Low-dimensional compartment models for biological systems can be fitted to time series data using Monte Carlo particle filter methods. As dimension increases, for example when analyzing a collection of spatially coupled populations, particle filter methods rapidly degenerate. We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution with favorable theoretical scaling properties under a weak coupling condition. The independent Monte Carlo calculations are called islands, and the operation carried out on each island is called adapted simulation, so the complete algorithm is called an adapted simulation island filter. We demonstrate this methodology and some related algorithms on a model for measles transmission within and between cities.[-]