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 <i>t</i>_FFD, <i>t</i>_SMD(_<em>T</em>_-1), <i>t</i>_VPD(_<em>T</em>_-1), <i>t</i>_SMD(_<em>T</em>₎, and <i>t</i>_VPD(_<em>T</em>₎, 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 <i>t</i> 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 <i>P</i>-value. We used the ‘bam’ function, <i>k</i> =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. <br>

公式4：我们采用广义加性模型（Generalized Additive Model, GAM），分析了物种、各站点的平均气候态与海拔，以及树木个体发育状况对*t*_FFD、*t*_SMD(T-1)、*t*_VPD(T-1)、*t*_SMD(T)和*t*_VPD(T)的影响。其中表征树木个体发育的变量包括采样时的树龄（单位：年）与树木大小（logBA）。为探究样条函数是否随物种差异发生变化，我们构建了协变量交互模型。该交互模型的拟合过程会优化模型性能，以适配不同物种与环境协变量交互作用下的差异化响应特征。

公式5：我们旨在探究气候敏感性*t*如何随协变量平滑变化，核心假说为：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、热边界（或干、湿边界）处。我们通过检验协变量预测拟合值的置信区间（Confidence Intervals, CIs，此处区间以零为中心）来验证该假说。当物种数据取值范围极端值处的置信区间不包含零时，即可拒绝“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，即未对响应的方向性作出预设。

协变量的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方法拟合上述物种特异性模型。本文件夹内的数据即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。