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

Particle configurations for branching Brownian motion with an inhomogeneous branching rate