  Most organisms grow in space, whether they are viruses spreading within a
host tissue or invasive species colonizing a new continent. Evolution typically
selects for higher expansion rates during spatial growth, but it has been
suggested that slower expanders can take over under certain conditions. Here,
we report an experimental observation of such population dynamics. We
demonstrate that the slower mutants win not only when the two types are
intermixed at the front but also when they are spatially segregated into
sectors. The latter was thought to be impossible because previous studies
focused exclusively on the global competitions mediated by expansion velocities
but overlooked the local competitions at sector boundaries. We developed a
theory of sector geometry that accounts for both local and global competitions
and describes all possible sector shapes. In particular, the theory predicted
that a slower, but more competitive, mutant forms a dented V-shaped sector as
it takes over the expansion front. Such sectors were indeed observed
experimentally and their shapes matched up quantitatively with the theory. In
simulations, we further explored several mechanism that could provide slow
expanders with a local competitive advantage and showed that they are all
well-described by our theory. Taken together, our results shed light on
previously unexplored outcomes of spatial competition and establish a universal
framework to understand evolutionary and ecological dynamics in expanding
populations.
