  We use semi-analytical modelling of galaxy formation to study the redshift
evolution of the galaxy merger fractions and merger ratesin Lambda CDM and
quintessence (QCDM) cosmologies, their dependence on physical parameters as the
environment, the merger timescale, the way major mergers are defined, and the
minimum mass of objects taken into account. We find that for a given final halo
mass the redshift dependence of the merger fraction F_mg and the resulting
merger rate can be fitted well by a power law for redshifts z <= 1. The
normalization F_{mg}(0) and the slope m depend on the final halo mass. For a
given merger timescale t_merg and an assumed maximum mass ratio R_major for
major mergers, F_mg(0) and m depend exponentially on each other. The slope m
depends logarithmically on the ratio of the final halo mass and the minimum
halo mass taken into account. In addition, the local normalization F_{mg}(0)
increases for larger R_{major} while m decreases. We compare the predicted
merger fractionwith recent observations and find that the model cannot
reproduce both the merger index and the normalization at the same time. In
general the model underestimates F_{mg}(0) and m by a factor of 2.
