Excess dimensions of Brill--Noether schemes of rank two stable bundles

We use results of M. Aprodu and E. Sernesi to extend a result by Fulton–Harris–Lazarsfeld in Brill–Noether theory of line bundles %and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to Brill–Noether loci of stable bundles inside the moduli space of rank two stable vector bundles on a smooth projective algebraic curve. As a consequence; if $B_{2,d}^k$ is of expected dimension, then we prove that its smoothness is equivalent with the smoothness of $B_{2,d+1}^k$.