Modeling Systematic Change in Stopover Duration Does Not Improve Bias in Trends Estimated from Migration Counts

The use of counts of unmarked migrating animals to monitor long term population trends assumes independence of daily counts and a constant rate of detection. However, migratory stopovers often last days or weeks, violating the assumption of count independence. Further, a systematic change in stopover duration will result in a change in the probability of detecting individuals once, but also in the probability of detecting individuals on more than one sampling occasion. We tested how variation in stopover duration influenced accuracy and precision of population trends by simulating migration count data with known constant rate of population change and by allowing daily probability of survival (an index of stopover duration) to remain constant, or to vary randomly, cyclically, or increase linearly over time by various levels. Using simulated datasets with a systematic increase in stopover duration, we also tested whether any resulting bias in population trend could be reduced by modeling the underlying source of variation in detection, or by subsampling data to every three or five days to reduce the incidence of recounting. Mean bias in population trend did not differ significantly from zero when stopover duration remained constant or varied randomly over time, but bias and the detection of false trends increased significantly with a systematic increase in stopover duration. Importantly, an increase in stopover duration over time resulted in a compounding effect on counts due to the increased probability of detection and of recounting on subsequent sampling occasions. Under this scenario, bias in population trend could not be modeled using a covariate for stopover duration alone. Rather, to improve inference drawn about long term population change using counts of unmarked migrants, analyses must include a covariate for stopover duration, as well as incorporate sampling modifications (e.g., subsampling) to reduce the probability that individuals will be detected on more than one occasion.

利用未标记迁徙动物（unmarked migrating animals）的计数开展长期种群趋势监测，其核心前提假设为每日计数相互独立且检测率恒定。然而，迁徙动物的停留期（migratory stopovers）通常持续数日乃至数周，这直接违背了计数独立性的假设。进一步而言，停留时长的系统性变化不仅会改变个体单次被检测到的概率，还会改变个体在多个采样时段（sampling occasion）被检测到的概率。我们通过两类实验探究停留时长的变异对种群趋势准确性与精确性的影响：其一，生成已知种群变化恒定速率的迁徙计数模拟数据，并令每日存活概率（作为停留时长的量化指标）保持恒定，或随时间以不同幅度随机波动、周期性变化或线性递增；其二，针对停留时长系统性递增的模拟数据集，测试两种缓解种群趋势偏差的方案——一是对检测变异的潜在来源进行建模，二是将数据每3日或5日进行一次子采样（subsampling）以降低重复计数的发生率。分析结果显示，当停留时长保持恒定或随时间随机波动时，种群趋势的平均偏差与0无显著差异；但随着停留时长系统性递增，偏差幅度以及虚假趋势的检出率均显著升高。值得注意的是，由于后续采样时段中个体被检测到以及被重复计数的概率上升，停留时长随时间增加会对计数产生复合效应。在此场景下，仅通过停留时长的协变量（covariate）无法有效校正种群趋势偏差。换言之，若要利用未标记迁徙动物的计数准确推断长期种群变化，分析过程中必须纳入停留时长的协变量，并结合采样优化措施（如子采样）以降低个体在多个时段被重复检测的概率。