Editing Quantitative genetics (section)

====GRC – genepool relationship coefficient====
In any pairwise relationship estimation, there is one '''Ρ<sub>k</sub>''' for each individual: it remains to average them in order to combine them into a single "Relationship coefficient". Because each ''Ρ''  is a '''fraction of a total genepool''', the appropriate average for them is the ''geometric mean'' <ref>the square-root of their product</ref><ref name="Moroney 1956">{{cite book |last1=Moroney|first1=M.J. |title=Facts from figures|date=1956 |publisher=Penguin Books |location=Harmondsworth|edition=third}}</ref>{{rp|34–55}} This average is their '''Genepool Relationship Coefficient'''—the "GRC".

For the first example (two full first-cousins), their GRC = 0.5; for the second case (a full first and second cousin), their GRC = 0.3536. 
 
All of these relationships (GRC) are applications of path-analysis.<ref name="Li 1977">{{cite book|last1=Li|first1=Ching Chun|title=Path analysis - a Primer|date=1977|publisher=Boxwood Press|location=Pacific Grove|isbn=0-910286-40-X|edition=Second printing with Corrections}}</ref>{{rp|214–298}} A summary of some levels of relationship (GRC) follow.

{| class="wikitable"
|-
! GRC !! Relationship examples
|-
| 1.00 || full Sibs
|-
| 0.7071 || Parent ↔ Offspring; Uncle/Aunt ↔ Nephew/Niece
|-
| 0.5 || full First Cousins;  half Sibs; grand Parent ↔ grand Offspring
|-
| 0.3536 || full Cousins First ↔ Second; full First Cousins {1 remove}
|-
| 0.25 || full Second Cousins; half First Cousins; full First Cousins {2 removes}
|-
| 0.1768 || full First Cousin {3 removes}; full Second Cousins {1 remove}
|-
| 0.125 || full Third Cousins; half Second Cousins; full 1st  Cousins {4 removes}
|-
|0.0884 || full First Cousins {5 removes}; half Second Cousins {1 remove}
|-
| 0.0625 || full Fourth Cousins; half Third Cousins
|}