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| 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'''.<ref>{{cite web|last=Gundacker|first=Felix|title=Genealogical Dictionary|url=http://www.felixgundacker.at/Files/fgGenealogicalDictionary.pdf|year=2013}}</ref>
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| == How it works ==
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| 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 [[exponential growth|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 <math>2^{30}</math> or roughly a billion ancestors, more than the total [[world population]] at the time.<ref name="River_Out_of_Eden">See the chapter ''All Africa and her progenies'' in {{cite book | first = Richard | last = Dawkins | authorlink = Richard Dawkins | title = [[River Out of Eden]] | publisher = Basic Books | location = New York | year = 1995 | isbn = 0-465-06990-8 }}</ref>
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| This apparent paradox is explained by shared ancestors. Instead of consisting of all unique individuals, a tree may have multiple places occupied by a single individual. This typically happens when the parents of an ancestor are cousins (sometimes unbeknownst to themselves).<ref>John E. Pattison (2001), A New Method of Estimating Inbreeding in Large Semi-isolated Populations with Application to Historic Britain, ''HOMO: Journal of Comparative Human Biology'' '''52'''(2):117-134; doi 10.1078/0018-442X-00024.</ref><ref>John E. Pattison (2007), Estimating Inbreeding in Large Semi-isolated Populations: Effects of Varying Generation Length and of Migration, ''American Journal of Human Biology'' '''19'''(4):495-510; doi 10.1002/ajhb.20610.</ref> 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]].
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| In some cultures, cousins were encouraged or required to marry to keep kin bonds, wealth and property within a family ([[endogamy]]). Among [[Royal family|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.
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| {{ahnentafel top|Pedigree of Alfonso XII of Spain|width=100%|collapsed=yes}}<center>
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| {{ahnentafel-compact5
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| |1= 1. '''Alfonso XII of Spain'''
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| |2= 2. [[Francis of Spain|Infante Francis of Spain, Duke of Cádiz]]
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| |3= 3. [[Isabella II of Spain]]
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| |4= 4. [[Infante Francisco de Paula of Spain]]
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| |5= 5. [[Princess Luisa Carlotta of Bourbon-Two Sicilies|Princess Luisa Carlotta of the Two Sicilies]]
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| |6= 6. [[Ferdinand VII of Spain]]
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| |7= 7. [[Maria Christina of the Two Sicilies|Princess Maria Christina of the Two Sicilies]]
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| |8= 8. [[Charles IV of Spain]]
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| |9= 9. [[Maria Luisa of Parma|Princess Maria Luisa of Parma]]
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| |10= 10. [[Francis I of the Two Sicilies]]
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| |11= 11. [[Maria Isabella of Spain|Infanta Maria Isabella of Spain]]
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| |12= 12. [[Charles IV of Spain]] (=8)
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| |13= 13. [[Maria Luisa of Parma|Princess Maria Luisa of Parma]] (=9)
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| |14= 14. [[Francis I of the Two Sicilies]] (=10)
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| |15= 15. [[Maria Isabella of Spain|Infanta Maria Isabella of Spain]] (=11)
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| |16= 16. [[Charles III of Spain]]
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| |17= 17. [[Maria Amalia of Saxony|Princess Maria Amalia of Saxony]]
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| |18= 18. [[Philip, Duke of Parma]]
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| |19= 19. [[Princess Louise-Élisabeth of France]]
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| |20= 20. [[Ferdinand I of the Two Sicilies]]
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| |21= 21. [[Marie Caroline of Austria|Archduchess Marie Caroline of Austria]]
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| |22= 22. [[Charles IV of Spain]] (=8)
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| |23= 23. [[Maria Luisa of Parma|Princess Maria Luisa of Parma]] (=9)
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| |24= 24. [[Charles III of Spain]] (=16)
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| |25= 25. [[Maria Amalia of Saxony|Princess Maria Amalia of Saxony]] (=17)
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| |26= 26. [[Philip, Duke of Parma]] (=18)
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| |27= 27. [[Princess Louise-Élisabeth of France]] (=19)
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| |28= 28. [[Ferdinand I of the Two Sicilies]] (=20)
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| |29= 29. [[Marie Caroline of Austria|Archduchess Marie Caroline of Austria]] (=21)
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| |30= 30. [[Charles IV of Spain]] (=8)
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| |31= 31. [[Maria Luisa of Parma|Princess Maria Luisa of Parma]] (=9)
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| }}</center>
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| {{ahnentafel bottom}}
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| {{ahnentafel top|Pedigree of Ferdinand I of Austria|width=100%}}
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| |1= 1. '''Ferdinand I of Austria'''
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| |2= 2. [[Francis II, Holy Roman Emperor]]<br /><small>(Francis I of Austria)</small>
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| |3= 3. [[Maria Teresa of the Two Sicilies]]
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| |4= 4. [[Leopold II, Holy Roman Emperor]]
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| |5= 5. [[Maria Luisa of Spain]]
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| |6= 6. [[Ferdinand I of the Two Sicilies]]
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| |7= 7. [[Maria Carolina of Austria]]
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| |8= 8. [[Francis I, Holy Roman Emperor]]
