Noun
linebreeding (countable and uncountable, plural linebreedings)
A form of inbreeding that may encompass crosses between individuals and their descendants or two cousins, used to increase a particular animal's contribution to the population.
The breed's characteristic gene mutation was maintained through linebreeding to the point where the condition was a fixed property in the Belgian Blue breed. Source: Internet
However, it is not always the case, and a form of distant linebreeding occurs. Source: Internet