入侵植物相对丰度

入侵植物相对丰度（Relative abundance of invasive plant species, P_i）按照以下公式计算（Theoharides and Dukes 2007 Theoharides KA, Dukes JS. 2007. Plant invasion across space and time, factors affecting nonindigenous species success during four stages of invasion. New Phytologist 176: 256‒273.; Rai 2015 Rai PK. 2015. Paradigm of plant invasion: multifaceted review on sustainable management. Environmental Monitoring and Assessment 187: 759.; Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.; Wang CY, Yu YL, Cheng HY, Du DL. 2022. Which factor contributes most to the invasion resistance of native plant communities under the co-invasion of two invasive plant species? Science of the Total Environment 813: 152628.）：

P_i = n_i / N

式中n_i为调查样方内入侵植物i的植株数量，N为调查样方内所有植物种类的植株数量总数。

植物群落入侵抵抗力指数（Invasion resistance index, IRI）

植物群落入侵抵抗力指数（Invasion resistance index, IRI）按照以下公式计算（Wang CY, Yu YL, Cheng HY, Du DL. 2022. Which factor contributes most to the invasion resistance of native plant communities under the co-invasion of two invasive plant species? Science of the Total Environment 813: 152628.）：

IRI = 1 ‒ (ΣP_iX_i / P_nX_n)

式中S为调查样方内所有植物种类的数量；P_i为调查样方内入侵植物i的相对丰度，即P_i = n_i / N，其中n_i为调查样方内入侵植物i的植株数量，N为调查样方内所有植物种类的植株数量总数；X_i为调查样方内入侵植物i的所有测定功能性状指标的算术平均值；P_n为调查样方内植物n的相对丰度，即P_n = n_n / N，其中n_n为调查样方内植物n的植株数量，N为调查样方内所有植物种类的植株数量总数；X_n为调查样方内植物n的所有测定功能性状指标的算术平均值。IRI值越大表示植物群落的入侵抵抗力越大。若调查样方内植物种类均为入侵植物，IRI值为0，表明植物群落入侵抵抗力最低；若调查样方内植物种类无入侵植物，IRI值为1，表明植物群落入侵抵抗力最高。

群落可入侵性指数（Community invasibility index, CII）

群落可入侵性指数（Community invasibility index, CII）按照以下公式计算（Wang CY, Wei M, Wang S, Wu BD, Cheng HY (2020) Erigeron annuus (L.) Pers. and Solidago canadensis L. antagonistically affect community stability and community invasibility under the co-invasion condition. Science of the Total Environment 716: 137128.）：

CII = 1 ‒ (MaxP_i ‒ P_i)

式中MaxP_i为所有调查样方内入侵植物相对丰度最大值，P_i为调查样方内入侵植物的相对丰度。CII值越大表示群落可入侵性越高。

群落可入侵性指数（Community invasibility index, CII）按照以下公式计算（Guo et al. 2015 Guo Q, Fei S, Dukes JS, Oswalt CM, Iannone III BV, Potter KM. 2015. A unified approach for quantifying invasibility and degree of invasion. Ecology 96: 2613‒2621.; Rijal et al. 2017 Rijal DP, Alm T, Nilsen L, Alsos IG. 2017. Giant invasive Heracleum persicum: Friend or foe of plant diversity? Ecology and Evolution 7: 4936‒4950.）：

CII = 1 ‒ (S_obs / S_max + B_obs / B_max) / 2

式中S_obs和B_obs分别为调查样方内所有植物种类的数量和总生物量。S_max和B_max分别为所有调查样方内所有植物种类的数量和总生物量最大值。

入侵植物入侵强度指数（Invasion intensity index, III）

入侵植物入侵强度指数（Invasion intensity index, III）按照以下公式计算（Wang CY, Wei M, Wang S, Wu BD, Cheng HY (2020) Erigeron annuus (L.) Pers. and Solidago canadensis L. antagonistically affect community stability and community invasibility under the co-invasion condition. Science of the Total Environment 716: 137128.）：

III = P_i / MaxP_i

式中MaxP_i为所有调查样方内入侵植物相对丰度最大值，P_i为调查样方内入侵植物的相对丰度。III值越大表示入侵植物的入侵强度越高。

The degree of invasion (DI) was calculated as follows (Guo et al., 2015 Guo Q, Fei S, Dukes JS, Oswalt CM, Iannone III BV, Potter KM. (2015) A unified approach for quantifying invasibility and degree of invasion. Ecology 96: 2613‒2621.):

DI = 1 ‒ (S_inv / S_tot + B_inv / B_tot) / 2

where S_inv and B_inv are observed invasive richness and biomass, respectively, and S_tot and B_tot are total (native plus invasive) richness and biomass in the community, respectively. In particular, plant communities with higher values of DI possess greater degree of invasion compared with those with lower values of DI.

