  This paper studies Manin-Radul supersymmetric KP hierarchy (MR-SKP) in three
related aspects: (i) We find an infinite set of additional (``ghost'') symmetry
flows spanning the same (anti-)commutation algebra as the ordinary MR-SKP
flows; (ii) The latter are used to construct consistent reductions of the
initial unconstrained MR-SKP hierarchy which involves a nontrivial modification
for the fermionic flows; (iii) For the simplest constrained MR-SKP hierarchy we
show that the orbit of Darboux-Backlund transformations lies on a
supersymmetric Toda lattice being a square-root of the standard one-dimensional
Toda lattice, and also we find explicit Wronskian-ratio solutions for the
super-tau function.
