Offspring risk and sibling risk for multilocus traits

The recurrence risk of a trait in a relative of type R is the probability t hat an individual who is in relationship of type R to an affected proband h as the trait, It is intuitively clear that closer relationships lead to hig her recurrence risks, However, no exact analysis of this phenomenon has bee n presented for multilocus traits, We prove a theorem that shows how recurr ence risks are influenced by the degree of closeness of the relationship R, For example, our theorem implies that sibling risk is always higher than o ffspring risk, The loci influencing the trait are assumed to be autosomal a nd unlinked, but arbitrary epistasis between the loci is allowed, We give a detailed proof of the theorem by using stochastic matrices, A shorter proo f based on the additive and dominance genetic variances is also sketched, A dditionally, we also give some empirical results and discuss generalization s of the theorem, Copyright (C) 2001 S. Karger AG, Basel.