  We consider the problem of drawing multiple gene trees inside a single
species tree in order to visualize multispecies coalescent trees. Specifically,
the drawing of the species tree fills a rectangle in which each of its edges is
represented by a smaller rectangle, and the gene trees are drawn as rectangular
cladograms (that is, orthogonally and downward, with one bend per edge) inside
the drawing of the species tree. As an alternative, we also consider a style
where the widths of the edges of the species tree are proportional to given
effective population sizes.
  In order to obtain readable visualizations, our aim is to minimize the number
of crossings between edges of the gene trees in such drawings. We show that
planar instances can be recognized in linear time and that the general problem
is NP-hard. Therefore, we introduce two heuristics and give an integer linear
programming (ILP) formulation that provides us with exact solutions in
exponential time. We use the ILP to measure the quality of the heuristics on
real-world instances. The heuristics yield surprisingly good solutions, and the
ILP runs surprisingly fast.
