  We study the static susceptibilities for charge and spin sectors in
paramagnetic states for Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ in $0.5\leq x \leq 2$
within random phase approximation on the basis of an effective Ru $t_{2g}$
orbital Hubbard model. We find that several modes of spin fluctuation around
$\boldq=(0,0)$ and $\boldq\sim(0.797\pi,0)$ are strongly enhanced for the model
of $x=0.5$. This enhancement arises from the increase of the corresponding
susceptibilities for the $d_{xy}$ orbital due to the rotation-induced
modifications of the electronic structure for this orbital (i.e., the
flattening of the bandwidth and the increase of the density of state near the
Fermi level). We also find that the ferromagnetic spin fluctuation becomes
stronger for a special model than for the model of $x=0.5$, while the
competition between the modes of spin fluctuation at $\boldq=(0,0)$ and around
$\boldq\sim (\pi,0)$ is weaker for the special model; in this special model,
the van Hove singularity (vHs) for the $d_{xy}$ orbital is located on the Fermi
level. These results indicate that the location of the vHs for the $d_{xy}$
orbital, which is controlled by substitution of Ca for Sr, is a parameter to
control this competition. We propose that the spin fluctuations for the
$d_{xy}$ orbital around $\boldq=(0,0)$ and $\boldq\sim (\pi,0)$ play an
important role in the electronic states around $x=0.5$ other than the
criticality approaching the usual Mott transition where all electrons are
localized.
