  We make use of four galaxy catalogs based on four different semi-analytical
models (SAMs) implemented in the Millennium simulation to study the
environmental effects and the model dependence of galaxy merger rate. We begin
the analyses by finding that galaxy merger rate in the SAMs has mild redshift
evolution, consistent with results of previous works. To study the
environmental dependence of galaxy merger rate, we adopt two estimators, the
local overdensity (1+{\delta}n) defined as the surface density from the
nth-nearest-neighbor (n = 6 is chosen in this study) and the host halo mass Mh.
We find that galaxy merger rate Fmg shows strong dependence on the local
overdensity (1+{\delta}n) and the dependence is similar at all redshifts. For
the overdensity estimator, the merger rate Fmg is found about twenty times
larger in the densest regions than in under-dense ones in two of the four
models while it is roughly four times higher in the other two. In other words,
the discrepancies of the merger rate difference between two extremes can differ
by a factor of ~ five depending on the SAMs adopted. On the other hand for the
halo mass estimator, Fmg does not monotonically increase with the host halo
mass Mh, but peaks in the $M_h$ range between 10^12 and 10^13 h-1 M{\Theta},
which corresponds to group environments. High merger rate in high local density
regions corresponds primarily to the high merge rate in group
environments......
