Range Expansion

Range Expansion: Bacteria reproduce and compete for new space

"Genetic drift at expanding frontiers promotes gene segregation,"

O. Hallatschek, P. Hersen, S. Ramanathan, & D.R. Nelson, PNAS 104, 19926 (2007).

Range expansion can also be initiated on a straight edge:

Stepping Stone model for range expansion:

"Genetic demixing and evolution in linear stepping stone models,"

K.S. Korolev, M. Avlund, O. Hallatschek & D.R. Nelson, Rev. Mod. Phys.82, 1691 (2010).

Layer by layer (flat growth)

Stepping Stone model predicts diffusive sector boundaries, but in experiments sector boundaries fluctuate super-diffusively

Remove the layer by layer growth constraint to allow for rough fronts:

The expansion velocity can be stochastic, and depend on the shape of the front (curvature and slope):

The generic scaling of fluctuations of the above equation is superdiffusive:

Next (Coalescence) Outline Range Expansions Coalescence Extinction Morphology Deterministic growth Summary