  We investigate the nature of genetic drift acting at the leading edge of
range expansions, building on recent results in [Hallatschek et al., Proc.\
Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed
population of two fluorescently labeled microbial species is grown in a
circular geometry. As the population expands, a coarsening process driven by
genetic drift gives rise to sectoring patterns with fractal boundaries, which
show a non-trivial asymptotic distribution. Using simplified lattice based
Monte Carlo simulations as a generic caricature of the above experiment, we
present detailed numerical results to establish a model for sector boundaries
as time changed Brownian motions. This is used to derive a general one-to-one
mapping of sector statistics between circular and linear geometries, which
leads to a full understanding of the sectoring patterns in terms of
annihilating diffusions.
