The set of active rivers of the Ganges-Brahmaputra-Meghna (GBM) Delta in Bangladesh overlies an active plate boundary that continually modifies the landscape of the delta by deformation. The response of rivers to spatially variable subsidence, from tectonic tilting or other causes, has been thought to include preferred occupation of regions of higher subsidence. In this paper, we develop further the theoretical framework for analysis of the interplay of tectonics and river dynamics, and apply this model to conditions in the GBM Delta. First, we examine the overall competition between variable subsidence and channel dynamics, and find that tilting in Bangladesh should be strong enough to influence river path selection. We then present new theory for the effect of subsidence that is spatially (not temporally) variable. We find a constant residence timescale on different parts of the delta, and differing frequencies of avulsion to these locations, and describe the effects of incision or floodplain deposition on these quantities. We present estimates of the channel residence timescale of the Jamuna (Brahmaputra) River reconstructed from the lithology, provenance, and dating of sediment cores. We apply our framework to a map of regional subsidence to predict the effects on avulsion for the Jamuna River. Comparison between our predicted (2150 years) and our stratigraphically based estimates of avulsion timescale (1800 years) shows encouraging consistency.