  Based on the combinatory theory of rooted colored trees, we investigate the
conditions for the explicit stochastic Runge-Kutta (SRK) methods to preserve
quadratic invariants (QI) up to certain orders of accuracy. These conditions
can supply a practical approach of constructing explicit nearly conservative
SRK methods. Meanwhile, we estimate errors in the preservation of QI resulting
from iterative implementation of implicit conservative SRK methods with
fixed-point and Newton's iterations. Finally, numerical experiments are
performed to test the behavior of the methods in preserving QI.
