  We prove the vanishing of many Welschinger invariants of real symplectic
$4$-manifolds. In some particular instances, we also determine their sign and
show that they are divisible by a large power of 2. Those results are a
consequence of several relations among Welschinger invariants obtained by a
real version of symplectic sum formula. In particular, this note contains
proofs of results announced in [BP13].
