Nicolau Pedro G, Sørbye Sigrunn H, Yoccoz Nigel G
Department of Mathematics and Statistics Faculty of Science and Technology UiT The Arctic University of Norway Tromso Norway.
Department of Arctic and Marine Biology Faculty of Biosciences, Fisheries and Economics UiT The Arctic University of Norway Tromso Norway.
Ecol Evol. 2020 Aug 31;10(23):12710-12726. doi: 10.1002/ece3.6642. eCollection 2020 Dec.
Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state-space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture-recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state-space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state-space models for density-dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz-Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R-package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray-sided voles from Northern Norway. We found that density-dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.
种群动态模型结合了密度依赖性和环境效应。忽略抽样不确定性可能会导致对密度依赖性强度的估计产生偏差。这通常使用状态空间模型方法来解决，该方法整合了抽样误差和种群过程估计。此类模型很少包括抽样程序与真实丰度之间的明确联系，而这在捕获再捕获设置中很常见。然而，许多为在存在捕获异质性的情况下估计丰度而提出的模型会导致似然函数不完整，并且不能直接纳入状态空间模型。我们通过在忽略丰度估计中的不确定性和基于自回归过程进行密度依赖性估计的完全指定状态空间模型之间采取中间方法，评估了明确估计抽样误差的重要性。首先，我们基于封闭种群的异质性模型，使用条件多项似然估计个体捕获概率，然后使用霍维茨 - 汤普森估计法估计丰度。其次，我们估计对数丰度的自回归模型系数。使用集成嵌套拉普拉斯近似（INLA）方法进行推断。我们进行了广泛的模拟研究，将我们的方法与忽略捕获历史信息的估计方法以及使用R包VGAM针对不同参数规格的方法进行比较。然后将这些方法应用于来自挪威北部的灰侧田鼠真实数据集。我们发现，在过程方差较低的情况下，明确对抽样误差进行建模时，密度依赖性估计得到了改善，在这种情况下，估计自回归过程系数时覆盖范围的差异高达8%。在这种情况下，假设观测模型为泊松分布，偏差也会增加。对于高过程方差，方法之间的差异很小，对异质性进行建模似乎不那么重要。
