If one combines a Y chromosome genealogy, which usually shows the paternal ancestry, with a mitochondrial genealogy, which usually shows the maternal ancestry, it is likely that the resulting phylogeny will be reticulate. After all, if a sexually reproducing group of organisms is monophyletic then there is, in theory, a common ancestral pair of organisms, although in practice it is likely to be a small group of inter-breeding organisms. That being so, the ancestry of each descendant individual must consist of a pair of intersecting trees, one maternal and one paternal.
This can be illustrated using this recent paper:
Pille Hallast, Pierpaolo Maisano Delser, Chiara Batini, Daniel Zadik, Mariano Rocchi, Werner Schempp, Chris Tyler-Smith, and Mark A. Jobling (2016) Great ape Y chromosome and mitochondrial DNA phylogenies reflect subspecies structure and patterns of mating and dispersal. Genome Research 26: 427-439.The authors sequenced autosomal DNA, as well as the Y chromosome (MSY) and the mitochondrial DNA (mtDNA), for each of 19 great ape males (orangutans, gorillas, chimpanzees, bonobos, and humans), and added this to the data for 24 published genomes. For the 19 individuals:
we carried out principal component analysis (PCA) of autosomal SNP variation (∼10,000–48,000 variable sites, depending on species) ... 17 of our 19 sequenced individuals lie within known subspecies clusters ... Two of the sequenced chimpanzees lie mid-way between clusters in the PCA, suggesting recent inter-subspecies hybridization in their ancestry (Tommy: Pan troglodytes verus / Pan troglodytes troglodytes hybrid; EB176JC: Pan troglodytes verus / Pan troglodytes ellioti hybrid).This seems quite clear in their ordination diagram, as shown here.
Furthermore, for the other two datasets (43 males) the authors note:
PHYLIP v3.69 was used to create maximum parsimony phylogenetic trees for both MSY and mtDNA. Three independent trees were constructed with DNAPARS using randomization of input order with different seeds, each 10 times. Output trees of these runs were used to build a consensus tree with the consense program included in the PHYLIP package. Intraspecific MSY trees were rooted using the ancestral sequence generated and described in the Supplemental Text [basically, the allele matching the outgroup]. Intraspecific mtDNA trees were rooted using the Human Revised Cambridge Reference Sequence.The two resulting trees for the 19 chimpanzees are shown here, with the MSY tree on the left and the mtDNA tree on the right.
One of the hybrid individuals identified in the autosomal analysis was labelled EBC176JV, and he is clearly shown in a different place in each of the two trees — he is shown as having a Pan troglodytes verus (PTV) father and a Pan troglodytes ellioti (PTE) mother. Consequently, he will be placed at a reticulation node in any attempt to combine the two trees
More oddly, the other individual, named Tommy, does not show this pattern at all. In the two trees he is shown as having both a Pan troglodytes troglodytes (PTT) father and mother, rather than one of them being identified as Pan troglodytes ellioti (PTE), as expected from the autosomes. The authors do not even note this apparently contradictory situation, let alone suggest an explanation. Clearly, however, no reticulation node will be needed in a combined phylogeny.