  We study a spatial birth-and-death process on the phase space of locally
finite configurations $\Gamma^+ \times \Gamma^-$ over $\mathbb{R}^d$. Dynamics
is described by an non-equilibrium evolution of states obtained from the
Fokker-Planck equation and associated with the Markov operator $L^+(\gamma^-) +
\frac{1}{\varepsilon}L^-$, $\varepsilon > 0$. Here $L^-$ describes the
environment process on $\Gamma^-$ and $L^+(\gamma^-)$ describes the system
process on $\Gamma^+$, where $\gamma^-$ indicates that the corresponding
birth-and-death rates depend on another locally finite configuration $\gamma^-
\in \Gamma^-$. We prove that, for a certain class of birth-and-death rates, the
corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique
evolution of states $\mu_t^{\varepsilon}$ on $\Gamma^+ \times \Gamma^-$.
Moreover, we give a sufficient condition such that the environment is ergodic
with exponential rate. Let $\mu_{\mathrm{inv}}$ be the invariant measure for
the environment process on $\Gamma^-$. In the main part of this work we
establish the stochastic averaging principle, i.e. we prove that the marginal
of $\mu_t^{\varepsilon}$ onto $\Gamma^+$ converges weakly to an evolution of
states on $\Gamma^+$ associated with the averaged Markov birth-and-death
operator $\overline{L} = \int_{\Gamma^-}L^+(\gamma^-)d
\mu_{\mathrm{inv}}(\gamma^-)$.
