Response to: a new method for estimating animal abundance with two sources of data in capture-recapture studies

Mark-recapture studies that rely on multiple marks to identify individuals pose modeling challenges if the marks for each individual are not always linked. If an individual with unlinked marks is encountered on two occasions and different marks are observed, then it will appear that two different individuals were captured. Failing to account for these missed matches will produce incorrect inference. Madon etal. (Methods in Ecology and Evolution 2011; 2: 390) proposes a modification of the Jolly-Seber estimator for such data computed by adjusting the observed counts of individuals first captured, recaptured or not captured but known to be alive on each occasion. The adjustment involves multiplying each of these counts by a constant factor, Iid, intended to correct for double counting of individuals and constrained between 0 and 1. Results of a simulation study provided in Madon etal. (Methods in Ecology and Evolution 2011; 2: 390) show that the proposed estimator is almost unbiased, but its uncertainty is underestimated and the true coverage of confidence intervals is consistently below the nominal value. I compute separate adjustment factors for each of the counts and show (i) that a constant adjustment is not appropriate and (ii) that the theoretical adjustment factor is sometimes >1. I believe that the use of a single adjustment factor between 0 and 1 is what causes the uncertainty to be underestimated and that complete models of the observation process are required to obtain valid results.