  We investigate in this paper the dependence relation between the space-time
periodic coefficients $A, q$ and $\mu$ of the reaction-diffusion equation
$\partial_t u - \nabla \cdot (A(t, x)\nabla u) + q(t, x) \cdot \nabla u =
\mu(t, x) u(1 - u)$, and the spreading speed of the solutions of the Cauchy
problem associated with this equation and compactly supported initial data. We
prove in particular that (1) taking the spatial or temporal average of $\mu$
decreases the minimal speed, (2) if the coefficients do not depend on $t$ and
$q\not\equiv 0$, then increasing the amplitude of the diffusion matrix $A$
increases the minimal speed, (3) if $A = I_N$, $\mu$ is a constant, then the
introduction of a space periodic drift term $q = \nabla Q$ increases the
minimal speed. To prove these results, we use a variational characterization of
the spreading speed that involves a family of periodic principal eigenvalues
associated with the linearization of the equation near 0. We are thus back to
the investigation of the dependence relation between this family of eigenvalues
and the coefficients.
