  Density dependent Markov population processes with countably many types can
often be well approximated over finite time intervals by the solution of the
differential equations that describe their average drift, provided that the
total population size is large. They also exhibit diffusive stochastic
fluctuations on a smaller scale about this deterministic path. Here, it is
shown that the individuals in such processes experience an almost deterministic
environment. Small groups of individuals behave almost independently of one
another, evolving as Markov jump processes, whose transition rates are
prescribed functions of time. In the context of metapopulation models, we show
that `individuals' can represent either patches or the individuals that migrate
among the patches; in host--parasite systems, they can represent both hosts and
parasites.
