  We consider a generalization of spatial branching coalescing processes in
which the behaviour of individuals is not (necessarily) independent, on the
contrary, individuals tend to take simultaneous actions. We show that these
processes have moment duals, which happen to be multidimensional diffusions
with jumps. Moment duality provides a general framework to study structural
properties of the processes in this class. We present some conditions under
which the expectation of the process is not affected by coordination and
comment on the effect of coordination on the variance. We analyse several
examples in more detail, including the nested coalescent, the peripatric
coalescent with selection and coordinated migration, and the Parabolic Anderson
Model.
