Improving the estimation of realized effective population sizes in farm animals

Computation of inbreeding rate (Δ F ) must consider that inbreeding is delayed with one generation with respect to the idealized population when addressed using individual inbreeding coefficients. The expression relating inbreeding in generation t with inbreeding rate F _t  = 1 – (1– ΔF ) ^t should be more correctly written in real animal populations as F _t  = 1 – (1– ΔF ) ^{t ?1}, as changes in allele frequencies occur in the equivalent co-ancestries in the previous generation. This simple approach is tested on simulated and real pedigrees thus demonstrating that: (i) the adjusted individual increase in inbreeding becomes stable in populations under random mating while the unadjusted parameter does not; (ii) regression of the unadjusted parameter over generations in pedigrees under random mating is highly significant while after correction it is not significant; and (iii) the variance of the adjusted parameter is reduced with the generations.