  In this paper we study spaces of algebras over an operad (non-symmetric) in
symmetric monoidal model categories. We first compute the homotopy fiber of the
forgetful functor sending an algebra to its underlying object, extending a
result of Rezk. We then apply this computation to the construction of geometric
moduli stacks of algebras over an operad in a homotopical algebraic geometry
context in the sense of To\"en and Vezzosi. We show under mild hypotheses that
the moduli stack of unital associative algebras is a Zariski open substack of
the moduli stack of non-necessarily unital associative algebras. The classical
analogue for finite-dimensional vector spaces was noticed by Gabriel.
