Pedigree collapse
In genealogy, pedigree collapse describes how reproduction between two individuals who share an ancestor causes the number of distinct ancestors in the family tree of their offspring to be smaller than it could otherwise be. Robert C. Gunderson coined the term, which is also known by the German term Ahnenschwund (loosely translated: “loss of lineage”) or the term implex.
Without pedigree collapse, a person's ancestor tree is a binary tree, formed by the person, the parents (2), the grandparents (4), great-grandparents (8), and so on. However, the number of individuals in such a tree grows exponentially and will eventually become impossibly high. For example, a single individual alive today would, over 30 generations going back to the High Middle Ages, have or roughly a billion ancestors, more than the total world population at the time.
This apparent paradox is explained by shared ancestors, referred to as pedigree collapse. Instead of consisting of all different individuals, a tree may have multiple places occupied by a single individual. This typically happens when the parents of an ancestor are related to each other (sometimes unbeknownst to themselves). For example, the offspring of two first cousins has at most only six great-grandparents instead of the normal eight. This reduction in the number of ancestors is pedigree collapse. It collapses the ancestor tree into a directed acyclic graph.
In some cultures, cousins and other relations were permitted, encouraged or required to marry. This may have been to keep kin bonds, wealth and property within a family (endogamy) or simply because there was a limited number of potential marriage partners available. Among royalty, the frequent requirement to only marry other royals resulted in a reduced gene pool in which most individuals were the result of extensive pedigree collapse. Alfonso XII of Spain, for example, had only four great-grandparents instead of the usual eight. Furthermore, two of these great-grandparents, Charles IV of Spain and Maria Luisa of Parma, who were first cousins, were parents of another twice great-grandmother, Maria Isabella of Spain. Charles IV was also the brother of another twice great-grandparent, Ferdinand I of the Two Sicilies; they were both sons of Charles III of Spain and Maria Amalia of Saxony.
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