入侵植物相对入侵力指数（Relative invasiveness index, RII）

入侵植物相对入侵力指数（Relative invasiveness index, RII）按照以下公式计算（Wang CY, Wei M, Wang S, Wu BD, Cheng HY (2020) Erigeron annuus (L.) Pers. and Solidago canadensis L. antagonistically affect community stability and community invasibility under the co-invasion condition. Science of the Total Environment 716: 137128.）：

RII = B_i / MaxB_i

式中MaxB_i为所有调查样方内入侵植物的总生物量最大值，B_i为调查样方内入侵植物的总生物量。RII值越大表示入侵植物的入侵竞争力越高。

入侵植物竞争优势度指数（Competitive advantage index of invasive plant species, CAI）

入侵植物竞争优势度指数（Competitive advantage index of invasive plant species, CAI）按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

CAI = Σ(P_iX_i) / (P_aX_a)

式中S为调查样方内所有植物种类的数量；P_i为调查样方内入侵植物i的相对丰度，即P_i = n_i / N，其中n_i为调查样方内入侵植物i的植株数量，N为调查样方内所有植物种类的植株数量总数；X_i为调查样方内入侵植物i的所有测定功能性状指标的算术平均值；P_a为调查样方内植物a的相对丰度，即P_a = n_a / N，其中n_a为调查样方内植物a的植株数量，N为调查样方内所有植物种类的植株数量总数；X_a为调查样方内植物a的所有测定功能性状指标的算术平均值。CAI值越大表示入侵植物的竞争优势度越大。

共同入侵下不同入侵植物的相对竞争优势度指数（Relative competitive advantage index of invasive plant species under co-invasion, RCAI）

共同入侵下不同入侵植物的相对竞争优势度指数（Relative competitive advantage index of invasive plant species under co-invasion, RCAI）按照以下公式计算（Wang CY, Li Y, Li C, Zhong SS, Xu ZL, Yu YL, Du DL. 2023. A method for quantifying relative competitive advantage and the combined effect of co-invasion for two invasive plants. Plant Diversity 45: 358‒361.）：

RCAI = Σ(P_xX_x) / (P_iX_i)

式中S为调查样方内所有入侵植物种类的数量；P_x为调查样方内入侵植物x的相对丰度，即P_x = n_x / N，其中n_x为调查样方内入侵植物x的植株数量，N为调查样方内所有植物种类的植株数量总数；X_x为调查样方内入侵植物x的所有测定功能性状指标的算术平均值；P_i为调查样方内所有入侵植物相对丰度的总和，即P_i = n_i / N，其中n_i为调查样方内所有入侵植物的植株数量，N为调查样方内所有植物种类的植株数量总数；X_i为调查样方内所有入侵植物的所有测定功能性状指标的算术平均值。RCAI值介于0和1之间，且RCAI值越大表示共同入侵下某一入侵植物的竞争优势度越大，反之亦然。

两种入侵植物共同入侵复合效应指数（Co-invasion combined effect index of two invasive plant species, CCEI）

两种入侵植物共同入侵复合效应指数（Co-invasion combined effect index of two invasive plant species, CCEI）按照以下公式计算（Wang CY, Li Y, Li C, Zhong SS, Xu ZL, Yu YL, Du DL. 2023. A method for quantifying relative competitive advantage and the combined effect of co-invasion for two invasive plants. Plant Diversity 45: 358‒361.）：

CCEI = CAI_xy / (CAI_x + CAI_y)

式中CAI_xy为两种入侵植物x和y共同入侵状态下的竞争优势度指数（Competitive advantage index of invasive plant species, CAI）；CAI_x和CAI_y分别为入侵植物x和入侵植物y单一入侵状态下的竞争优势度指数。若CCEI大于2，表明两种入侵植物共同入侵复合效应为促进；若CCEI等于2，表明两种入侵植物共同入侵复合效应为叠加；若CCEI大于1但小于2，表明两种入侵植物共同入侵复合效应为竞争；若CCEI等于1，表明两种入侵植物共同入侵复合效应为中和；若CCEI大于0但小于1，表明两种入侵植物共同入侵复合效应为拮抗。

