Let $f:U\longrightarrow \overline{M}_{0,n}(\mathbb{P}^m,d)$ is the universal family with morphism $\pi:U\longrightarrow\mathbb{P}^m$ and let $X\subset\mathbb{P}^m$ be a hypersurface defined by a global section $x$ of $\mathcal{O}(X)$ then $f_{\ast}\pi^{\ast}\mathcal{O}(X)$ is a vectorbundle on $\overline{M}_{0,n}(\mathbb{P}^m,d)$ with global section $f_{\ast}\pi^{\ast}x$. It seems to be known that the zero locus of the section $f_{\ast}\pi^{\ast}x$ is the virtual fundamental class of $\overline{M}_{0,n}(X,\beta)$ (for a suitable $\beta$ ).

Does anyone know a good reference for this? I had a look at the paper of Behrend and Fantechi about virtual fundamental classes, but I was not able to figure this out from that paper. Thank you in advance.