  We consider the Fleming-Viot particle system consisting of $N$ identical
particles evolving in $\mathbb{R}_{>0}$ as Brownian motions with constant drift
$-1$. Whenever a particle hits $0$, it jumps onto another particle in the
interior. It is known that this particle system has a hydrodynamic limit as
$N\rightarrow\infty$ given by Brownian motion with drift $-1$ conditioned not
to hit $0$. This killed Brownian motion has an infinite family of
quasi-stationary distributions (QSDs), with a Yaglom limit given by the unique
QSD minimising the survival probability. On the other hand, for fixed
$N<\infty$, this particle system converges to a unique stationary distribution
as time $t\rightarrow\infty$. We prove the following selection principle: the
empirical measure of the $N$-particle stationary distribution converges to the
aforedescribed Yaglom limit as $N\rightarrow\infty$. The selection problem for
this particular Fleming-Viot process is closely connected to the microscopic
selection problem in front propagation, in particular for the $N$-branching
Brownian motion. The proof requires neither fine estimates on the particle
system nor the use of Lyapunov functions.
