We consider the large sibship situation where the correlation matrix is characterized by Eq.(4). It can be shown that each submatrix (the 3 × 3 block in Eq.(4)) contributes an eigenvalue equal to 1 + (3 − 1)r = 1 + 2r, and two eigenvalues equal to 1 − r. The variance of the eigenvalues for Eq.(4) is then equal to 2r2(N/(N −1)). Inserting it to Eq.(13), we have the Cheverud’s effective number of variables: N − 2r2. Compared to the ESS of N/(1 + 2r) determined by Eq.(5), Cheverud’s formula leads to a larger effective number of degrees of freedom, and less reduction, in particular in the large N limit.
