  The aim of the paper is to investigate the rigidity and the deformability of
pseudoholomorphic curves in the nearly K{\"a}hler sphere $\mathbb{S}^6,$ among
minimal surfaces in spheres. Under various assumptions we describe the moduli
space of all noncongruent minimal surfaces $f\colon M\to\mathbb{S}^n$ that are
isometric to a pseudoholomorphic curve in $\mathbb{S}^6.$ Moreover, we prove a
Schur type theorem (see \cite[p. 36]{Chnew}) for minimal surfaces in spheres.
