Linebreeding is a form of inbreeding (usually mild) directed toward keeping the offspring closely related to one ancestor (usually a much admired one). All inbreeding not necessary for holding this relationship high is avoided as far as possible.
It is practiced to conserve, among the descendants, the good traits of an outstanding sire or dam, increasing those descendants in numbers without lessening their resemblance to this ancestor even for many generations after that ancestor’s death.
The more superior a breeder’s herd or flock is to the average merit of its breed, the more reason he has to practice linebreeding to his very best animals or to the very best of their recent ancestors. Breeders of grades cannot often afford to do much linebreeding.