1. Many studies in ecology and management aim at quantifying absolute abundance based on counts at a set of surveyed sites. As time for data collection is typically limited, methods for reliable estimation of occupancy or abundance from low‐cost data are desirable. Time‐to‐detection (TTD) models have shown promise for the estimation of occupancy. However, they remain heavily underutilized, and restricted to inference about occupancy, rather than abundance.
2. We developed a binomial N‐mixture model for species‐level TTD protocols that allows estimation of abundance with multiple‐ or single‐visit data. An extension of the multi‐visit version allows estimating availability per visit, given temporary emigration is random. We provide JAGS code and a new function (nmixTTD) in the R package unmarked for fitting a variety of such models.
3. Simulations showed accurate parameter estimation from single‐visit species‐level TTD data if individual detection probability is high (≥~0.7) and the number of visited sites is in the hundreds (≥~300). Additional visits improved the accuracy of estimates considerably. A comparison with the Royle‐Nichols‐ and the classic binomial N‐mixture‐model revealed that the performance of our model is between these two, but requires data that are less expensive and less error‐prone than count data required for binomial N‐mixture‐models. In a case study, we found similar results when analysing data with the Royle‐Nichols‐, the binomial N‐mixture‐model or the multi‐visit version of our TTD model. Analysing single‐visit data with our model yielded lower abundance and higher detectability estimates. Presumably these differences are due to temporary emigration, as the single‐visit method estimates the abundance of individuals available at one sampling occasion, whereas the multi‐visit methods refer to the superpopulation, that is, the number of individuals present over the study period.
4. Our new TTD‐N‐mixture model shows promise because it enables estimation of abundance, corrected for imperfect detection, for single‐ and multiple‐visit data, based on data that are less expensive and that will be available in large quantities in the near future thanks to technical advances like autonomous recording units. The effects of unmodelled heterogeneity in detection rate and imperfect availability require further study.

中文翻译：

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根据检测时间数据估算丰度

1. 生态学和管理学方面的许多研究旨在根据一组调查点的数量来量化绝对丰度。由于数据收集的时间通常很有限，因此需要一种从低成本数据可靠地估计占用率或丰度的方法。检测时间（TTD）模型已显示出估计占用率的希望。但是，它们仍然未被充分利用，并且只能推断出占用率，而不是数量。
2. 我们针对物种水平的TTD协议开发了一个二项式N混合模型，该模型可通过多次或单次访问数据估算丰度。考虑到临时移民是随机的，多次访问版本的扩展允许估计每次访问的可用性。我们在R软件包中提供了JAGS代码和一个新功能（nmixTTD），这些标记未标记为适合各种此类模型。
3. 仿真表明，如果单个检测的可能性高（≥〜0.7）并且访问站点的数量在数百个（≥〜300），则从单次访问物种级别的TTD数据进行准确的参数估计。额外的访问大大提高了估计的准确性。与Royle-Nichols模型和经典的二项式N混合模型进行比较后，我们的模型的性能介于两者之间，但所需的数据比二项式N混合所需的计数数据便宜，并且不易出错-楷模。在一个案例研究中，当使用Royle-Nichols，二项式N混合模型或TTD模型的多次访问版本分析数据时，我们发现了相似的结果。使用我们的模型分析单次访问数据可得出较低的丰度和较高的可检测性估计值。这些差异大概是由于临时移民造成的，
4. 我们新的TTD-N混合物模型显示出了希望，因为它可以基于便宜的数据在不久的将来提供大量数据，并针对不完整的检测，单次和多次访问数据进行校正。得益于自主录音装置等技术进步。未建模的异质性对检测率和不完善可用性的影响需要进一步研究。