We compare the use of galaxy asymmetry and pair proximity for measuring galaxy merger fractions and rates for a volume limited sample of 3184 galaxies with -21 < M(B) -5 log h < -18 mag. and 0.010 < z < 0.123 drawn from the Millennium Galaxy Catalogue. Our findings are that: (i) Galaxies in close pairs are generally more asymmetric than isolated galaxies and the degree of asymmetry increases for closer pairs. At least 35% of close pairs (with projected separation of less than 20 h^{-1} kpc and velocity difference of less than 500 km s^{-1}) show significant asymmetry and are therefore likely to be physically bound. (ii) Among asymmetric galaxies, we find that at least 80% are either interacting systems or merger remnants. However, a significant fraction of galaxies initially identified as asymmetric are contaminated by nearby stars or are fragmented by the source extraction algorithm. Merger rates calculated via asymmetry indices need careful attention in order to remove the above sources of contamination, but are very reliable once this is carried out. (iii) Close pairs and asymmetries represent two complementary methods of measuring the merger rate. Galaxies in close pairs identify future mergers, occurring within the dynamical friction timescale, while asymmetries are sensitive to the immediate pre-merger phase and identify remnants. (iv) The merger fraction derived via the close pair fraction and asymmetries is about 2% for a merger rate of (5.2 +- 1.0) 10^{-4} h^3 Mpc^{-3} Gyr^{-1}. These results are marginally consistent with theoretical simulations (depending on the merger time-scale), but imply a flat evolution of the merger rate with redshift up to z ~1.
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