(Neutral) Range Expansion
Range Expansion: Bacteria reproduce and compete for new space
"Genetic drift at expanding frontiers promotes gene segregation," Hallatschek, Hersen, Ramanathan, & Nelson, PNAS 104, 19926 (2007).
The boundaries between domains fluctuate `super-diffusively'
Sector boundaries: Asynchronous stepping Stone models for neutral range expansion justify scaling reminiscent of other growth processes
"Genetic demixing and evolution in linear stepping stone models," Korolev, Avlund, Hallatschek & Nelson, Rev. Mod. Phys.82, 1691 (2010).
Neutral growth on a sloped surface:
Sector boundaries drift on a sloped surfaces, as
Stochastic fluctuations in height profile of the rough surface thus lead to random drift of the sector boundary, such that
Variations of the height profile (hence slope) are due to the random additions, which are described by
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The generic scaling of fluctuations of the above equation is super-diffusive:
