  We describe a reproduction procedure which, given a solution of the
$\mathfrak{gl}_{M|N}$ Gaudin Bethe ansatz equation associated to a tensor
product of polynomial modules, produces a family $P$ of other solutions called
the population. To a population we associate a rational pseudodifferential
operator $R$ and a superspace $W$ of rational functions.
  We show that if at least one module is typical then the population $P$ is
canonically identified with the set of minimal factorizations of $R$ and with
the space of full superflags in $W$.
  We conjecture that the singular eigenvectors (up to rescaling) of all
$\mathfrak{gl}_{M|N}$ Gaudin Hamiltonians are in a bijective correspondence
with certain superspaces of rational functions.
