  Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of
interacting Fleming-Viot diffusions with mutation and selection which is a
strong Markov process with continuous paths and state space
$(\CP(\I))^{\Omega_N}$, where $\I$ is the type space, ${\Omega_N}$ the
geographic space is assumed to be a countable group and $\CP$ denotes the
probability measures.
  We establish various duality relations for this process. These dualities are
function-valued processes which are driven by a coalescing-branching random
walk, that is, an evolving particle system which in addition exhibits certain
changes in the function-valued part at jump times driven by mutation.
  In the case of a finite type space $\I$ we construct a set-valued dual
process, which is a Markov jump process, which is very suitable to prove
ergodic theorems which we do here. The set-valued duality contains as special
case a duality relation for any finite state Markov chain.
  In the finitely many types case there is also a further tableau-valued dual
which can be used to study the invasion of fitter types after rare mutation.
This is carried out in \cite{DGsel} and \cite{DGInvasion}.