入侵植物和本地植物功能差异指数（Functional difference index, FD_j）

入侵植物和本地植物功能差异指数（Functional difference index, FD_j）按照以下公式计算（Gross et al. 2013 Gross N, Börger L, Duncan RP, Hulme PE. 2013. Functional differences between alien and native species: do biotic interactions determine the functional structure of highly invaded grasslands? Functional Ecology 27: 1262‒1272.）：

FD_j = (|CWT_ij ‒ CWT_nj|) / (CWT_i ‒ CWT_n)

式中FD_j为样方j内入侵植物特征加权值（CWT_ij）与本地植物特征加权值（CWT_nj）的功能差异指数。CWT_i为所有样方或某一处理下所有样方入侵植物特征加权值，CWT_n为所有样方或某一处理下所有样方本地植物特征加权值。若FD_j大于0表明入侵植物和本地植物功能性状存在明显的差异性，即趋向功能分化（Functionally diverge），生态位分化（Niche differentiation）起主要作用；若FD_j小于0表明入侵植物和本地植物功能性状存在明显的相似性，即趋向功能相似（Functionally converge），生境过滤（Habitat filtering）起主要作用。

入侵植物对植物物种多样性生态影响风险评估量化方法-入侵植物对植物物种多样性影响幅度指数

1. 入侵植物对植物种类多样性影响幅度指数[The degree of influence index of invasive plant species on species diversity (S), DII_S]按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

DII_S = 1 ‒ (S_i / S_ck)

式中S_i为入侵植物已入侵样方的植物种类多样性（即：所有植物种类的数量），S_ck为入侵植物未入侵样方的植物种类多样性。DII_S值越大表示入侵植物对植物种类多样性的生态影响风险越大。

2. 入侵植物对植物Shannon多样性影响幅度指数[The degree of influence index of invasive plant species on Shannon’s diversity (H'), DII_H']按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

DII_H' = 1 ‒ (H'_i / H'_ck)

式中H'_i为入侵植物已入侵样方的植物Shannon多样性，H'_ck为入侵植物未入侵样方的植物Shannon多样性。DII_H'值越大表示入侵植物对植物Shannon多样性的生态影响风险越大。

3. 入侵植物对植物Simpson优势度影响幅度指数[The degree of influence index of invasive plant species on Simpson’s dominance (D), DII_D]按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

DII_D = 1 ‒ (D_i / D_ck)

式中D_i为入侵植物已入侵样方的植物Simpson优势度，D_ck为入侵植物未入侵样方的植物Simpson优势度。DII_D值越大表示入侵植物对植物Simpson优势度的生态影响风险越大。

4. 入侵植物对植物Pielou均匀度影响幅度指数[The degree of influence index of invasive plant species on Pielou’s evenness (E_H), DII_EH]按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

DII_EH = 1 ‒ (E_Hi / E_Hck)

式中E_Hi为入侵植物已入侵样方的植物Pielou均匀度，E_Hck为入侵植物未入侵样方的植物Pielou均匀度。DII_EH值越大表示入侵植物对植物Pielou均匀度的生态影响风险越大。

5. 入侵植物对植物Margalef丰富度影响幅度指数[The degree of influence index of invasive plant species on Margalef’s richness (F), DII_F]按照以下公式计算（Wang CY, Cheng HY, Wang S, Wei M, Du DL. 2021. Plant community and the influence of plant taxonomic diversity on community stability and invasibility: A case study based on Solidago canadensis L. Science of the Total Environment 768: 144518.）：

DII_F = 1 ‒ (F_i / F_ck)

式中F_i为入侵植物已入侵样方的植物Margalef丰富度，F_ck为入侵植物未入侵样方的植物Margalef丰富度。DII_F值越大表示入侵植物对植物Margalef丰富度的生态影响风险越大。

入侵植物-土壤反馈系数（Plant-soil feedbacks index, PSF index）

入侵植物-土壤反馈系数（Plant-soil feedbacks index, PSF index）按照以下公式计算(Van Nuland, M., Bailey, J., Schweitzer, J. 2017. Divergent plant–soil feedbacks could alter future elevation ranges and ecosystem dynamics. Nature Ecology & Evolution 1: 0150.)：

PSF index = ln (B_Local / B_Foreign)

式中B_Local和B_Foreign分别为植物i在本土土壤下以及在非本土土壤下的生物量。若PSF index大于0，表明植物-土壤反馈为正反馈；若PSF index小于0，表明植物-土壤反馈为负反馈。

