Eliminating Bias in Survival Estimates Due to the Effect of Tag Failure on Right-Skewed Travel Time Distributions: A Bayesian Approach

Tag loss or failure is a primary consideration when estimating survival from marked or telemetered animals.  Traditional mark-recapture methods used to estimate animal survival cannot distinguish between tag loss and mortality, and so tag loss may lead to negatively biased survival estimates.  In particular, fish telemetry studies inherently involve limitations due to battery power such that tags will fail at some point.  When tags fail, estimating survival requires accounting for the probability of tag failure in the model.  

Current methods try to account for tag failure by modeling tag failure as a function of observed travel times through the study area.  However, travel times are only observed for fish whose tags do not fail.  Consequently, missing information from fish with longer travel times may still lead to negatively biased estimates of survival.  We used Bayesian methods within a complete data likelihood structure to simulate missing values from a travel time distribution.  This approach allowed us to recover the shape of a complete travel time distribution, given observed travel time data and observed tag failure times from an auxiliary tag life study, and thus the method may be used to obtain unbiased estimates of tag failure and survival.