  We consider a system of particles which perform branching Brownian motion
with negative drift and are killed upon reaching zero, in the near-critical
regime where the total population stays roughly constant with approximately N
particles. We show that the characteristic time scale for the evolution of this
population is of order $(\log N)^3$, in the sense that when time is measured in
these units, the scaled number of particles converges to a variant of Neveu's
continuous-state branching process. Furthermore, the genealogy of the particles
is then governed by a coalescent process known as the Bolthausen-Sznitman
coalescent. This validates the nonrigorous predictions by Brunet, Derrida,
Muller and Munier for a closely related model.