入侵植物生长竞争力

相对竞争强度指数（Relative competition intensity index, R'）按照以下公式计算（Armas et al. 2004 Armas C, Oodiales R, Pugnaire FI (2004) Measuring plant interactions: A new comparative index. Ecology 85: 2682‒2686.; Domènech and Vilà 2008 Domènech R, Vilà M 2008. Response of the invader Cortaderia selloana and two coexisting natives to competition and water stress. Biological Invasions, 10(6), 903–912.; He et al. 2012 He WM, Li JJ, Peng PH (2012) Simulated warming differentially affects the growth and competitive ability of Centaurea maculosa populations from home and introduced ranges. PLoS One 7: e31170.; Gruntman et al. 2014 Gruntman M, Pehl AK, Joshi S, Tielbörger K. 2014. Competitive dominance of the invasive plant Impatiens glandulifera: using competitive effect and response with a vigorous neighbour. Biological Invasions 16: 141‒151.; Li et al. 2015 Li WH, Luo JN, Tian XS, Chow WS, Sun ZY, Zhang TJ, Peng SL, Peng CL. 2015. A new strategy for controlling invasive weeds: Selecting valuable native plants to defeat them. Scientific Reports, 5, 11004–11015.）：

R'_ij = (B_coi ‒ B_mi) / (B_coi ＋ B_mi)

式中R'_ij为物种i对物种j的相对竞争强度指数，B_coi为物种i和物种j混植时单株生物量，B_mi为物种i单植时单株生物量。若R'_ij大于0表明物种i的相对竞争强度大于物种j，若R'_ij小于0表明物种i的相对竞争强度小于物种j，若R'_ij等于0表明物种i的相对竞争强度等于物种j。

The relative competition intensity (RCI) index was determined as the difference between biomass when grown alone and biomass when grown in competition divided by biomass when grown alone, i.e., RCI = (Biomass_alone – Biomass_competition) / Biomass_alone (Weigelt and Jolliffe 2003 Weigelt A, Jolliffe P. 2003. Indices of plant competition. Journal of Ecology 91: 707–720.; Fahey and Flory 2022 Fahey C, Flory SL. 2022. Soil microbes alter competition between native and invasive plants. Journal of Ecology 110: 404-414.).

相对优势度指数（Relative dominance index, RDI）按照以下公式计算（Niu et al. 2007 Niu HB, Liu WX, Wan FH, Liu B. 2007. An invasive aster (Ageratina adenophora) invades and dominates forest understories in China: altered soil microbial communities facilitate the invader and inhibit natives. Plant and Soil 294: 73‒85.; Ding et al. 2012 Ding W, Wang R, Yuan Y, Liang X, Liu J. 2012. Effects of nitrogen deposition on growth and relationship of Robinia pseudoacacia and Quercus acutissima seedlings. Dendrobiology 67: 3‒13.; Yuan et al. 2013 Yuan YF, Guo WH, Ding WJ, Du N, Luo YJ, Liu J, Xu F, Wang RQ. 2013. Competitive interaction between the exotic plant Rhus typhina L. and the native tree Quercus acutissima Carr in Northern China under different soil N: P ratios. Plant and Soil 372: 389‒400.）：

RDI_ij = B_coi / B_coij

式中RDI_ij为物种i对物种j的相对优势度指数，B_coij为物种i和物种j混植时两种物种的总生物量，B_coi为物种i和物种j混植时物种i的生物量。若RDI大于0.5表明物种i的相对竞争力大于物种j，若RDI小于0.5表明物种i的相对竞争力小于物种j，若RDI等于0.5表明物种i的相对竞争力等于物种j。

入侵植物直接化感效应和化感遗留效应值

To assess the role of allelopathy in invasive plant species in co-cultivation condition, we calculated an index for immediate allelopathy and allelopathic legacy from the competitive responses of invasive plant species and native species. To do this we used log-response ratios, which is defined as the logarithm of the species biomass in the co-cultivation condition relative to the monoculture condition (Hedges et al. 1999 Hedges LV, Gurevitch J, Curtis PS. 1999. The meta-analysis of response ratios in experimental ecology. Ecology 80: 1150–1156.).

In particular, the immediate allelopathy index and allelopathic legacy index were calculated respectively as follows (Del Fabbro and Prati 2015 Del Fabbro C, Prati D. 2015. The relative importance of immediate allelopathy andallelopathic legacy in invasive plant species. Basic and Applied Ecology 16: 28–35):

Immediate allelopathy index = (Competitive response in native soil without activated carbon ‒ Competitive response in native soil with activated carbon)

Allelopathic legacy index = (Competitive response in invaded soil without activated carbon ‒ Competitive response in invaded soil with activated carbon) ‒ (Competitive response in native soil without activated carbon ‒ Competitive response in native soil with activated carbon)