Does anyone has a nontrivial example of Cartier divisor $D$ on a projective variety $X$, such that $D$ is pseudoeffective but $-D$ is nef?



Pseudoeffective but anti-nef divisor
A nef divisor is also pseudo-effective so if $D$ is pseudo-effective and $-D$ is nef, then both $D$ and $-D$ are pseudo-effective and hence $D\equiv 0$ (numerically trivial). I assume this is not considered a non-trivial example.


