High inbreeding in sheep or erroneous estimation?

Paiva et al. (2011) examined how microsatellite loci data from sheep surveys in the United States and Brazil could be merged when they are analyzed in different laboratories. In addition, they calculated the inbreeding coefficient using F IS from the software FSTAT (Goudet 2001) using the formula F H H IS O E 1 = − / , where H O and H E are the observed and expected Hardy–Weinberg heterozygosities. For 11 microsatellite loci, they found that for the 12 sheep breeds from the United States, the average F IS value was 0.205, and for the 9 sheep breeds from Brazil, the F IS was –0.005. They suggested that " The higher levels of inbreeding (F IS) observed in some US breeds could possibly be due to smaller population sizes or a higher level of selection pressure " (Paiva et al. 2011). It is unclear how either smaller population sizes or more selection pressure could increase F IS to this high level found in the US breeds. On the other hand, the high F IS values found in the US breeds could have been generated not by inbreeding within each breed but by heterogeneity among the flocks sampled within each breed, caused by the Wahlund effect (Hedrick 2011), and the sampling of only a few animals per flock. Specifically, the formula used above for F IS assumes that there is no population structure within each breed among the flocks sampled, that is, no Wahlund effect, which occurs when heterogeneous samples (different flocks here) with different allele frequencies are lumped together. Even with Hardy–Weinberg proportions within each flock (no inbreeding), combining heterogeneous samples results in an apparent deficiency of observed heterozygotes, a finding that Paiva et al. (2011) attributed to inbreeding. In another article (Blackburn et al. 2011), some of the same authors also found, using some of the same data, similarly high F IS values in the US breeds when 31 microsatellite loci were used. Hedrick (2012), in a theoretical effort to replicate these data for the Navajo-Churro sheep breed, showed that the F IS values in the study by Blackburn et al. (2011) were probably generated by a combination of population structure and small sample size from different flocks within a breed and not inbreeding within a breed. More specifically, Hedrick (2012) assumed that individual flocks within a breed were founded by samples of a given size, assumed …