Kinship coefficient and genetic index of familiality
Details
The genetic index of familality is defined as the mean kinship between all pairs of individuals in a set multiplied by 100,000. Formally, it is defined in (Gholami and Thomas 1994) as $$100,000 \times \frac{2}{n(n-1)}\sum_{i=1}^{n-1}\sum_{j=i+1}^n k_{ij}$$ where \(n\) is the number of individuals in the set and \(k_{ij}\) is the kinship coefficient between individuals \(i\) and \(j\).
The scaling is purely for convenience of presentation.
Note
Adapted from gif.c, testable with -Dexecutable as standalone program, which can be use for any pair of indidivuals
References
Gholami K, Thomas A (1994). “A linear time algorithm for calculation of multiple pairwise kinship coefficients and the genetic index of familiality.” Comput Biomed Res, 27(5), 342-50. doi:10.1006/cbmr.1994.1026 .
Examples
if (FALSE) { # \dontrun{
test<-c(
5, 0, 0,
1, 0, 0,
9, 5, 1,
6, 0, 0,
10, 9, 6,
15, 9, 6,
21, 10, 15,
3, 0, 0,
18, 3, 15,
23, 21, 18,
2, 0, 0,
4, 0, 0,
7, 0, 0,
8, 4, 7,
11, 5, 8,
12, 9, 6,
13, 9, 6,
14, 5, 8,
16, 14, 6,
17, 10, 2,
19, 9, 11,
20, 10, 13,
22, 21, 20)
test<-matrix(test,ncol=3,byrow=TRUE)
gif(test,gifset=c(20,21,22))
# all individuals
gif(test,gifset=1:23)
} # }