Pedigrees and phylogenies are networks not trees

There is nothing in the etymology of the words 'genealogy' and 'phylogeny' that necessarily implies that they must be tree-like. Indeed, all genealogies are networks. For example, a human family "tree" is a tree only if it includes one sex alone. Otherwise, it must be a network when traced backwards from any single individual through both parents, because the lineages must eventually coalesce in a pair of shared common ancestors. This must happen if there is a single origin for Homo sapiens (ie. the species is monophyletic). The coalescence may not occur for thousands of years in the past, or it may be quite recent.

So, all pedigrees of sexually reproducing species involve conjoined lineages at both "ends", one in the common ancestor and one in the contemporary offspring.

Given the extent of inbreeding among royal families, this ancestral coalescence is quite likely to be recent among monarchs. For example, the most recent common ancestors of all of the currently reigning monarchs of Europe are John William Friso, Prince of Orange (1687-1711), and his wife, Marie Louise of Hesse-Kassel, Princess consort of Orange (1688-1765). This situation has existed since the abolition of the Albanian monarchy in 1939 (this particular monarchy was not related to the house of Orange).

Marie Louise (left) and her two children.

There used to be a Wikipedia page listing the contemporary descendants of this royal Dutch couple, but it has been deleted. It is, however, still available in the Internet Archive WayBack Machine (Royal descendants of John William Friso, Prince of Orange). This page shows that the lineages of all of the current monarchs coalesce in this couple in 7-11 generations. This is true of all 10 current monarchs (in Belgium, Denmark, Liechtenstein, Luxembourg, Monaco, the Netherlands, Norway, Spain, Sweden, the United Kingdom), many former monarchies (13 or so), many so-called pretenders or claimants (at least 21), plus two royal consorts. Interestingly, the progenitor couple achieved this set of family relationships even though they had only one daughter (Princess Amalia of Nassau-Dietz) and one son (William IV, Prince of Orange), who was born six weeks after his father's death by drowning.

Family trees were originally devised as a way for nobles to assert their nobility, by tracing their direct male ancestry from some "important" progenitor (see the picture below). The female lineages were usually ignored in such ancestries, with each woman appearing alone, solely as an isolated wife and mother. This was, of course, modelled on the genealogies listed in the christian Bible, in both Genesis 5 and 11, in which females are mentioned but only males appear to be named. However, the ancestral relationships of the current European monarchs do involve females as part of the direct lines of descent, in all cases (ie. none of the direct lines of descent can be traced solely through males).

On the left is part of a genealogy of Christ (from c. 1130-1205);
on the right is a genealogy of the House of Habsburg (c. 1540).
Reproduced from the Visual Complexity blog.

Thus, in the modern world, we should be constructing family networks not family trees, with all of the male and female lineages sharing equal prominence. This will make it clear that genealogies are networks not trees. This assumes, of course, that enough historical information can be collected to locate the actual points of coalescence. This is unlikely to be so for the likes of you and me, but the nobility seem to be able to do it quite regularly.

Family networks that reticulate within a few generations are not necessarily good things, of course. Sex-linked recessive traits such as heamophilia B are widespread among the royalty of Europe (Stevens 1999, Rogaev et al. 2009), as are autosomal dominant traits such as variegate porphyria (Cox et al. 2005). These diseases are much rarer amongst commoners.

A similar situation applies to phylogenies showing species relationships. If there is a single origin to life, then tracing phylogenies backwards in time must lead to the eventual coalescence of all lineages. Any species whose ancestry involves hybridization, introgression or horizontal gene transfer must form a network. Parts of this network might be tree-like if isolated from the rest, but the whole phylogeny cannot be anything other than a network.

Consider the following points:

Definitions:
A network is a series of overlapping groups
A tree is a set of nested groups

Observation:
Each evolutionary event defines a group (all of the descendants of the ancestor in which the event occurred)

Conclusions:
Dichotomous speciation leads to a tree, by definition
Other processes will lead to a network, by definition

We know that in biology there are both vertical (speciation) and horizontal (reticulation) evolutionary processes. Therefore, no biological data fit a tree perfectly (unless the data are carefully selected to do so). A network analysis will allow you to evaluate the relative contribution of the horizontal and vertical processes that have occurred.

References

Cox TM, Jack N, Lofthouse S, Watling J, Haines J, Warren MJ (2005) King George III and porphyria: an elemental hypothesis and investigation. Lancet 366: 332-335.

Rogaev EI, Grigorenko AP, Faskhutdinova G, Kittler ELW, Moliaka YK (2009) Genotype analysis identifies the cause of the "Royal Disease". Science 326: 817.

Stevens R. (1999) The history of hemophilia in the royal families of Europe.  British Journal of Haematology 105: 25-32.