Wright proposed a path formula for computing inbreeding coefficients that can be generalized to computing kinship coefficients [15]. The pedigree formula is

Φij =

pij

1 2

n(pij )

[1 + fa(pij )], where the sum extends over all pairs pij of nonintersecting paths descending from a common ancestor a(pij ) of i and j to i and j, respectively, and where n(pij ) is the number of people counted along the two paths. The common ancestor is counted only once. If i = j, there is only the degenerate pair of paths that start and end at i but possess no arcs connecting a parent to a child. In this case, the formula reduces to the fact Φii = 1 2 (1 + fi). In general, a path is composed of arcs connecting parents to their children. Two paths intersect when they share a common arc. To get a feel for Wright’s formula, verify it for the case of siblings of unrelated parents. Next prove it in general by induction. Note that although founders are allowed to be inbred, no two of them can be related. (Hint: Consider first the founders of a pedigree and then, recursively, each child of parents already taken into account.)