Dendroidal sets and simplicial operads

We establish a Quillen equivalence relating the homotopy theory of Segal operads and the homotopy theory of simplicial operads, from which we deduce that the homotopy coherent nerve functor is a right-Quillen equivalence from the model category of simplicial operads to the model category structure for infinity-operads on the category of dendroidal sets. By slicing over the monoidal unit, this also gives the Quillen equivalence between Segal categories and simplicial categories proved by Bergner, as well as the Quillen equivalence between quasi-categories and simplicial categories proved by Joyal and Lurie. We also explain how this theory applies to the usual notion of operad (that is, with a single colour) in the category of spaces.