Improving the estimation of realized effective population sizes in farm animals

Computation of inbreeding rate (DeltaF) 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-DeltaF)(t) should be more correctly written in real animal populations as F(t) = 1 - (1-DeltaF)(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.