Hi, there are two many issues about stream functioning (i.e. primary or secondary productivity; animal communities, etc), and therefore it's a broad subject. Maybe the work of Belinda Gallardo can be helpful:
There are many aspects of stream functioning that may be explained through a mathematical model.
Of course if you want to understand the River continuum concept efectively you may look in the original Vannote's paper. If you want to get a broader idea of stream processess you may also start with a more general reference.
There is a lot of bibliography but in my opinion "Stream Ecology: Structure and function of running waters" from Prof. J.D. Allan would be a nice starting point. There you may also find an updated explanation of the RCC.
For the time beeing, it look like that stream functioning modeling have to be considered partially - process by process. Even the direct link between water and sediment chemistry and communities present within some stretch is still open question. A lot of literature is available, but I would say that there are still to many oposite explanations/discussions on the same issue.
For the beggining, the community patterns such as feeding types (FFG) distribution within the stretch could be used to see the differenceas along the watercourse. Further, you can analyse current and bottom type preference. The major problem is that for considerable number of taxa (e.g. macrozoobenthos) we do not have confident data about some biological characteristics. It is enough to analyse your dataset by using ASTERICS (AQEM) software. Although the dataset which is behind this softtware cover a lot of authecological characteristics for considerable number of taxa, still for a large percentage of the total community, there is no confident data about e.g. current preference, characteristic bottom type(s) for the species, the relation with saprobic conditions....
The Riverstrahler model describes the biogeochemical functioning of an entire river system, from 100 to 100,000 km2 or more, taking into account the constraints set by the morphology of the drainage network, the meteorological/hydrological conditions, and the inputs of material from point and non-point sources in the watershed.
This tool has been applied for research purpose to several river and stream systems which differ in hydrological regime and anthropogenic influences.