  Traveling waves describe diverse natural phenomena from crystal growth in
physics to range expansions in biology. Two classes of waves exist with very
different properties: pulled and pushed. Pulled waves are driven by high growth
rates at the expansion edge, where the number of organisms is small and
fluctuations are large. In contrast, fluctuations are suppressed in pushed
waves because the region of maximal growth is shifted towards the population
bulk. Although it is commonly believed that expansions are either pulled or
pushed, we found an intermediate class of waves with bulk-driven growth, but
exceedingly large fluctuations. These waves are unusual because their
properties are controlled by both the leading edge and the bulk of the front.
