We investigate redshift evolution in the galaxy merger and accretion rates , using a well-defined sample of 4184 galaxies with 0.12 \leq z \leq 0.55 and R _ { C } \leq 21.5 . We identify 88 galaxies in close ( 5 \leq r _ { p } \leq 20 ~ { } h ^ { -1 } kpc ) dynamical ( \Delta v \leq 500 km/s ) pairs . These galaxies are used to compute global pair statistics , after accounting for selection effects resulting from the flux limit , k -corrections , luminosity evolution , and spectroscopic incompleteness . We find that the number of companions per galaxy ( for -21 \leq M _ { B } ^ { k,e } \leq - 18 ) is N _ { c } = 0.0321 \pm 0.0077 at z =0.3 . The luminosity in companions , per galaxy , is L _ { c } = 0.0294 \pm 0.0084 \times 10 ^ { 10 } ~ { } h ^ { 2 } L _ { \odot } . We assume that N _ { c } is proportional to the galaxy merger rate , while L _ { c } is directly related to the mass accretion rate . After increasing the maximum pair separation to 50 h ^ { -1 } kpc , and comparing with the low redshift SSRS2 pairs sample , we infer evolution in the galaxy merger and accretion rates of ( 1 + z ) ^ { 2.3 \pm 0.7 } and ( 1 + z ) ^ { 2.3 \pm 0.9 } respectively . These are the first such estimates to be made using only confirmed dynamical pairs . When combined with several additional assumptions , this implies that approximately 15 % of present epoch galaxies with -21 \leq M _ { B } \leq - 18 have undergone a major merger since z =1 .