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The authors replied as follows:

When a nonparametric mixture model is adopted to deal with the heterogeneity among individual capture probabilities, the population size is nonidentifiable (Link, 2003, Biometrics 59, 1123–1130). Holzmann, Munk, and Zucchini (2006, Biometrics 62, 934–936) discussed the conditions under which a subfamily of mixing distributions is identifiable. Link (2006, Biometrics 92, 936–939) found that the nonidentifiability occurs across identifiable subfamilies. It is shown that there is a subfamily in which each mixing distribution is determined by its mixture, and the population size admits estimable lower bounds that can be used to construct lower confidence limits.