Effects of environmental covariates on growth sensitivity

Equation 4: We examined the effects of species, mean climatologies and elevation at each site, and tree ontogeny, on tFFD, tSMD(T-1), tVPD(T-1), tSMD(T), and tVPD(T), using a Generalized Additive Model (GAM). Variables characterizing tree ontogeny included tree age (years) and size (logBA) at time of sampling. To determine whether the splines vary with species, we run an interaction model of covariates. In this interaction model, the fitting process optimizes the performance where some species may behave differently from others, in interactions with environmental covariates.Equation 5: We were interested in knowing how climate sensitivity t depends smoothly on covariates, the hypothesis being that the effects of MAT and MAP are felt toward the cold and warm edges (or wet and dry edges) of the tree species' sample distributions. This hypothesis is tested by examining the confidence intervals (CIs) of the covariate’s predicted fits, which here are zero-centered. The null hypothesis ‘no edge effect’ is rejected whenever the CIs at the extremes or limits of the range of the species’ data exclude zero (see Figure S2; Simpson, 2018). All tests were two-sided, i.e., we made no hypothesis about the directionality of responses.The strength and significance of covariates was determined using the associated F-ratio and P-value. We used the ‘bam’ function, k =5, and the fREML method to fit these species’ models. The data contained in this folder are raw outputs from these models.A subset of the tree-ring data extracted from the CFS-TRenD repository is also included.方程4：我们采用广义加性模型（Generalized Additive Model, GAM），分析了各采样点的物种、平均气候条件、海拔，以及树木个体发育阶段对tFFD、tSMD(T-1)、tVPD(T-1)、tSMD(T)和tVPD(T)的影响。表征树木个体发育的变量包括采样时的树龄（年）与体型指标（logBA）。为探究样条函数是否随物种而异，我们构建了协变量交互模型。该模型的拟合过程会优化模型性能，以适配与环境协变量交互时表现存在差异的不同物种。 方程5：我们旨在探究气候敏感性t如何随协变量平滑变化，其核心假设为：年平均气温（Mean Annual Temperature, MAT）与年平均降水量（Mean Annual Precipitation, MAP）的效应会体现在树种样本分布的冷、热（或湿、干）边界处。我们通过检验协变量预测拟合值的置信区间（confidence intervals, CIs，此处以0为中心）来验证该假设。当物种数据范围极值处的置信区间不包含0时，则拒绝“无边界效应”的原假设（详见补充图S2；Simpson, 2018）。所有检验均为双侧检验，即不对响应的方向性作出假设。 协变量的效应强度与显著性通过对应的F比值与P值确定。我们采用“bam”函数、k=5以及fREML方法拟合上述物种模型。本文件夹内的数据为这些模型的原始输出结果。此外，本数据集还包含从CFS-TRenD数据库中提取的部分树轮数据。