  We consider one-dimensional reaction-diffusion equations of Fisher-KPP type
with random stationary ergodic coefficients. A classical result of Freidlin and
Gartner [16] yields that the solutions of the initial value problems associated
with compactly supported initial data admit a linear spreading speed almost
surely. We use in this paper a new characterization of this spreading speed
recently proved in [8] in order to investigate the dependence of this speed
with respect to the heterogeneity of the diffusion and reaction terms. We prove
in particular that adding a reaction term with null average or rescaling the
coefficients by the change of variables x $\rightarrow$ x/L, with L
\textgreater{} 1, speeds up the propagation. From a modelling point of view,
these results mean that adding some heterogeneity in the medium gives a higher
invasion speed, while fragmentation of the medium slows down the invasion.
