We obtain a representation of Feller's branching diffusion with logistic
growth in terms of the local times of a reflected Brownian motion H with a
drift that is affine linear in the local time accumulated by H at its current
level. As in the classical Ray-Knight representation, the excursions of H are
the exploration paths of the trees of descendants of the ancestors at time
t=0, and the local time of H at height t measures the population size at
time t (see e.g. \cite{LG4}). We cope with the dependence in the reproduction
by introducing a pecking order of individuals: an individual explored at time
s and living at time t=Hs is prone to be killed by any of its
contemporaneans that have been explored so far. The proof of our main result
relies on approximating H with a sequence of Harris paths HN which figure
in a Ray-Knight representation of the total mass of a branching particle
system. We obtain a suitable joint convergence of HN together with its local
times {\em and} with the Girsanov densities that introduce the dependence in
the reproduction
