Inbreeding coefficients for stochastically varying small population sizes—bias of calculation based on effective numbers

The commonly used procedure to calculate inbreeding coefficients by effective population numbers (Ne) by the harmonic mean of generation-by-generation population sizes involves a computational bias. If the individual population sizes are considered as realizations of a binomially distributed random variable with sample size N and probability p, this bias can be investigated for the two cases p=constant and p=variable (Markov chain). The bias is of practical relevance only for small probabilities p, short period of initial successive generations, and small population sizes. The largest values for this computational bias are in the range of 0.05–0.06. It is concluded that for most practical purposes the approximate procedure is appropriate.