  Aiming to understand the distribution of fitness levels of individuals in a
large population undergoing selection, we study the particle configurations of
branching Brownian motion where each particle independently moves as Brownian
motion with negative drift, particles can die or undergo dyadic fission, and
the difference between the birth rate and the death rate is proportional to the
particle's location. Under some assumptions, we obtain the limit in probability
of the number of particles in any given interval and an explicit formula for
the asymptotic empirical density of the fitness distribution. We show that
after a sufficiently long time, the fitness distribution from the lowest to the
highest fitness levels approximately evolves as a traveling wave with a profile
which is asymptotically related the the Airy function. Our work complements the
results in Roberts and Schweinsberg (2021), giving a fuller picture of the
fitness distribution.
