  We show that propagation speeds in invasion processes modeled by
reaction-diffusion systems are determined by marginal spectral stability
conditions, as predicted by the marginal stability conjecture. This conjecture
was recently settled in scalar equations; here we give a full proof for the
multi-component case. The main new difficulty lies in precisely characterizing
diffusive dynamics in the leading edge of invasion fronts. To overcome this, we
introduce coordinate transformations which allow us to recognize a leading
order diffusive equation relying only on an assumption of generic marginal
pointwise stability. We are then able to use self-similar variables to give a
detailed description of diffusive dynamics in the leading edge, which we match
with a traveling invasion front in the wake. We then establish front selection
by controlling these matching errors in a nonlinear iteration scheme, relying
on sharp estimates on the linearization about the invasion front. We briefly
discuss applications to parametrically forced amplitude equations, competitive
Lotka-Volterra systems, and a tumor growth model.
