Relative tree growth and mortality responses to the 2012 midwestern US drought in the central hardwood ecoregion

This dataset contains relative drought-driven tree growth and mortality responses derived from the USDA FS Forest Inventory and Analysis dataset (Gray et al., 2012) in the North American central hardwood ecoregion (a region representing the four US states of Indiana, Illinois, Kentucky, and Brandt et al., 2014). Data represents a period of 2000 – 2018 and characterizes relative responses to the severe 2012 midwestern drought (Mallya et al., 2013) between co-located trees with a diameter at breast height greater than 12.7 cm. Analyses were limited to regions of the study area that experienced  ‘Severe’ or ‘Extreme’ drought conditions from March to October of 2012, as defined by the US drought monitor program (Svoboda et al., 2002). Co-located trees were defined as those growing within the same discrete 875 km2 hexagonal boundary following a tessellation approach by which Forest Inventory and Analysis plots were aggregated across 560 uniform hexagons imposed over the study area.

Relative drought-driven responses were quantified among the following tree species: Acer rubrum, Acer saccharum, Carya alba, Carya glabra, Carya ovata, Carya texana, Celtis occidentalis, Fagus grandifolia, Juglans nigra, Liriodendron tulipifera, Nyssa sylvatica, Pinus echinata, Prunus serotina, Quercus alba, Quercus coccinea, Quercus rubra, Quercus stellata, Quercus velutina, Sassafras albidum, and Ulmus americana.

Methods
Relative growth and relative growth sensitivity

To calculate relative growth (gr_ij) we first quantified species-specific growth in each hexagon as a relative growth rate across three successive inventories from 2000 – 2018. The relative growth rate equation (RGR_i) was expressed as (Brzostek et al., 2014):

RGR_i  = [(BA_i,1 ‒ BA_i,0)/BA_i,0] × 100          (Equation 1)   

where BA_i,0 is the species-specific tree basal area at the initial inventory and BA_i,1 is the species-specific tree basal area at the next inventory. Next, the impact of drought on RGR_i was characterized as a rate change parameter, ΔRGR_i (% growth/year), whereby RGR_i after 2012 was subtracted by the RGR_i of the conspecific individuals occupying the same hexagon prior to drought disturbance. Specifically, ΔRGR_i was quantified as:

ΔRGR_i =  RGR_i,post_drought  ‒ RGR_i,pre_drought     (Equation 2)

where RGR_i,post_drought is species-specific relative tree growth following drought (when BA_i,1 was sampled during the years 2012−2018; Equation 1) and RGR_i,pre_drought is the relative tree growth of the same species and locations from two successive inventories during a non-droughted period (i.e., when BA_i,1 was sampled during the years 2000−2011; Equation 1). gr_ij is then calculated as the pairwise difference between corrected growth rates between species i and j, expressed as:

gr_ij =   ΔRGR_i  ‒ ΔRGR_j         (Equation 3)

Relative growth sensitivity (%) was then quantified as:

Relative growth sensitivity_i = [(n_gr_ij<0  ‒ n_gr_ij>0)/n_tot] × 100     (Equation 4)   

where n_gr_ij<0 are the number of co-occurring species that experienced lower growth reductions and n_gr_ij>0 are the number of species whose growth was more limited by drought. n_gr_ij<0 and n_gr_ij>0 were determined by a one sample t-test of the species-specific gr_ij comparisons. n_tot is the number of species that were able to be compared.

Relative mortality and relative mortality sensitivity

To calculate relative mortality (mr_ij), we first quantified species-specific mortality in each hexagon as a stem loss rate (m_i) across three successive inventories from 2000 – 2018 using the following equation (Sheil et al., 1995):

m_i = [1 ‒ (N_i,1/N_i,0)^(1/t)] × 100     (Equation 5)       

where N_i,0 is the species-specific number of live stems at the initial inventory (at year = t_0) and N_i,1 is the species-specific number of live stems at the next inventory (at year = t_1). The variable t (years) is the difference in time between inventory periods, and equal to t_1 – t_0.  Next, we evaluated the impact of drought as a change in stem loss rate (Δm_i) (% stem loss/year), where species-specific m_i after 2012 were subtracted by m_i quantified in the same hexagon during previous non-drought periods. The Δm_i equation took the following form:         

Δm_i = m_i,post_drought ‒ m_i,pre_drought     (Equation 6)

where m_i,post_drought is a species-specific drought-driven stem loss rates (when N_i,1 was sampled during the years 2012−2018; Equation 5) and m_i,pre_drought is the stem loss rate for the same species and locations from two successive inventories during a non-droughted period (when N_i,1 was sampled during the years 2000−2011; Equation 5). mr_ij is then calculated as the pairwise difference between corrected stem loss rates between species i and j, expressed as:

mr_ij =  Δm_i ‒ Δm_j     (Equation 7)               

Relative mortality sensitivity (%) was then quantified as:

Relative mortality sensitivity_i =  [(n_mr_ij>0 ‒ n_mr_ij<0)/n_tot] × 100     (Equation 8)   

where n_mr_ij>0 are the number of co-occurring species that experienced lower drought-driven stem loss change and n_mr_ij<0 are the number of species that experienced greater drought-driven stem loss change. n_mr_ij>0 and n_mr_ij<0 were determined by a one sample t-test of the species-specific mr_ij comparisons. n_tot is the number of species that were able to be compared.

