Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS‐Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS‐Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.

中文翻译：

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在photo-ID研究中估计鲸类动物标记率的建议：对现场采样协议和方差估计的批判

必须确定标记率或具有唯一，可识别标记的人口比例，以便根据照片识别数据估算人口规模。在这项研究中，我们解决了现场采样协议和估计方法，以可靠地估计鲸类种群中的标记率及其不确定性。我们提供了两种替代方法来估计标记率的方差：（1）不等大小簇（SRCS）的方差估计器和（2）分层贝叶斯模型（SRCS-Bayes），并将它们与简单随机抽样（SRS）进行比较）方差估算器。我们使用模拟测试了这些方差估计量，以查看它们在不同的标记率，采样的组数，每组的照片以及平均组大小下的表现。分层贝叶斯模型的表现优于常方差估计器，在91.9％的时间中，其95％HDI中拥有人口的真实标记率（相比之下，SRS方法的覆盖率为79％，SRCS-Cochran方法的覆盖率为76.3％）。仿真结果表明，理想情况下，应使用分层贝叶斯建模对标记率及其精度进行量化，研究人员应尝试对尽可能多的唯一组进行采样，以提高准确性和精度。