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| |9= 9. [[Maria Theresa of Austria]]<br /><small>Queen of Hungary & Bohemia</small>
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| |10= 10. [[Charles III of Spain]]
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| |11= 11. [[Maria Amalia of Saxony]]
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| |12= 12. [[Charles III of Spain]] (= #10)
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| |13= 13. [[Maria Amalia of Saxony]] (= #11)
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| |14= 14. [[Francis I, Holy Roman Emperor]] (= #8)
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| |15= 15. [[Maria Theresa of Austria]] (= #9)<br /><small>Queen of Hungary & Bohemia</small>
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| |16= 16. [[Leopold, Duke of Lorraine]]
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| |17= 17. [[Élisabeth Charlotte d'Orléans]]
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| |18= 18. [[Charles VI, Holy Roman Emperor]]
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| |19= 19. [[Elisabeth Christine of Brunswick-Wolfenbüttel]]
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| |20= 20. [[Philip V of Spain]]
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| |21= 21. [[Elisabeth Farnese]]
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| |22= 22. [[Augustus III of Poland]]
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| |23= 23. [[Maria Josepha of Austria]]
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| |24= 24. [[Philip V of Spain]] (= #20)
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| |25= 25. [[Elisabeth of Parma]] (= #21)
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| |26= 26. [[Augustus III of Poland]] (= #22)
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| |27= 27. [[Maria Josepha of Austria]] (= #23)
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| |28= 28. [[Leopold, Duke of Lorraine]] (= #16)
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| |29= 29. [[Élisabeth Charlotte d'Orléans]] (= #17)
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| |30= 30. [[Charles VI, Holy Roman Emperor]] (= #18)
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| |31= 31. [[Elisabeth Christine of Brunswick-Wolfenbüttel]] (= #19)
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| }}</center>
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| {{Ahnentafel bottom}}
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| ==Ancestry==
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| The [[House of Habsburg]] gives a well-documented example of pedigree collapse. In the case of [[Charles II of Spain|Charles II]], the last Habsburg King of Spain, there were three uncle-niece marriages among the seven unions of his immediate ancestry (i.e. parents, grandparents and great-grandparents). 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.
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| {{Ahnentafel top|Pedigree collapse in the ancestry of Charles II of Spain}}
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| {{Ancestors of Charles II of Spain}}
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| {{Ahnentafel bottom}}
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| 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 usual four. If two half-siblings procreate, their children have three grandparents instead of four (25%).
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| 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.
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| 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. (See [[inbreeding]].)
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| 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.
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| 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 [[geneticist]]s believe that everybody on Earth is at most [[Cousin#Basic definitions|50th cousin]] to everybody else.<ref>[http://www.straightdope.com/classics/a2_083b.html The Straight Dope: 2, 4, 8, 16, ... how can you always have MORE ancestors as you go back in time?<!-- Bot generated title -->]</ref>
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| == See also ==
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| {{Div col}}
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| * [[Coefficient of relationship]]
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| * [[Consanguinity]]
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| * [[Cousin marriage]]
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| * [[Haplotype]]
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| * [[Identical ancestors point]]
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| * [[Inbreeding]]
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| * [[Most recent common ancestor]]
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| * ''[[The Seven Daughters of Eve]]''
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| {{Div col end}}
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| ==Notes==
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| {{reflist}}
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| ==References==
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| [1] [http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0005174#pone-0005174-t001 The Role of Inbreeding in the Extinction of a European Royal Dynasty]
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| * ''[[The Mountain of Names]]'' by [[Alex Shoumatoff]] (1985).
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| ==External links==
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| * [http://www.straightdope.com/classics/a2_083b.html The Straight Dope: 2, 4, 8, 16, ... how can you always have MORE ancestors as you go back in time?] – August 21, 1987
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| * [http://www.dispatchesfromthevanishingworld.com/pastdispatches/mountain/mountain_1.html The Mountain of Names (Genealogy)]
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| {{DEFAULTSORT:Pedigree Collapse}}
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| [[Category:Genealogy]]
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| [[Category:Incest]]
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| [[Category:Kinship and descent]]
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| [[Category:Marriage]]
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| [[Category:Population genetics]]
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