使用RTMB对生态和进化模型中的离散潜变量进行序贯约简
Sequential reduction for discrete latent variables in ecological and evolutionary models using RTMB
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中文总结 AI 辅助
本文提出RTMB包中的序贯约简方法，结合自动微分和拉普拉斯近似高效拟合含离散和连续潜变量的混合模型，并展示其在生态和系统发育应用中的速度与灵活性。
中文摘要 AI 辅助
生态和进化动态的统计模型通常包含连续型（如平均体型）或离散型（如数值丰度）的潜变量。包含两者的混合类型层次模型通常使用马尔可夫链蒙特卡洛（MCMC）方法拟合，但对于大型模型而言，这种方法可能极其缓慢。在此，我们介绍R包RTMB中的一种替代方案，该方案自动对相关离散变量的小组进行序贯约简，使其能够被高效地边缘化。序贯约简与自动微分和拉普拉斯近似相结合，用于估计参数并预测连续和离散变量。我们使用人口统计学示例（占用、动态占用、N-混合和开放动态N-混合模型）展示了速度和灵活性，并将RTMB与JAGS和unmarked进行了基准比较。随后，我们开发了两个新颖的应用。第一个是带有空间潜变量的多点开放N-混合模型，该潜变量控制特定地点的初始丰度和补充量，结果表明连续高斯马尔可夫随机场可以在不到一分钟内与离散丰度动态联合估计。第二个是对已发表的雌性Liolaemus蜥蜴数据集进行系统发育性状插补，我们在祖先状态重建过程中联合插补一个二元性状（胎生），估计其状态转换速率，并估计其对连续性状（体型）的影响。这表明系统发育比较方法可以估计离散和连续性状之间的联系。我们设想，直观且高效的混合类型模型规范将能够更富有表现力地表示生态和进化动态。
英文摘要
Statistical models of ecological and evolutionary dynamics often include latent variables that are either continuous (e.g., average body size) or discrete (e.g., numerical abundance). Mixed-type hierarchical models containing both are typically fitted using Markov chain Monte Carlo (MCMC), which can be prohibitively slow for large models. Here, we introduce an alternative in the R package RTMB that automates the sequential reduction of small groups of related discrete variables, allowing them to be efficiently marginalized. Sequential reduction is combined with automatic differentiation and the Laplace approximation to estimate parameters and predict both continuous and discrete variables. We demonstrate speed and flexibility using demographic examples (occupancy, dynamic occupancy, N-mixture, and open dynamic N-mixture models), benchmarking RTMB against JAGS and unmarked. We then develop two novel applications. The first is a multi-site open N-mixture model with a spatial latent variable governing site-specific initial abundance and recruitment, which shows that continuous Gaussian Markov random fields can be estimated jointly with discrete abundance dynamics in under a minute. The second is phylogenetic trait imputation for a published data set of female Liolaemus lizards, where we jointly impute a binary trait (viviparity), estimate its state-switching rates, and estimate its effect on a continuous trait (body size) during ancestral state reconstruction. This indicates that phylogenetic comparative methods can estimate linkages among discrete and continuous traits. We envision that intuitive and efficient specification of mixed-type models will allow more expressive representation of ecological and evolutionary dynamics.
发表机构
- Cahill Analytics
- Technical University of Denmark（丹麦技术大学）
- Alaska Fisheries Science Center, National Marine Fisheries Service（阿拉斯加渔业科学中心，国家海洋渔业服务局）
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