  Reaction-diffusion waves have long been used to describe the growth and
spread of populations undergoing a spatial range expansion. Such waves are
generally classed as either pulled, where the dynamics are driven by the very
tip of the front and stochastic fluctuations are high, or pushed, where
cooperation in growth or dispersal results in a bulk-driven wave in which
fluctuations are suppressed. These concepts have been well studied
experimentally in populations where the cooperation leads to a
density-dependent growth rate. By contrast, relatively little is known about
experimental populations that exhibit density-dependent dispersal.
  Using bacteriophage T7 as a test organism, we present novel experimental
measurements that demonstrate that the diffusion of phage T7, in a lawn of host
E. coli, is hindered by steric interactions with host bacteria cells. The
coupling between host density, phage dispersal and cell lysis caused by viral
infection results in an effective density-dependent diffusion coefficient akin
to cooperative behavior. Using a system of reaction-diffusion equations, we
show that this effect can result in a transition from a pulled to pushed
expansion. Moreover, we find that a second, independent density-dependent
effect on phage dispersal spontaneously emerges as a result of the viral
incubation period, during which phage is trapped inside the host unable to
disperse. Additional stochastic agent-based simulations reveal that lysis time
dramatically affects the rate of diversity loss in viral expansions. Taken
together, our results indicate both that bacteriophage can be used as a
controllable laboratory population to investigate the impact of
density-dependent dispersal on evolution, and that the genetic diversity and
adaptability of expanding viral populations could be much greater than is
currently assumed.
