Revised Calculation of Kalinowski's Ancestral and New Inbreeding Coefficients

To test for the presence of purging in populations, the classical pedigree-based inbreeding coefficient (F) can be decomposed into Kalinowski's ancestral (F-ANC) and new (F-NEW) inbreeding coefficients. The F-ANC and F-NEW can be calculated by a stochastic approach known as gene dropping. However, the only publicly available algorithm for the calculation of F-ANC and F-NEW, implemented in GRain v 2.1 (and also incorporated in the PEDIG software package), has produced biased estimates. The F-ANC was systematically underestimated and consequently, F-NEW was overestimated. To illustrate this bias, we calculated F-ANC and F-NEW by hand for simple example pedigrees. We revised the GRain program so that it now provides unbiased estimates. Correlations between the biased and unbiased estimates of F-ANC and F-NEW, obtained for example data sets of Hungarian Pannon White rabbits (22,781 individuals) and Dutch Holstein Friesian cattle (37,061 individuals), were high, i.e., >0.96. Although the magnitude of bias appeared to be small, results from studies based on biased estimates should be interpreted with caution. The revised GRain program (v 2.2) is now available online and can be used to calculate unbiased estimates of F-ANC and F-NEW.