space and a lineage that loses its place on that edge is left behind in the interior, alive but no longer expanding.

The model couples two standard descriptions. The first is the KPZ equation, introduced in 1986 by Kardar with Giorgio Parisi and Yi-Cheng Zhang, which describes how a rough growing interface evolves; it is one of the central results in non-equilibrium statistical physics, and Kardar received the 2025 Boltzmann Medal.

The second is the Fisher equation, long used in population genetics to describe how an advantageous variant spreads through space.

“In this work, the central model combines the KPZ equation with the Fisher equation, a classic model in evolutionary biology that describes how a population with a selective advantage spreads through space,” Eraso said.

Each equation alone is well understood. The point of joining them is that the shape of the front and the competition on it are not independent: the interface determines who is positioned to reproduce, and the competition reshapes the interface.

Three shapes, and a surprise

The coupled model produces three characteristic front shapes where two populations meet: a rounded bulge, a composite bulge with sloping sides, and a V-shaped dent.

The V-shaped case is the counterintuitive one. There the fitter population invades from the sides but falls behind at the centre, because it expands more slowly — and the result is that superior fitness buys territory at the flanks while ceding the middle.

“It may seem surprising, but what we find is that greater expansion speed does not necessarily lead to greater success in colonizing new territory,” Eraso said.

Fitness and expansion speed are being treated here as distinct properties, which is the move that makes the result possible. A lineage can be better at turning resources into offspring without being better at pushing into empty space, and in a spatial setting those two capacities are rewarded differently.

Luck of position

The consequence the authors emphasise is that a less fit population sitting in a favourable position — on a peak or a protrusion of the front — can persist for long periods. The same population on a flat front could go extinct.

“You could say that the ancestors happened to be in the right place to ensure the success of their descendants,” Eraso said. “Had the same population started from a less favorable position, its adaptive disadvantage might have led to its extinction.”

This is a statement about contingency rather than about selection failing. Selection still operates; it is simply not the only thing that determines the outcome, because the front’s geometry decides which lineages get access to the growing edge where selection is expressed. A disadvantage can be held off indefinitely by a lineage that happens to occupy the part of the boundary that is moving outward fastest.

The practical reach of this is wider than bacterial colonies. Range expansions, invasive species moving into new habitat and tumours growing into tissue all share the structure the model describes: growth confined to a moving boundary, with the interior effectively frozen.

Resemblance is not identity

The model’s shapes closely resemble those seen in earlier microbial colony experiments, and the authors are careful about what that does and does not demonstrate.

“This does not mean that we have proved that the underlying mechanism is exactly the same, but it shows that only a few ingredients — differences in competitive ability and expansion speed — are enough to reproduce these shapes qualitatively,” Eraso said.

That is the appropriate claim for this kind of work. A minimal model matching observed patterns establishes sufficiency, not necessity: it shows that the ingredients included can generate the phenomenon, while leaving open whether real colonies also rely on mechanisms the model omits, such as nutrient gradients, mechanical interactions or chemical signalling between cells.

“We tried to identify the minimum number of ingredients needed to reproduce these shapes,” Eraso said. “Experiments can now test how far the same mechanisms are at work in real populations.”

A testable prediction

The study also predicts that spatial structure leaves a measurable fingerprint on how fitness is distributed across a population — which is the part most useful to experimentalists, because it is checkable.

If the model is right, a population that has expanded across a rough front should show fitness varying with position in a specific way, rather than fitness being evenly distributed or simply increasing over time. Sequencing a colony by location is a tractable experiment, and a test of this sort is what would move the result from a suggestive shape match to a claim about mechanism.

Until then the honest summary is narrow and still interesting: in populations growing at an edge, position is a variable alongside fitness, and a model with very few assumptions is enough to show how far position can go.

The release does not state a DOI for the paper, and does not state the study’s funding sources.

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Notes

1. Eraso, S., Kardar, M. “Competition at the front of expanding populations.” Journal of Statistical Mechanics: Theory and Experiment, 2026. The release does not state a DOI.
2. Sissa Medialab. “In the right place, even a less fit species can win.” EurekAlert!, 3 August 2026. https://www.eurekalert.org/news-releases/1137846.

Matthew J. Arduino, DRPH; Janice Carr