There is a difference between line breeding and inbreeding. Inbreeding is breeding (human terms) children back to parents and siblings to siblings. This is most often done to increase chances of proving a mutation can be genetically passed on.
Line breeding is similar but it is more often cousin to cousin or breeding to a grandparent. Outcrossing is done but usually only for ensuring the health of the animals. This is most often done to ensure that desired traits that are already established stay true for visual morphs.
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