We describe a class of one-dimensional chain binomial models of use in studying metapopulations (population networks). Limit theorems are established for time-inhomogeneous Markov chains that share the salient features of these models. We prove a law of large numbers, which can be used to identify an approximating deterministic trajectory, and a central limit theorem, which establishes that the scaled fluctuations about this trajectory have an approximating autoregressive structure.
"Limit theorems for discrete-time metapopulation models." Probab. Surveys 7 53 - 83, 2010. https://doi.org/10.1214/10-PS158