本数据集包含由美国农业部林务局（United States Department of Agriculture Forest Service, USDA FS）森林清查与分析（Forest Inventory and Analysis, FIA）数据集（Gray等，2012）衍生得到的干旱驱动林木相对生长与死亡响应数据，研究区域为北美中部硬木生态区（该区域涵盖美国印第安纳州、伊利诺伊州、肯塔基州及Brandt等（2014）所界定的范围）。本数据集时间跨度为2000年至2018年，聚焦2012年中西部严重干旱（Mallya等，2013）背景下，胸径（diameter at breast height, DBH）大于12.7 cm的同域林木间的相对响应特征。本分析仅纳入研究区域内2012年3月至10月期间，达到美国干旱监测项目（US Drought Monitor program，Svoboda等，2002）所定义“严重”或“极端”干旱等级的区域。同域林木被定义为生长在同一离散875 km²六边形边界内的个体，本研究采用镶嵌（tessellation）划分方法，将研究区域内的森林清查样地聚合为560个均匀六边形网格。

本研究针对以下林木物种量化了干旱驱动的相对响应：红花槭（Acer rubrum）、糖枫（Acer saccharum）、白山核桃（Carya alba）、光滑山核桃（Carya glabra）、灰山核桃（Carya ovata）、德克萨斯山核桃（Carya texana）、北美朴树（Celtis occidentalis）、美国山毛榉（Fagus grandifolia）、黑胡桃（Juglans nigra）、北美鹅掌楸（Liriodendron tulipifera）、紫树（Nyssa sylvatica）、短叶松（Pinus echinata）、黑樱桃（Prunus serotina）、白栎（Quercus alba）、猩红栎（Quercus coccinea）、红栎（Quercus rubra）、星毛栎（Quercus stellata）、黑栎（Quercus velutina）、檫木（Sassafras albidum）以及北美榆（Ulmus americana）。

## 研究方法

### 相对生长量与相对生长敏感性
为计算相对生长量（gr_ij），我们首先以2000年至2018年的三次连续调查数据为基础，将每个六边形网格内的物种特异性生长量化为相对生长速率。相对生长速率（RGR_i）的计算公式如下（Brzostek等，2014）：
RGR_i = [(BA_i,1 ‒ BA_i,0)/BA_i,0] × 100 （公式1）
其中BA_i,0为初始调查时的物种特定林木断面积（basal area, BA），BA_i,1为下一次调查时的物种特定林木断面积。随后，将干旱对RGR_i的影响表征为速率变化参数ΔRGR_i（%生长量/年），即2012年干旱后的RGR_i减去干旱扰动前同一六边形网格内同种个体的RGR_i。具体而言，ΔRGR_i的计算公式为：
ΔRGR_i = RGR_i,post_drought ‒ RGR_i,pre_drought （公式2）
其中RGR_i,post_drought为干旱后的物种特定林木相对生长量（即BA_i,1于2012−2018年调查得到的RGR_i，公式1），RGR_i,pre_drought为非干旱时段内同一物种、同一位置的两次连续调查得到的相对生长量（即BA_i,1于2000−2011年调查得到的RGR_i，公式1）。随后，通过物种i与j的校正生长速率的成对差值计算gr_ij，公式如下：
gr_ij = ΔRGR_i ‒ ΔRGR_j （公式3）
相对生长敏感性（%）的计算公式如下：
Relative growth sensitivity_i = [(n_gr_ij<0 ‒ n_gr_ij>0)/n_tot] × 100 （公式4）
其中n_gr_ij<0为生长受干旱抑制程度更低的共存物种数量，n_gr_ij>0为生长受干旱限制更严重的物种数量。n_gr_ij<0和n_gr_ij>0通过对物种特异性gr_ij比较进行单样本t检验确定。n_tot为可进行比较的物种总数。

### 相对死亡率与相对死亡敏感性
为计算相对死亡率（mr_ij），我们首先以2000年至2018年的三次连续调查数据为基础，将每个六边形网格内的物种特异性死亡率量化为枯损速率（stem loss rate），计算公式如下（Sheil等，1995）：
m_i = [1 ‒ (N_i,1/N_i,0)^(1/t)] × 100 （公式5）
其中N_i,0为初始调查（t0年份）时的物种特定活立木株数，N_i,1为下一次调查（t1年份）时的物种特定活立木株数。变量t（年）为两次调查的时间间隔，即t1 – t0。随后，将干旱的影响表征为枯损速率变化参数Δm_i（%枯损量/年），即2012年后的物种特定枯损速率减去同一六边形网格内非干旱时段测得的枯损速率。Δm_i的计算公式如下：
Δm_i = m_i,post_drought ‒ m_i,pre_drought （公式6）
其中m_i,post_drought为干旱驱动的物种特定枯损速率（即N_i,1于2012−2018年调查得到的枯损速率，公式5），m_i,pre_drought为非干旱时段内同一物种、同一位置的两次连续调查得到的枯损速率（即N_i,1于2000−2011年调查得到的枯损速率，公式5）。随后，通过物种i与j的校正枯损速率的成对差值计算mr_ij，公式如下：
mr_ij = Δm_i ‒ Δm_j （公式7）
相对死亡敏感性（%）的计算公式如下：
Relative mortality sensitivity_i = [(n_mr_ij>0 ‒ n_mr_ij<0)/n_tot] × 100 （公式8）
其中n_mr_ij>0为干旱驱动的枯损变化程度更低的共存物种数量，n_mr_ij<0为干旱驱动的枯损变化程度更高的物种数量。n_mr_ij>0和n_mr_ij<0通过对物种特异性mr_ij比较进行单样本t检验确定。n_tot为可进行比较的物种总数。