Macroscopic Manifestations

Deterministic (noise-less) limit can be solved exactly (in certain limit) via the Cole-Hopf transformation:

A non-flat initial profile grows into a series of coarsening paraboloids:

Each paraboloid is dominated by a single species located at an initial peak.

In the above picture, the blue species is less fit than the gray, and would have gone extinct on a flat front,

the advantage of initial location allows it to carve out its own geographic niche.

In this system the advantage of height h is equivalent to a exponentially larger population.

"Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation,"

Jordan Horowitz & M.Kardar, arxiv:1901.07956.

Next (Summary) Outline Range Expansion Extinction & Coalescence Directed Percolation Macroscopic Manifestations Summary