Application
For lineal ancestors, this can be approximated by 10th degree consanguinity. The reason this is approximate, and not exact, is that common ancestry is halved every time the degree of consanguinity is increased by one. For example the degree of consanguinity of a parent is one. This means that a parent provides 1/2^1 or 1/2 of a persons ancestry (the other parent provides the other half). A 7th great grandparent has a 9th degree consanguinity, and therefore providing 1/2^9 or 1/512 common ancestry. An 8th great grandparent provides 1/1024 common ancestry which is as close as one can come to 1/1000, and so this is the cutoff used.
For collateral relatives, 1/1000 common ancestry can be approximated by 10th degree consanguinity for relationships derived through half-siblings and 11th degree consanguinity for relationships derived through full siblings. For example, siblings share 100% common ancestry, as they share 2 common parents (1/2^1 + 1/2^1 = 1). Half siblings share 50% common ancestry.
8th great aunt/uncles (can also be called 7th great grand aunt/uncles); 1st cousins 7x removed; 2nd cousins 5x removed; 3rd cousins 3x removed; and 4th cousins once removed are all at the 1/1024th common ancestry levels, and therefore used as the cutoffs.
Complicating factors such as pedigree collapse can increase the percentage of common ancestry to a higher number than it would be otherwise.
Read more about this topic: Rule Of 1/1000 Common Ancestry
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