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 version 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 non-rigorous predictions by brunet, derrida, muller, and munier for a closely related model. this is joint work with julien berestycki and nathanael berestycki.