Methods of Estimating Mortality and Movement Rates from Single-Tag Recovery Data that are Unbiased by Tag Non-Reporting

Abstract

Single-tag recovery data are widely available for stocks of exploited fish and invertebrates. However, tag non-reporting, short-term tag shedding, and short-term tag-induced mortality cause potentially large bias in population parameter estimates using standard models of exploitation rate (Petersen) and movement (Hilborn). Here, I review estimators of mortality and movement rates that are not biased by these tag loss effects. Mortality can be estimated using the times-at-large of recaptures. The reciprocal of the mean time-at-large of recaptured fish is the maximum likelihood estimate of instantaneous total mortality rate. Chapman refined this to derive a time-at-large mortality rate estimate that is both finite-sample unbiased and minimum variance, thus statistically optimal. With movement estimation, a constant non-reporting rate, by appearing top and bottom in a “recapture-conditioned” model, cancels from the likelihood. Non-reporting rate thereby disappears from the estimator and so is not required to estimate fish movement rates. Tag shedding and tag-induced mortality rates also cancel. These mortality and movement estimators do not use the number of animals tagged and released; using only information from recaptured animals, they are denoted “recapture-conditioned.” Recapture-conditioned estimators offer relatively unbiased single-tag recovery data analysis tools that, to date, have gone largely unnoticed.

Keywords:

• time-at-large
• instantaneous mortality rate
• movement rates
• tag non-reporting
• recapture-conditioned estimators
• tag shedding
• tag-induced mortality

ACKNOWLEDGMENTS

Ken Pollock, Terry Quinn, and John Feenstra contributed valuable comments. I thank Suzanne Bennett and Janet Matthews for literature search assistance.