Fuzzy classification of phantom parent groups in an animal model.
BACKGROUND
Genetic evaluation models often include genetic groups to account for unequal genetic level of animals with unknown parentage. The definition of phantom parent groups usually includes a time component (e.g. years). Combining several time periods to ensure sufficiently large groups may create problems since all phantom parents in a group are considered contemporaries.


METHODS
To avoid the downside of such distinct classification, a fuzzy logic approach is suggested. A phantom parent can be assigned to several genetic groups, with proportions between zero and one that sum to one. Rules were presented for assigning coefficients to the inverse of the relationship matrix for fuzzy-classified genetic groups. This approach was illustrated with simulated data from ten generations of mass selection. Observations and pedigree records were randomly deleted. Phantom parent groups were defined on the basis of gender and generation number. In one scenario, uncertainty about generation of birth was simulated for some animals with unknown parents. In the distinct classification, one of the two possible generations of birth was randomly chosen to assign phantom parents to genetic groups for animals with simulated uncertainty, whereas the phantom parents were assigned to both possible genetic groups in the fuzzy classification.


RESULTS
The empirical prediction error variance (PEV) was somewhat lower for fuzzy-classified genetic groups. The ranking of animals with unknown parents was more correct and less variable across replicates in comparison with distinct genetic groups. In another scenario, each phantom parent was assigned to three groups, one pertaining to its gender, and two pertaining to the first and last generation, with proportion depending on the (true) generation of birth. Due to the lower number of groups, the empirical PEV of breeding values was smaller when genetic groups were fuzzy-classified.


CONCLUSIONS
Fuzzy-classification provides the potential to describe the genetic level of unknown parents in a more parsimonious and structured manner, and thereby increases the precision of predicted breeding values.
Fikse
Freddy
F
Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, 75007 Uppsala, Sweden. Freddy.Fikse@hgen.slu.se
D000465:Algorithms; D000818:Animals; D001947:Breeding; D005260:Female; D017143:Fuzzy Logic; D008297:Male; D023421:Models, Animal; D008957:Models, Genetic; D010375:Pedigree