  Kearton observed that mutation can change the concordance class of a knot. A
close examination of his example reveals that it is of 4-genus 1 and has a
mutant of 4-genus 0. The first goal of this paper is to construct examples to
show that for any pair of nonnegative integers m and n there is a knot of
4-genus m with a mutant of 4-genus n.
  A second result of this paper is a crossing change formula for the algebraic
concordance class of a knot, which is then applied to prove the invariance of
the algebraic concordance class under mutation. The paper concludes with an
application of crossing change formulas to give a short new proof of Long's
theorem that strongly positive amphicheiral knots are algebraically slice.
