  We give an explicit combinatorial proof of a weighted version of strong
log-concavity for the generating polynomial of increasing spanning forests of a
finite simple graph equipped with a total ordering of the vertices. In contrast
to similar proofs in the literature, our injection is local in the sense that
it proceeds by moving a single edge from one forest to the other. In the
particular case of the complete graph, this gives a new combinatorial proof of
log-concavity of unsigned Stirling numbers of the first kind where a pair of
permutations is transformed into a new pair by breaking a single cycle in the
first permutation and gluing two cycles in the second permutation, while all
the other spectator cycles are left untouched.
