We illustrate the use of tropical methods by generalizing a formula due to Abramovich and Bertram, extended later by Vakil. Namely, we exhibit relations between enumerative invariants of the Hirzebruch surfaces
Σ
n
\Sigma _n
and
Σ
n
+
2
\Sigma _{n+2}
, obtained by deforming the first surface to the latter.
Our strategy involves a tropical counterpart of deformations of Hirzebruch surfaces and tropical enumerative geometry on a tropical surface in three-space.