  We establish selection of critical pulled fronts in invasion processes. Our
result shows convergence to a pulled front with a logarithmic shift for open
sets of steep initial data, including one-sided compactly supported initial
conditions. We rely on robust, conceptual assumptions, namely existence and
marginal spectral stability of a front traveling at the linear spreading speed.
We demonstrate that the assumptions hold for open classes of spatially extended
systems. Previous results relied on comparison principles or probabilistic
tools with implied non-open conditions on initial data and structure of the
equation. Technically, we describe the invasion process through the interaction
of a Gaussian leading edge with the pulled front in the wake. Key ingredients
are sharp linear decay estimates to control errors in the nonlinear matching
and corrections from initial data.
