  We show analytically and numerically that the appearance of lumps and gaps in
the distribution of n competing species along a niche axis is a robust
phenomenon whenever the finiteness of the niche space is taken into account. In
this case depending if the niche width of the species $\sigma$ is above or
below a threshold $\sigma_c$, which for large n coincides with 2/n, there are
two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges
directly from the dominant eigenvector of the competition matrix because its
corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy
pattern disappears. Furthermore, this clumping transition exhibits critical
slowing down as $\sigma$ is approached from above. We also find that the number
of lumps of species vs. $\sigma$ displays a stair-step structure. The positions
of these steps are distributed according to a power-law. It is thus
straightforward to predict the number of groups that can be packed along a
niche axis and it coincides with field measurements for a wide range of the
model parameters.
