  Recently, Bern, Carrasco and Johansson conjectured dual identities inside the
gluon tree scattering amplitudes. In this paper, we use the properties of the
heterotic string and open string tree scattering amplitudes to refine and
derive these dual identities. These identities can be carried over to loop
amplitudes using the unitarity method. Furthermore, given the $M$-gluon (as
well as gluon-gluino) tree amplitudes, $M$-graviton (as well as
graviton-gravitino) tree scattering amplitudes can be written down immediately,
avoiding the derivation of Feynman rules and the evaluation of Feynman diagrams
for graviton scattering amplitudes.
