  A knot K is the resultant of a knot H if there exists a minimal crossing
diagram D of K such that some crossings of D can be altered to produce H. K is
fertile if every prime knot H with crossing number less than c(K) is a
resultant of K. K is n-fertile if every prime knot H with crossing number less
than n is a resultant of K. We classify the fertility and fertility number of
all rational links. This requires the introduction of the analogous concept of
link fertility.
