Everybody on earth is at least 50th cousins. Without pedigree collapse, a person’s ancestor tree is a binary tree, formed by the person, the parents, grandparents, 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 roughly a billion ancestors, more than the total world population at the time. This apparent paradox occurs because the individuals in the binary tree are not distinct: instead, a single individual may occupy multiple places in the binary tree. This typically happens when the parents of an ancestor are cousins (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 binary tree into a directed acyclic graph with two different, directed paths starting from the ancestor who in the binary tree would occupy two places.
In some cultures, cousins were encouraged or required to marry to keep kin bonds, wealth and property within a family (endogamy). 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, were parents of another twice great-grandmother, Maria Isabella of Spain. More generally, in many cultures intermarriage may frequently occur within a small village, limiting the available gene pool.
Most historians consider the House of Habsburg as an example of genetically-induced disease as the direct result of pedigree collapse. The last Habsburg King of Spain, Charles II, makes an instructive case. In anyone’s family tree, there are seven unions in the most recent three generations. In Charles’ case, there were three uncle-niece marriages among those seven unions. His father and two of his great-grandfathers married their nieces. His paternal grandparents were first cousins, once removed, but they comprised two of the seven marriages because they were also parents to his maternal grandmother. His maternal grandparents’ marriage and the final marriage of great-grandparents was between first cousins. Like most people, the family tree of Elizabeth II to six generations has 62 different people in the 62 different positions. The family tree of Charles II had only 32 different persons in the 62 positions. Going back two more generations, he had only 82 different people in 254 positions. Charles II was born with extensive physical, intellectual and emotional problems and was incapable of producing an heir, a fact which resulted in the War of Spanish Succession. His lineage was so intermarried that he had a higher inbreeding ratio than if he had been born to a brother-sister couple.
The maximum pedigree collapse of 50% within a single generation is caused by procreation between full siblings. Such children have only two different grandparents, instead of the maximum four. If a child and parent were to procreate, their offspring would have four grandparents, although one of these would also be a parent and therefore introduce no additional genes – thus procreation between parents and children would result in less pedigree collapse than procreation between full siblings. If two half-siblings procreate, their children have three grandparents instead of four. If a person procreates with a full sibling of one of their parents, the offspring have four different persons as grandparents, and eight great-grandparents, but again some of these contribute no additional genes.
Small, isolated populations such as those of remote islands represent extreme examples of pedigree collapse, but the common historical tendency to marry those within walking distance, due to the relative immobility of the population before modern transport, meant that most marriage partners were at least distantly related. Even in America around the 19th century, the tendency of immigrants to marry among their ethnic, language or cultural group produced many cousin marriages.
If one considers as a function of time t the number of a given individual’s ancestors who were alive at time t, it is likely that for most individuals this function has a maximum at around 1200 AD. Some geneticists believe that everybody on Earth is at least 50th cousin to everybody else.