line breeding

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun Selective inbreeding to perpetuate certain desired qualities or characteristics in a strain of livestock.

from The Century Dictionary.

• noun Another name for in-and-in breeding.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun stockbreeding Breeding by a certain family line of descent, especially in the selection of the dam or mother.