Pedigree collapse

Loss of ancestors or ancestors loss referred to in the family history (genealogy ) to reduce the actual number of forefathers (ancestors ) of a person with respect to the theoretically possible total number by at least one ancestor occupied at the same two ancestral positions within the ancestor list of the person - it is missing then at least one of all the other distinguishable ancestor. In mathematical terms, the number of logically possible ancestors of living beings with bisexual reproduction is 2 to the power n in the nth generation of ancestors, for example, the great-grandparents ( 3rd generation): 2 high 3 = 2 × 2 × 2 = 8 different Urgroßelternteile.

The most widespread is ancestral loss in the offspring of cousin - cousin pairings (see also cross- cousin marriage, Bint'amm - marriage, family, marriage). If the cousins ​​parents are first degree, their children and grandchildren have an ancestor loss of about 25 percent, as they already in the Ancestry generation of grandparents only six ancestors have held a total of eight different: two grandparents are identical because they parents are of a pair of siblings. This reduction ( shrinkage ) continues in all previous generations.

Within certain limits ancestral loss is a statistically normal phenomenon that affects many generations of ancestors considers each person in the case of human inbreeding but is much more pronounced (see also ancestral community of humankind ).

Also in animal breeding ancestor loss may play a role, the so-called ancestral loss coefficient of an individual is calculated, for example, in dog breeding; it can with its mathematical inbreeding coefficients match (see below: ancestor - loss inbreeding ).

Ancestor loss at different degrees of relationship

The maximum reduction of ancestors has a person whose parents originate itself from each other, one of whose parents ie child or grandchild of the other (see also incest taboo ). For example, if a father with his own ( biological or adopted ) Daughter testifies to a child, completely overlap for this child the father side and the nut side relationships: the paternal grandfather ( father's father ) is also the maternal grandfather (father of the mother), the grandmother is also the mother of the father and mother; Ancestry four positions are occupied by only two ancestors, and so on. In addition, his father is also his grandfather ( father because his mother ), his grandfather at the same time his great-grandfather, and so on in ascending order.

A 50 percent loss Ancestry has a person whose parents are vollbürtige brother and sister ( see also sibling marriage): Even with her ​​father and the nut-side relationship are congruent, because their parents have the same mother and the same father. It lacks the complete relationship tree of an unrelated with the other parent - Since all the individual's ancestors occupy the same two positions in its ancestor list, the total number of their actual ancestors halved. The ancestral loss coincides here with the kinship coefficient of vollbürtigen siblings: 0.5 = 50 percent.

The third largest ancestral loss have offspring of uncle - niece or nephew - aunt - compound (Example: uncle - niece marriages in the Bible); he covers himself in about the ancestral loss of offspring from a compound of half- sibling or grandparent with his grandchild.

Explanation

In the sibling marriage it is already in its second generation the ancestor loss, since the participant has not four but only two grandparents. As an incest taboo applies in most human societies, ancestral loss usually only in later generations at the earliest in the third generation, but usually. In these cases, siblings appear as ancestors, so that in the next generation whose parents occur more than once as ancestors. It may also happen that a person acts as Ahn in different generations. Thus, the number reduces the actually different compared to the number of theoretically possible ancestors, from which the inbreeding coefficient of the ancestor list can be estimated.

If one follows the sequence of generations far enough into the past, ancestral loss is mathematically inevitable, since the number of ancestors numbers doubled in each generation of ancestors in the nth generation of ancestors so is 2n. If one performs a human 30 generations back (ie about 500 to 1000 years), are then obtained for this a generation more than one billion ancestors, which exceeds the number of the then world population. In the ancestor list therefore necessarily come many ancestors several times before, the further back you go.

Examples

High nobility

Examples of strong ancestral loss can be found in a long time isolated populations, such as island residents or religious minorities. Since the noble ancestors are particularly well documented and published and for reasons of equality and the right of inheritance, marriages between close relatives were particularly common, most examples of the literature relating to members of European dynasties.

A prime example of ancestral loss is Alfonso XII. Whose grandfathers were brothers and sisters whose grandmothers. He thus has only four great-grandparents ( instead of eight ), as both Urgroßelternpaare appear on both the father's and on the maternal side. Thus his parents, Francisco de Asís de Borbón and Isabella II together only four grandparents and have thus only one gene pool, which is normally found in siblings.

Another particularly clear example of ancestral loss in the high nobility is Charles II, all of whose great-grandparents (some multiple times) descended from Joanna of Castile, but he had only six great-grandparents, as the "missing" 2 great-grandparents already occur as grandparents in his pedigree. In the 5th generation ( great-great -great- grandparents) only 10 new individuals occur, the remaining 22 (out of a possible total of 32) are available in the 4th generation or occur multiple times in the 5th generation.

For Frederick the Great, Maria Theresa and August the Strong, the ancestral loss leaves absolutely and determine a percentage over 12 generations ( after the publication of Erich Brandenburg, 1934-1937 ). And even in today's members of the nobility such as the Spanish Crown Prince Felipe and King Harald V of Norway, the ancestral loss can be clearly seen.

Charlemagne

To illustrate the loss of ancestors is often found (especially in internet forums ) the claim that this would also mean that " statistically speaking, all Europeans alive today would have descended from Charlemagne and thus every European aristocratic ancestors had (whether about marital or illegitimate line) "or - in the English language - " that all of British King Edward I (or optionally Alfred the Great) derived ".

Claims of this kind, however, are based not on statistics, but on the erroneous assumption that the 2n forefathers numbers were evenly distributed among the then living people. Thus, the subject would, however, just as often descended from Charlemagne as a childless contemporaries Charles, which is obviously not the case.

For quantitative statements lead highly simplified computational models (in this case a Poisson distribution ) through a series of assumptions to force a particular statistical distribution, such as:

• A homogeneous population mixing ( the fishmonger from Hamburg marries the Bavarian milkmaid; Frankish nobleman marries a blacksmith from Württemberg, in Wroclaw marries a Catholic citizens a Jewish citizen )
• A homogeneously growing population ( no immigration, equal chances of survival for all )

However, these models are the reality from not good. Further guidance on this aspect of the loss of ancestors can be found in the literature.

Mitochondrial Eve

A new approach to the subject ancestral loss form genetic studies that have been developed since about 1990 under the theme of mitochondrial Eve. These data suggest that all living humans are descended from a single woman and so all are mutually related by blood (see also Adam of the Y chromosome ).

Ancestor loss versus inbreeding

Especially in dog breeding the so-called ancestral loss coefficient ( AVK ) is used as a measure of the inbreeding of an individual occasionally. For this purpose, we calculate the ratio of existing () and maximum possible ancestors () over a defined number generations. The difference between the result and 1 ( or 100 percent ) corresponds to the desired value.

In contrast to the inbreeding coefficient of the ancestral loss coefficient, however, does not take into account how close father and mother are related to each other (see kinship coefficient). In inbred, but not closely related to each other breeders this can lead to the junior high loss of ancestors, but at the same time has a low inbreeding coefficient.

Since the degree of inbreeding depression which varies according to homozygosity, which in turn is measured by the inbreeding coefficient, in such cases the inbreeding coefficient to give more importance than the loss of ancestors. Thus, the ancestral loss coefficient provides at best an estimate, but at worst, completely useless information to the true inbreeding. It is therefore not used in the scientific genetics.