  The space T_{d,n} of n tropically collinear points in a fixed tropical
projective space TP^{d-1} is equivalent to the tropicalization of the
determinantal variety of matrices of rank at most 2, which consists of real d x
n matrices of tropical or Kapranov rank at most 2, modulo projective
equivalence of columns. We show that it is equal to the image of the moduli
space M_{0,n}(TP^{d-1},1) of n-marked tropical lines in TP^{d-1} under the
evaluation map. Thus we derive a natural simplicial fan structure for T_{d,n}
using a simplicial fan structure of M_{0,n}(TP^{d-1},1) which coincides with
that of the space of phylogenetic trees on d+n taxa. The space of phylogenetic
trees has been shown to be shellable by Trappmann and Ziegler. Using a similar
method, we show that T_{d,n} is shellable with our simplicial fan structure and
compute the homology of the link of the origin. The shellability of T_{d,n} has
been conjectured by Develin in 2005.
