Henderson originally described breeding values (EPDs) as sums of gene effects. Meuwissen, Hayes, Goddard re-expressed this as sums of effects estimated for genotyped DNA variants.
In current selection we have two models for genetic prediction, one for genotyped animals and a separate model for animals not genotyped.
You can combine a pedigree based relationship matrix with a genomic based relationship, we call this single-step BLUP or HBLUP (Aguilar et al., 2010).
There is a second approach which Garrick refers to as a hybrid approach. Now breeding values for nongenotyped animals are expressed as the part explained by genotyped relatives and the part not explained by genotyped relatives. This is similar to the animal model where we have the breeding value explained by relatives and the breeding value due to the random shuffle of genes across generations.
This model is in press and should be out later this summer (Fernando, Dekkers and Garrick 2014 GSE).
If everyone is genotyped, this hybrid approach reduces to the genomic selection models such as BayesA, BayesB, and BayesC. If no one is genotyped the model reduces to the traditional models used to calculate pedigree EPDs. Garrick also states that HBLUP is a special case of their hybrid model, but HBLUP has certain assumptions not needed in the hybrid model.
Garrick then transitioned to discussing improvements in computing. He showed that memory continues to improve according to Moore's Law. But, he showed that clock speed has stopped increasing since 2004 due the heat produced by fast processors. Super fast processors were producing as much heat as a rocket nozzle. But, we have have seen increased use of multiple core processors and graphical processors.
Garrick has been working to improve parallel computing of genetic . The data available on genotyped animals is not large enough to see speed ups of genomic predictions by use of parallel computing. But, single-step BLUP and hybrid models are a perfect size for speed up with parallel computing.