Data from: Assessing the joint behavior of species traits as filtered by environment

Understanding and predicting how species traits are shaped by prevailing environmental conditions is an important yet challenging task in ecology. Functional trait based approaches can replace potentially idiosyncratic species-specific response models in learning about community behavior across environmental gradients. Customarily, models for traits given environment consider only trait means to predict species and functional diversity, as intra-taxon variability in traits is often thought to be negligible. A growing body of literature indicates that intra-taxon trait variability is substantial and critical in structuring plant communities and assessing ecosystem function.
We propose flexible joint trait distribution models given environment and across species that incorporate intra-taxon variability as well as inter-site/plot variability. Using a Bayesian framework, our joint trait distribution models allow for mixed continuous, binary, and ordinal trait variables and incorporate dependence among traits enabling both joint and conditional trait prediction at unobserved sites. The models can be used to inform about the well-known fourth-corner problem, which attempts to interpret trait-by-environment matrices.
We demonstrate the utility of our methodology through joint predictive trait distributions for individual species as well as joint community-weighted trait distributions for environments while incorporating intra-taxon trait variability. Explicit details on the probabilistic interpretations of the random trait-by-environment matrices obtained arising under our model are also provided to address the fourth-corner problem. Finally, our joint trait distribution model is applied to simulated and real vegetation data collected from the Greater Cape Floristic Region of South Africa.
The proposed methodology places a fully model-based foundation on explaining intra-taxon trait variation given environment. It extends the utility and interpretability of commonly applied techniques for investigating community-weighted traits and illuminates randomness in the fourth-corner problem.

理解并预测物种性状如何受当前环境条件塑造，是生态学领域一项重要却极具挑战性的任务。基于功能性状 (functional trait) 的研究方法，可替代传统上针对特定物种的特异响应模型，用于解析环境梯度下的群落动态。传统上，基于环境的性状模型仅以性状均值来预测物种与功能多样性，因为类群内性状变异 (intra-taxon variability) 常被认为可忽略不计。但越来越多的研究表明，类群内性状变异显著且对植物群落构建与生态系统功能评估至关重要。
本研究提出了适用于环境与跨物种的灵活联合性状分布模型，该模型同时纳入类群内变异与样地间变异。基于贝叶斯框架 (Bayesian framework)，所提出的联合性状分布模型可兼容混合类型的性状变量（包括连续型、二分类型与有序分类型），并刻画性状间的相关性，从而实现未观测样地的联合与条件性状预测。该模型可用于解析广为人知的第四角问题 (fourth-corner problem)——该问题旨在阐释性状-环境矩阵的生物学意义。
本研究通过针对单个物种的联合预测性状分布，以及纳入类群内性状变异的环境对应联合群落加权性状分布，验证了所提方法的实用性。此外，本文还针对模型所生成的随机性状-环境矩阵，详细阐释了其概率学意义，以解决第四角问题。最后，我们将所提出的联合性状分布模型应用于南非大开普植物区 (Greater Cape Floristic Region) 收集的模拟植被数据与实测植被数据。
该方法为基于环境解释类群内性状变异提供了完备的模型化基础，拓展了当前用于研究群落加权性状的常用方法的实用性与可解释性，并阐明了第四角问题中的随机性来源。