A family tree is technically called a pedigree. This is because it is not really a tree. Branches do not fuse in a tree, whereas in a pedigree every individual is the fusion of two genealogical branches. That is, in sexually reproducing species, every offspring is the hybrid of two parents. A family tree is only a tree if you trace one pair of ancestors through their descendants while ignoring the spouses.
So, a pedigree is a network not a tree, and specifically it is a hybridization network. This can be seen most clearly when there is a considerable level of inbreeding going on. Under these circumstances, both spouses are likely to be offspring of the same ancestors in the not-too-distant past, and so they will both be connected by the network branches. We are all of us connected in the human pedigree network, of course, but for most of us our (shared) common ancestor is a long way back in the past.
A high degree of inbreeding is common in many human cultures, but it is particularly prevalent among royalty, even in cultures with relatively little inbreeding among the common populace. I will illustrate this phenomenon with what is often considered to be the most extreme example recorded — the inbreeding that lead to the demise of the Spanish branch of the Habsburg dynasty in 1700 (other branches of the House of Austria continued until 1780).
The Spanish branch of the Habsburgs were kings of Spain from 1516 to 1700. Under Habsburg rule, Spain reached the peak of its power in Europe (covering Spain, the Netherlands and parts of Italy), and the world-wide Spanish Empire reached its greatest extent. The last king of this dynasty was Charles II, who was the product of such serious inbreeding that he was disfigured, physically disabled and mentally retarded (see Alvarez et al. 2009 for a full description). The fact that he had no children lead to the War of the Spanish Succession, although this was mostly precipitated by the reaction of the reigning French king, Louis XIV.
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The basic issue here is that the Spanish Habsburgs tried to keep power by literally "keeping it in the family". During the last three-quarters of their time, from 1551 to 1700, no outsider married into the Spanish royal family. Indeed, if one looks at the six kings from 1497 (when Philip the Fair married Joanna I of Castile and Aragon, and thus became Philip I), then we note that there were 11 marriages, most of which were among blood relatives — two uncle-niece marriages, one double first cousin marriage, one first cousin marriage, two first cousins once removed marriages, one second cousin marriage, and two third cousin marriages. (See Wikipedia for an explanation of these relationship terms.) This gave Charles II an inbreeding coefficient of 0.254 (calculated by Alvarez et al. 2009) — for comparison, the offspring of a brother-sister union would have a value of 0.250, as would the offspring of a parent-child union. Phillip III (Charles II's grandfather) also reached a high level: 0.218. Both of these people were the offspring of uncle-niece marriages.
This first diagram (linked from Wikipedia) shows the pedigree of Charles II, the final member of the dynasty. It illustrates the above points in the usual manner for a family tree. It shows only the royal lineage, as there were many other offspring, and indeed other marriages (Philip II married four times, Philip IV twice, and Charles II also twice). However, none of the male offspring were alive at the time of the death of Charles II, and nor were most of the females. Another of the consequences of the inbreeding was a poor survival rate among the children.
My point with this blog post is that the family tree can also be drawn as a network, as shown in the second diagram (which is also called a "path diagram" by geneticists). This illustrates the same pedigree as above, but with a few additions (at the left) to illustrate the lineage to Don Carlos (crown prince Charles), another highly inbred male (coefficient 0.211), being the offspring of double first cousins. This form of the diagram makes the connection between a family tree and a hybridization network clear — they are both ways of drawing a pedigree.
Basically, the two diagrams illustrate the same point — the Habsburg's defeated their own purpose, because they ultimately lost power by refusing to share it with anyone else. Biology is about biodiversity, and conserving biodiversity applies within your own family just as much as anywhere else.
There are several follow-up posts on this topic, about other famous people:
Charles Darwin's family pedigree network
Toulouse-Lautrec: family trees and networks
Albert Einstein's consanguineous marriage
Alvarez G., Ceballos F.C., Quinteiro C. (2009) The role of inbreeding in the extinction of a European royal dynasty. PLoS ONE 4: e5147.
If you know little about the pros and cons of inbreeding, then this blog post will enlighten you:
Why inbreeding really isn’t as bad as you think it is.