  We consider a system of interacting Moran models with seed-banks. Individuals
live in colonies and are subject to resampling and migration as long as they
are $active$. Each colony has a seed-bank into which individuals can retreat to
become $dormant$, suspending their resampling and migration until they become
active again. The colonies are labelled by $\mathbb{Z}^d$, $d \geq 1$, playing
the role of a $geographic\, space$. The sizes of the active and the dormant
population are $finite$ and depend on the $location$ of the colony. Migration
is driven by a random walk transition kernel. Our goal is to study the
equilibrium behaviour of the system as a function of the underlying model
parameters.
  In the present paper we show that, under mild condition on the sizes of the
active population, the system is well-defined and has a dual. The dual consists
of a system of $interacting$ coalescing random walks in an $inhomogeneous$
environment that switch between active and dormant. We analyse the dichotomy of
$coexistence$ (= multi-type equilibria) versus $clustering$ (= mono-type
equilibria), and show that clustering occurs if and only if two random walks in
the dual starting from arbitrary states eventually coalesce with probability
one. The presence of the seed-bank $enhances\, genetic\, diversity$. In the
dual this is reflected by the presence of time lapses during which the random
walks are dormant and do not move.
