Bayesian Averaging of Generalized Linear Models for Passive Integrated Transponder Tag Recoveries from Salmonids in the Snake River

Abstract

Bayesian methods provide a means of explicitly accounting for uncertainty in the choice of model used to interpret fisheries data. The probability of a given model being the correct model conditional on the data, the posterior probability, is a measure of the degree of belief and strength of evidence for the model. Bayesian model averaging uses these posterior probabilities to make weighted inferences, thus providing a solution to the problem of selecting a single model from a group of models that seem nearly equivalent by conventional statistical criteria. The approach is applied to a generalized linear model analysis of survival for juvenile and mature adult spring chinook salmon Oncorhynchus tshawytscha and steelhead Oncorhynchus mykiss from the Snake River. The fish, tagged as juveniles with passive integrated transponders (PIT), outmigrated from freshwater habitat to the ocean during 1989–1991, and include some of the first PIT tag recoveries of adult fish. Covariates used to model survival were year of outmigration, rearing type (hatchery or wild), and distance upstream at time of release, The Bayesian approach sometimes yielded simpler models than those selected with Akaike's information criterion, and averaging models by their posterior probabilities smoothed out differences between models ón estimated survival rates. All three covariates were important in modeling juvenile survival of spring chinook salmon and steelhead, but not in modeling adult survival (for fish detected as juveniles). For spring chinook salmon, the adult survival rates were a function of rearing type alone, and wild fish had survival rates over seven times higher than hatchery fish. In contrast, juvenile survival rates, as measured from time of tagging to time of detection at a downstream dam, for spring chinook salmon were higher for the hatchery fish than the wild fish, but this is largely because wild fish were tagged in the fall preceeding the spring of emigration and hatchery fish were tagged during that spring. For steelhead, none of the factors had a significant effect on adult survival rates. The failure to identify factors affecting adult survival rates may be because too few fish were tagged and adult recovery rates were low. It will be necessary to increase the number of fish tagged and released if managers want to more precisely measure and compare the relative strengths of effects of such factors on survival to the adult stage. Many outmigrating juvenile salmonids are captured at upstream dams and barged beyond downstream dams. Assuming that most of the juvenile salmonids detected at upstream dams were barged and that those undetected were not barged, the effect of barging on adult survival rates was estimated as a function of juvenile detection rates. For example, if the juvenile detection rate is 60%, spring chinook salmon adult survival is estimated to be 2.7 times greater for barged fish and 22.1 times greater for steelhead.