  The effects of spatial correlations of density fluctuations on merger
histories of dark matter haloes (so-called `{\it merger trees}') are analysed.
We compare the mass functions of dark haloes derived by a new method for
calculating merger trees, that proposed by Rodrigues \& Thomas (RT), with those
given by other methods such as the Block model, the Press-Schechter formula and
our own formula in which the mass functions are analytically expressed in a way
that takes into consideration the spatial correlations. It is found that the
mass functions given by the new method are well fit by those given by our
formula. We believe that new method (RT) {\it naturally} and correctly takes
into account the spatial correlations of the density fluctuations due to a
calculated, grid-based realisation of the density fluctuations and so is very
useful for estimating the merger tree accurately in a way that takes into
consideration spatial correlations.
  Moreover, by applying our formula, we present an analytic expression which
reproduces the mass function derived by the Block model. We therefore show
clearly why and how the mass functions given by the new method and the Block
model are different from each other. Furthermore, we note that the construction
of merger trees is sensitive to the criterion of collapse and merging of
overlapped haloes in cases in which two or more haloes happen to overlap. In
fact, it is shown that the mass function is very much affected when the
criterion of overlapping is changed.
