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现有环境条件塑造，是生态学领域一项重要却极具挑战的任务。基于功能性状（functional trait）的研究方法，可替代潜在具有特异性的物种专属响应模型，以探究环境梯度下的群落动态。传统上，关联环境与性状的模型仅考虑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，类群内性状变异不仅幅度可观，而且在植物群落构建与生态系统功能评估中至关重要。 本研究提出了适配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）的联合性状分布模型，可处理混合类型的性状变量，包括连续型、二分类与有序型，并纳入性状间的相关性，从而实现未调查样地的联合性状预测与条件性状预测。该模型可用于解析广为人知的第四角问题（fourth-corner problem）——该问题旨在解读性状-环境矩阵。 本研究通过针对单个物种的联合预测性状分布，以及对应环境的群落加权性状联合分布（同时纳入类群内性状变异），验证了所提方法的实用性。此外，本文还针对模型下生成的随机性状-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，我们将联合性状分布模型应用于模拟数据，以及从南非大卡普植物区系区（Greater Cape Floristic Region）采集的真实植被数据。 所提方法为"基于环境解释类群内性状变异"提供了完全基于模型的理论基础。它拓展了当前常用于研究群落加权性状的方法的实用性与可解释性，同时阐明了第四角问题中的随机性。