1. Estimating the contribution of demographic parameters to changes in population growth is essential for understanding why populations fluctuate. Integrated population models (IPMs) offer a possibility to estimate the contributions of additional demographic parameters, for which no data have been explicitly collected—typically immigration. Such parameters are often subsequently highlighted as important drivers of population growth. Yet, accuracy in estimating their temporal variation, and consequently their contribution to changes in population growth rate, has not been investigated.
2. To quantify the magnitude and cause of potential biases when estimating the contribution of immigration using IPMs, we simulated data (using northern wheatear Oenanthe oenanthe population estimates) from controlled scenarios to examine potential biases and how they depend on IPM parameterization, formulation of priors, the level of temporal variation in immigration and sample size. We also used empirical data on populations with known rates of immigration: Soay sheep Ovis aries and Mauritius kestrel Falco punctatus with zero immigration and grey wolf Canis lupus in Scandinavia with near-zero immigration.
3. IPMs strongly overestimated the contribution of immigration to changes in population growth in scenarios when immigration was simulated with zero temporal variation (proportion of variance attributed to immigration = 63% for the more constrained formulation and real sample size) and in the wild populations, where the true number of immigrants was zero or near-zero (kestrel 19.1%–98.2%, sheep 4.2%–36.1% and wolf 84.0%–99.2%). Although the estimation of the contribution of immigration in the simulation study became more accurate with increasing temporal variation and sample size, it was often not possible to distinguish between an accurate estimation from data with high temporal variation versus an overestimation from data with low temporal variation. Unrealistically, large sample sizes may be required to estimate the contribution of immigration well.
4. To minimize the risk of overestimating the contribution of immigration (or any additional parameter) in IPMs, we recommend to: (a) look for evidence of variation in immigration before investigating its contribution to population growth, (b) simulate and model data for comparison to the real data and (c) use explicit data on immigration when possible.

中文翻译：

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综合人口模型未能准确估计移民对人口的贡献

1. 估计人口参数对人口增长变化的贡献对于理解人口波动的原因至关重要。综合人口模型 (IPM) 提供了一种可能性，可以估计其他人口统计参数的贡献，但尚未明确收集这些数据——通常是移民。这些参数随后经常被强调为人口增长的重要驱动因素。然而，尚未研究估计它们的时间变化的准确性，以及它们对人口增长率变化的贡献。
2. 为了在使用 IPM 估计移民的贡献时量化潜在偏差的大小和原因，我们模拟了来自受控场景的数据（使用北麦穗 Oenanthe oenanthe人口估计）来检查潜在偏差以及它们如何依赖 IPM 参数化、先验公式、移民和样本量的时间变化水平。我们还使用了具有已知移民率的种群的经验数据：Soay 绵羊Ovis aries和 Mauritius Kestrel Falco punctatus 的移民为零，而斯堪的纳维亚的灰狼Canis lupus 的移民几乎为零。
3. IPM 强烈高估了移民对人口增长变化的贡献，当移民是用零时间变化模拟的情况下（归因于移民的方差比例 = 63%，对于更受约束的公式和实际样本量）和野生种群，其中真实的移民数量为零或接近零（红隼 19.1%–98.2%，绵羊 4.2%–36.1% 和狼 84.0%–99.2%）。尽管随着时间变化和样本量的增加，对模拟研究中移民贡献的估计变得更加准确，但通常无法区分来自高时间变化数据的准确估计与来自低时间变化数据的高估。不切实际，
4. 为了尽量减少高估移民（或任何其他参数）在 IPM 中的贡献的风险，我们建议：(a) 在调查移民对人口增长的贡献之前寻找移民变化的证据，(b) 模拟和建模数据以进行比较真实数据，(c) 尽可能使用明确的移民数据。