Inbreeding coefficient under a grandparental regression model.

CANTET, R. J. C.; MUNILLA, SEBASTIÁN

Madison, Wisconsin

Congreso; 5th International Conference on Quantitative Genetics; 2016

International Conference on Quantitative Genetics

The linear regression of the breeding value of an individual on his parents? breeding values is termed the ?parental regression?. Under this representation, the regression coefficients are equal to one half and the regression error term is called the Mendelian residual. If the parents are not inbred, the variance of the Mendelian residuals equals to half the additive variance. More generally, the variance is a function of the parent?s inbreeding coefficients and the additive variance. Mendelian residuals are interpreted as terms that reflect uncertainty due to not knowing which fractions of grandparental genome were passedto the individual over or below one‐fourth. Genomic information, however, may help disentangling the realized inheritance process. To take advantage of this fact, we expanded the parental regression model with a linear combination of breeding values from all four grandparents, and termed this new representation as ?grandparental regression model?. The new regression coefficients are related to the fraction of genome shared identical by descent between the individual and the corresponding grandparent. Precisely, they are defined as half the difference between the genome shared identical by descent between the individual and their paternal (or maternal) grandparents due to recombination. The halving is due to segregation of the grandparental chromosomes into the parental gamete that originated the zygote. By operating algebraically on this model we provide formulae for the inbreedingcoefficient and the variance of the Mendelian residuals. The resulting inbreeding coefficient is a composition, over each common ancestor that connects both parents, of three terms: 1. the parent?s expected relationship as defined by the genealogy; 2. a product of the grand parental regression coefficients; 3. a combination of both, resulting from counting all possible paths connecting the parents to the common ancestor under a directed acyclic graph representation.