If a tagged fish is predated by another fish, for how long time is the tag retained in the stomach of the predator? Are there any published studies? Anything on salmon smolts and in-river predation?
Because I cannot answer your question specifically for salmon smolts, I will speak in a general sense with regard to evacuation of prey. Gastric evacuation times in fish are dependent upon several factors such as the metabolic rate of the predator and the chemical composition (e.g. lipids) of the prey. Once the tagged fish is consumed, the tag is essentially treated as another hard part (e.g. an otolith). Hard parts will eventually either be digested or regurgitated, but the time required for each process is dependent upon the physiological make-up of the predator. Regardless, once the prey is digested, the tag will be treated as any other intragastric tag. The use of intragastric tags is not a novel thing of interest in fisheries research. Doing a quick google scholar search, I found that retention times of intragastric times can be greater than 21 days. But, once again, these times are likely dependent upon the predator. I would suggest searching for the keywords "intragastric tags" in similar search engines (e.g. google scholar, scopus, web of science, etc) for further information on the topic. I hope this helps.
I think this article about 'Evacuation Rates of Coded Wire Tags Implanted in Prey of Northern Pike' by Niva & Hyvärinen (2001) would be of interest to you.
Sometimes a difference between intragastric tags and predated tags should be that the former are designed to be retained. For salmon they are (to my understanding) mainly used for adult non actively feeding adults and if lost typically regurgitated. Predated smaller tags pass through the fish more rapidly?
Anyway, it should also depend on predator species and temperature?
I found this on striped bass and salmon smolts: http://link.springer.com/article/10.1186%2Fs40317-015-0034-y
David Aldvén (https://www.researchgate.net/profile/David_Aldven) got some DST tags from sea trout back from the coast outside of Uddevalla. The fish + tags had apparently been eaten by seals, and stayed for a day or so inside the seal, if I remember correctly (indicated by temperature of approx 37 degrees). Then we have had some PIT-tagged brown trout juveniles being eaten by resident brown trout adults, and they seem to stay for quite a while in the predator fish - however, I have no data on how long, just a gut-feeling.
As long as the exterior coating of the tag retains it's structure, I do not see how a predated tag would be treated any different from an intagastric tag. In other words, I fail to see how a fish could distinguish between the two tag types. Asolutely, the predator species and water temps will affect the length of internal tag times. Fish with higher metabolic rates will have faster turnover.
Armstrong et al. 1992 feed acoustic tags to cod and the time for tag excretion varied between individuals 5- >21 days (DOI: 10.1111/j.1095-8649.1992.tb02560.x).
Similar it took 5 days for excretion when a tagged pike was eaten by other tagged pike. Baktoft el at. 2013 (http://onlinelibrary.wiley.com/doi/10.1111/fme.12040/full), which I guess is more what you are looking for as I assume you are talking about Klarälven.
The Danish guys (e.g. Niels Jepsen and Kim Aarestrup) have done a lot of radio tagging on smolts and if you read between the lines it seems the tags pass through pike fairly quick (in par with Baktofts data). However it should be highly correlated with temperature as Christopher wrote.
A way to go around the problem (know if you are tracking a smolt or a predator) in the future is to use a pressure sensor then you see changes in diving behavior, assuming desmoltification is not an issue.
Without having gone through all of the suggested studies above: For some fish species in aquaculture evacuation speed has been examined since it is closely related to appetite. It is though slightly different for fish in culture since their feed is more "efficient" than wild prey. The evacuation rate is dependent on temperature and fish size (and type of fish) and In a report I have the author (Alanärä 2002, pelletologi - läran om fiskens foder) combined data from two earlier studies (Ruhonen 1994 (Gastrointestinal responses of rainbow trout (Oncorhynchus mykiss) to dry pellet and low-fat herring diets: consequences for growth, feed utilisation and nutrient load into the water. PhD-thesis) and Grove et al 1978 (Satiation amount, frequency of feeding and gastric emptying rate in Salmo gairdneri. J. Fish Biol.,5: 507-516.) and constructed an equation to calculate evacuation rate for Rainbow trout that has not been published in any reviewed paper unfortunately. The model is based on rather few data points but might give a hint on what you are after. If you are interested I can send you the report. Good luck!
Hanna is correct that evacuation rates are dependent upon temperature, fish size and the type of fish. One thing to keep in mind when you are reading these papers and posts is that evacuation rate is not synonymous to evacuation time. Evacuation time is the time necessary to completely empty a stomach after a feeding event. My specific research focuses on the feeding ecology of Atlantic bluefin tuna. Bluefin posses a rete mirable system which allows them to maintain internal temperatures greater than their ambient water temperature. This regional endothermy comes at a cost and results in some of the highest metabolic rates observed for any fish species. Both field and aquaculture derived experimentation have determined complete evacuation times of approximately 20 hours for this species. Additionally, Carey et al. (1984; J. Exp. Biol. 109, 1-20) used internal transmitters to record postprandial increases in temperature and stomach contractions. Peak stomach contractions were assumed to be a result of food being forced into the caeca from the stomach. They state, "The strong contractions around the time of the temperature maximum probably represent the emptying of the remaining fluid into the intestine." All transmitters were eventually regurgitated within approximately one day after the initial feeding event. Perhaps intragastric tags would be a valuable addition to your research if funds allow you to do so.
Other than suggesting you look for gastric evacuation rate literature (with the caveat CM Butler noted), I can offer some insight from a field study we did recently. We had many juvenile Chinook salmon about 130 mm fork length swimming within a series of acoustic hydrophones we were using to estimate fish positions in three dimensions plus time for an a evaluation of dam passage. We have tracks of three particular fish that were first traveling separately but ended up traveling identical paths (in x, y, z, and time) for a day or two, then one tag fell to the bottom of the water body. That was pretty neat to see in the tag position data, and I conclude all three fish were eaten by the same predator (likely a Smallmouth Bass Micropterus dolomieu or Bull Trout Salvelinus confluentus) and while in the hydrophone array one tag was defecated. They may have been schooling, but it does not seem likely for that close that long, and we have data from hundreds of fish and this behavior was unusual. As I recall the time from presumptive prey to presumptive defecation was about 30 hours (in freshwater at a temperature of 8-10 C). Fun stuff.
Le Doux-Bloom, C.M. (2012). Distribution, habitat use, and movement patterns of sub-adult striped bass morone saxatilis in the San Francisco Estuary Watershed, California. UNIVERSITY OF CALIFORNIA, DAVIS.