Short communication: Genetic lag represents commercial herd genetic merit more accurately than the 4-path selection model.

Expectation of genetic merit in commercial dairy herds is routinely estimated using a 4-path genetic selection model that was derived for a closed population, but commercial herds using artificial insemination sires are not closed. The 4-path model also predicts a higher rate of genetic progress in elite herds that provide artificial insemination sires than in commercial herds that use such sires, which counters other theoretical assumptions and observations of realized genetic responses. The aim of this work is to clarify whether genetic merit in commercial herds is more accurately reflected under the assumptions of the 4-path genetic response formula or by a genetic lag formula. We demonstrate by tracing the transmission of genetic merit from parents to offspring that the rate of genetic progress in commercial dairy farms is expected to be the same as that in the genetic nucleus. The lag in genetic merit between the nucleus and commercial farms is a function of sire and dam generation interval, the rate of genetic progress in elite artificial insemination herds, and genetic merit of sires and dams. To predict how strategies such as the use of young versus daughter-proven sires, culling heifers following genomic testing, or selective use of sexed semen will alter genetic merit in commercial herds, genetic merit expectations for commercial herds should be modeled using genetic lag expectations.