  We introduce a hybrid metaphor for the visualization of the reconciliations
of co-phylogenetic trees, that are mappings among the nodes of two trees. The
typical application is the visualization of the co-evolution of hosts and
parasites in biology. Our strategy combines a space-filling and a node-link
approach. Differently from traditional methods, it guarantees an unambiguous
and `downward' representation whenever the reconciliation is time-consistent
(i.e., meaningful). We address the problem of the minimization of the number of
crossings in the representation, by giving a characterization of planar
instances and by establishing the complexity of the problem. Finally, we
propose heuristics for computing representations with few crossings.
