(Neutral) Range Expansion

red ballRange Expansion: Bacteria reproduce and compete for new space

yellow ball"Genetic drift at expanding frontiers promotes gene segregation," Hallatschek, Hersen, Ramanathan, & Nelson, PNAS 104, 19926 (2007).

yellow ball The boundaries between domains fluctuate `super-diffusively'

red ball Sector boundaries: Asynchronous stepping Stone models for neutral range expansion justify scaling reminiscent of other growth processes

yellow ball"Genetic demixing and evolution in linear stepping stone models," Korolev, Avlund, Hallatschek & Nelson, Rev. Mod. Phys.82, 1691 (2010).

yellow ball Front roughness is key to superdiffusive sector-boundary fluctuations:

Synchronous    versus  Asynchronous growth

red ball Stochastic surface growth depends on local curvature and slope according to

yellow ball The geometric construction that justifies the nonlinear term, also indicate that sector boundaries drift on a sloped surfaces, as

yellow ball Stochastic fluctuations in height profile of the rough surface thus lead to random drift of the sector boundary, such that

yellow ballThe dynamic scaling exponent z is inherited from the front roughness fluctuations, and follows from