Based on the idea that the overall amount of correlation among several variables can be measured by the variance of the eigenvalues derived from their correlation matrix, Cheverud proposed a formula to calculate the effective number of variables (Cheverud, 2001): (13)NE=N(1−(N−1)Var[λ]N2) where N is the number of variables, and λ = (λ1, λ2,…λN) are the eigenvalues of the N × N correlation matrix for these N variables. Eq.(13) has been applied to QTL mapping in the inbreeding system and to human association analysis to determine the number of independent markers in a linkage disequilibrium block (Cheverud, 2001; Nyholt, 2004). Although this formula has not been used to determine the number of independent samples, it can be interesting to compare Eq.(13) with the ESS formula derived in this paper.
