  We prove that the generic maximal independent family obtained by iteratively
forcing with the Mathias forcing relative to diagonalization filters is densely
maximal. Moreover, by choosing the filters with some care one can ensure the
family is selective and hence forcing indestructible in a strong sense. Using
this we prove that under $\mathfrak{p} = 2^{\aleph_0}$ there are selective
independent families and also we show how to add selective independent families
of any desired size.
