  In this work we study the non-equilibrium Markov state evolution for a
spatial population model on the space of locally finite configurations
$\Gamma^2 = \Gamma^+ \times \Gamma^-$ over $\mathbb{R}^d$ where particles are
marked by spins $\pm$. Particles of type '+' reproduce themselves independently
of each other and, moreover, die due to competition either among particles of
the same type or particles of different type. Particles of type '-' evolve
according to a non-equilibrium Glauber-type dynamics with activity $z$ and
potential $\psi$. Let $L^S$ be the Markov operator for '+' -particles and $L^E$
the Markov operator for '-' -particles. The non-equilibrium state evolution
$(\mu_t^{\varepsilon})_{t \geq 0}$ is obtained from the Fokker-Planck equation
with Markov operator $L^S + \frac{1}{\varepsilon}L^E$, $\varepsilon > 0$, which
itself is studied in terms of correlation function evolution on a suitable
chosen scale of Banach spaces. We prove that in the limiting regime
$\varepsilon \to 0$ the state evolution $\mu_t^{\varepsilon}$ converges weakly
to some state evolution $\overline{\mu}_t$ associated to the Fokker-Planck
equation with (heuristic) Markov operator obtained from $L^S$ by averaging the
interactions of the system with the environment with respect to the unique
invariant Gibbs measure of the environment.
