A simple method to account for natural selection when predicting inbreeding depression

It has been widely appreciated that natural selection opposes the progress of inbreeding in small populations, thus limiting the actual inbreeding depression for fitness traits. However, no method to account for the consequences of this process has been given so far. I give a simple and intuitive method to predict inbreeding depression, taking into account the increase in selection efficiency against recessive alleles during inbreeding. It is based on the use of a “purged inbreeding coefficient” g_t that accounts for the reduction of the probability of the deleterious homozygotes caused by the excess d of detrimental effect for deleterious alleles in the homozygous condition over its additive expectation. It is shown that the effect of purging can be important even for relatively small populations. For between-loci variable deleterious effects, accurate predictions can be obtained using the effective homozygous deleterious excess d_e, which can be estimated experimentally and is robust against variation of the ancestral effective population size. The method can be extended to any trait and it is used to predict the evolution of the mean viability or fecundity in a conservation program with equal or random family contributions.