  Welschinger's invariant bounds from below the number of real rational curves
through a given generic collection of real points in the real projective plane.
We estimate this invariant using Mikhalkin's approach which deals with a
corresponding count of tropical curves. In particular, our estimate implies
that, for any positive integer $d$, there exists a real rational curve of
degree $d$ through any collection of $3d-1$ real points in the projective
plane, and, moreover, asymptotically in the logarithmic scale at least one
third of the complex plane rational curves through a generic point collection
are real. We also obtain similar results for curves on other toric Del Pezzo
surfaces.
