Bias and Loss of Precision Due to Tag Loss in Jolly–Seber Estimates for Mark–Recapture Experiments

Abstract

A crucial, though often ignored, assumption of mark-recapture experiments is that animals do not lose their marks (tags). Results of theoretical analyses of the effects of tag loss on estimates of population size (.cxa.N), survival .cxa..vphi., births or new entries (.cxa.B), and on their standard errors (SE( )), for the Jolly-Seber (full) model allowing birth and death are presented. .cxa.N, SE(.cxa.N) and SE(.cxa..vphi.) are not biased by tag loss; .cxa..vphi. .cxa.B and SE(.cxa.B) are biased. A similar analysis for the Jolly-Seber (death-only) model where births are known not to occur shows that .cxa.N, .cxa..vphi. and SE(.cxa..vphi.) are strongly biased by tag loss; only SE(.cxa.N) is unbiased. For both models, tag loss causes a loss in precision in all estimates (i.e., an increase in the standard error of the estimate, leading to wider confidence intervals). Tag loss is assumed to be homogeneous among animals; that is, it is the same for all marked animals regardless of age, sex or tag-retention time, although the rate per unit time may change over time (e.g., over years or seasons within years). Analytic formulae are developed for both models, allowing calculation of the expected bias and SE in an estimate at given tag loss rates in a population of given size, subject to specified sampling, survival and birth rates. The analytic formulae are large sample approximations but are shown, by simulations, to be adequate provided marked captures (mi) and subsequent recoveries (ri) are no lower than around 5. How these calculations can be used in practical situations to plan experiments yielding adequately precise estimates is discussed. Whether corrections to compensate for tag loss are necessary is determined. Corrections are unnecessary if bias is slight or precision is poor. Otherwise, they should be corrected. The biased estimates from the full model (.cxa..vphi., SE(.cxa..vphi.) and .cxa.B) are correctable only if an estimate of tag-loss rate is available. The death-only model estimates can all be corrected to eliminate bias due to tag loss both with and without knowledge of the tag-loss rate. Knowledge of the tag-loss rate usually will give higher precision of the corrected estimates over those corrected without knowing the tag-loss rate. The Robson-Regier method of estimating tag loss can be used in experiments with double tagging where 1 tag is a permanent batch mark and where all recaptured animals are removed. This method is extended to allow for the multiple mark-recapture case where recaptures may be returned to the population. An example of the methods of estimating tag loss and then correcting the death-only model estimates is presented for some lake whitefish (Coregonus clupeaformis) data. Without the corrections, the estimates for these data would have been in serious error. The example provides some evidence that the correction may work even when the tag loss is not homogeneous across all animals. Recommendations are presented for planning mark-recapture experiments to minimize the problems created by tag loss.