Frailty models for the estimation of tag shedding rates with tagger effects

Double tagging studies are used to estimate the proportion of originally tagged fish that shed their tags prior to recapture, but models typically fitted to double tag recoveries have been subject to restrictive assumptions. For example, a common assumption is that the shedding rates of all tags are identical. Hearn et al. (Hearn, W.S., Leigh, G.M., Beverton, R.J.H., 1991. ICES J. Mar. Sci. 48, 41-51) found differences in shedding rates between taggers, and demonstrated algebraically that such differences lead to biases in estimators of shedding rates. However, widely applicable models that account for differences in shedding rates between taggers have not been developed. We adapt the proportional hazards model to the problem of estimating tag shedding rates from double-tag recovery data. Differences in shedding rates between taggers are modelled using multiplicative random effects or frailties. The frailty models are fitted to recoveries from a 1990s tagging study of southern bluefin tuna (Thunnus maccoyii) at exact times-at-liberty and the results compared with models previously applied for this species.