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). We present results of theoretical analyses of the effects of tag loss on estimates of population size ([Formula: see text]), survival ([Formula: see text]), births or new entries ([Formula: see text]), and on their standard errors (SE()), for the Jolly–Seber (full) model allowing birth and death. We show that[Formula: see text], SE([Formula: see text]) and SE([Formula: see text]) are not biased by tag loss, while [Formula: see text], [Formula: see text], and SE([Formula: see text]) are biased. A similar analysis for the Jolly–Seber (death-only) model where births are known not to occur shows that [Formula: see text], [Formula: see text], and SE([Formula: see text]) are strongly biased by tag loss while only SE([Formula: see text]) is unbiased. Moreover, 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). Throughout the paper, we assume that tag loss is 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).We develop analytic formulae for both models that allow 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.We discuss how these calculations can be used in practical situations to plan experiments that will yield adequately precise estimates and to determine whether corrections to compensate for tag loss are necessary. In general, corrections are unnecessary if bias is slight or precision is poor. Otherwise, they should be corrected. The biased estimates from the full model ([Formula: see text], SE([Formula: see text]), and [Formula: see text]) 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 will usually 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 one tag is a permanent batch mark and where all recaptured animals are removed. We extend this method 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.Key words: marking methods, tag loss, bias of estimates, capture–recapture, Jolly–Seber estimates, population estimates, survival, mortality, lake whitefish