Supplemental Material for "Estimating abundance based on time-to-detection data"

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 require 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, i.e. 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 is 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.1. 生态学与管理学领域的诸多研究旨在基于一系列调查样地的计数结果量化物种绝对多度。由于数据采集时间通常有限，因此亟需能够依托低成本数据实现占有率（occupancy）或多度可靠估计的方法。检测耗时（Time-to-detection, TTD）模型在占有率估计方面已展现出应用潜力，但目前该模型仍未得到充分利用，且仅局限于占有率推断，而非多度估计。 2. 本研究针对物种种级的检测耗时（Time-to-detection, TTD）方案开发了一种二项式N混合模型（binomial N-mixture model），该模型可依托单次或多次到访数据实现多度估计。针对多次到访版本的扩展模型，在临时扩散为随机过程的前提下，可估计单次到访的种群可获得性。我们提供了用于拟合各类此类模型的JAGS代码，以及R包unmarked中的全新函数`nmixTTD`。 3. 模拟结果表明，当个体检测概率较高（≥约0.7）且调查样地数量达到数百个（≥约300）时，依托单次到访的物种种级检测耗时数据可实现准确的参数估计。额外的到访次数可显著提升估计精度。将本模型与罗伊尔-尼科尔斯（Royle-Nichols）模型以及经典二项式N混合模型进行对比后发现，本模型的性能介于两者之间，但相较于二项式N混合模型所需的计数数据，本模型所需的数据成本更低、出错概率更小。在一项案例研究中，当分别采用罗伊尔-尼科尔斯模型、二项式N混合模型以及本研究提出的检测耗时模型的多次到访版本分析数据时，得到了相似的结果。而采用本模型分析单次到访数据时，则得到了更低的多度估计值与更高的检测率估计值。此类差异大概率源于临时扩散：单次到访方法估计的是单次采样事件中可被检测到的个体多度，而多次到访方法则对应超种群（superpopulation），即研究周期内出现的所有个体总数。 4. 我们提出的新型检测耗时-N混合模型展现出良好的应用前景：依托自主录音单元（autonomous recording units）等技术进步带来的低成本、大规模易得数据，该模型可基于单次或多次到访数据实现对不完善检测（imperfect detection）校正的多度估计。目前，检测率未建模异质性与不完善可检测性带来的影响仍有待进一步研究。