  In this work we address the analysis of discrete-time models of structured
metapopulations subject to environmental stochasticity. Previous works on these
models made use of the fact that migrations between the patches can be
considered fast with respect to demography (maturation, survival, reproduction)
in the population. It was assumed that, within each time step of the model,
there are many fast migration steps followed by one slow demographic event.
This assumption allowed one to apply approximate reduction techniques that
eased the model analysis. It is however a questionable issue in some cases
since, in particular, individuals can die at any moment of the time step. We
propose new non-equivalent models in which we re-scale survival to consider its
effect on the fast scale. We propose a more general formulation of the
approximate reduction techniques so that they also apply to the proposed new
models. We prove that the main asymptotic elements in this kind of stochastic
models, the Stochastic Growth Rate (SGR) and the Scaled Logarithmic Variance
(SLV), can be related between the original and the reduced systems, so that the
analysis of the latter allows us to ascertain the population fate in the first.
Then we go on to considering some cases where we illustrate the reduction
technique and show the differences between both modelling options. In some
cases using one option represents exponential growth, whereas the other yields
extinction.
