生物多样性 ›› 2023, Vol. 31 ›› Issue (12): 23299. DOI: 10.17520/biods.2023299
高德1,2(
), 王彦平1,*()(
)
收稿日期:2023-08-24
接受日期:2023-12-11
出版日期:2023-12-20
发布日期:2023-12-30
通讯作者:
E-mail: 基金资助:
De Gao1,2(), Yanping Wang1,*()()
Received:2023-08-24
Accepted:2023-12-11
Online:2023-12-20
Published:2023-12-30
Contact:
E-mail: 摘要：
小岛屿效应(small-island effect, SIE)描述了种-面积关系(species-area relationship, SAR)的一种特殊现象: 在面积低于某个阈值时, 物种数不随岛屿面积的增加而增加或以一种比大岛屿低的速率增加的现象。由于小岛屿效应的面积阈值可能是多种生物地理格局和生态学过程在空间尺度上的转折点, 另外该现象在生物多样性保护领域具有重要指导意义, 因此小岛屿效应已经成为岛屿生物地理学和生物多样性研究领域的一种重要格局。目前主要有5种分析和检验小岛屿效应的方法, 包括种-面积关系形状比较法(SAR shape comparison)、断点回归法(breakpoint/piecewise regression)、零模型法(null model)、路径分析法(path analysis)和树模型法(tree-based model)。本文首先简要介绍了小岛屿效应与种-面积关系的关联, 然后重点总结了文献中记载的小岛屿效应检测的5种方法的优点和不足。在SAR形状比较法中, 受大岛屿离群值效应的影响, SAR的形状往往很难呈现出“S”形曲线。在断点回归法中, 数据的对数转换使检测到的SIE可能只是一种假象。在零模型法中, 随机化过程忽略了物种之间生态特征的差异, 降低了岛屿物种丰富度预期值的可信度。在路径分析法中, 生境多样性难以量化以及SIE范围内如果SAR具有斜率则会降低该方法的适用性。在树模型法中, 如果面积不是物种丰富度变异的最佳预测因子, 树模型不会首先选择面积对样本进行拆分; 另外如果SAR存在两个面积阈值, 树模型可能不会从SIE阈值处进行拆分。因此, 为了避免因某种方法的自身不足而造成的错误判断, 我们建议: 首先应同时使用多种方法来进行SIE检测, 当至少有两种方法同时检测出SIE时, 方可认为系统中存在SIE; 其次, 针对现有检测方法中存在的缺陷加以改进也是今后重要的发展方向。最后, 本文针对国内学者从事较多的生境岛屿中SIE的特征以及导致全球变化的人类活动如何影响SIE的出现等问题给出了一些启发性建议。本文将为小岛屿效应的准确检测提供参考依据并为完善小岛屿效应的理论框架起到推动作用。
高德, 王彦平 (2023) 小岛屿效应检测方法研究进展. 生物多样性, 31, 23299. DOI: 10.17520/biods.2023299.
De Gao, Yanping Wang (2023) A review of the small-island effect detection methods and method advancement. Biodiversity Science, 31, 23299. DOI: 10.17520/biods.2023299.
| 模型形状 Model shape | 模型 Model | 公式 Equation1 | 参数数量 Number of parameters |
|---|---|---|---|
| 直线形 Linear shape | 线性模型 Linear | S = c + z × A | 2 |
| “C”形 Convex shape | 渐近模型 Asymptotic | S = d − c × z^A | 3 |
| “C”形 Convex shape | 对数模型 Logarithmic | S = c + z × log(A) | 2 |
| “C”形 Convex shape | 小林模型 Kobayashi | S = c × log(1 + A/z) | 2 |
| “C”形 Convex shape | 莫诺模型 Monod | S = d/(1 + c × A^(−1)) | 2 |
| “C”形 Convex shape | 负指数模型 Negative exponential | S = d × (1 − exp(−z × A)) | 2 |
| “C”形 Convex shape | 持久性函数1模型 Persistence function 1 | S = c × A^z × exp(−d × A) | 3 |
| “C”形 Convex shape | 幂函数模型 Power | S = c × A^z | 2 |
| “C”形 Convex shape | 罗森茨魏格幂函数模型 Power Rosenzweig | S = f + c × A^z | 3 |
| “C”形 Convex shape | 有理函数模型 Rational | S = (c + z × A)/(1 + d × A) | 3 |
| “S”形 Sigmoidal shape | 扩展幂函数2模型 Extended power 2 | S = c × A^(z − (d/A)) | 3 |
| “S”形 Sigmoidal shape | 冈珀茨模型 Gompertz | S = d × exp(−exp(−z × (A − c))) | 3 |
| “S”形 Sigmoidal shape | 逻辑斯蒂模型 Logistic | S = c/(f + A^(−z)) | 3 |
| “S”形 Sigmoidal shape | 摩根-默瑟-弗洛丁模型 Morgan-Mercer-Flodin | S = d/(1 + c × A^(−z)) | 3 |
| “S”形 Sigmoidal shape | 持久性函数2模型 Persistence function 2 | S = c × A^z × exp(−d/A) | 3 |
| “S”形 Sigmoidal shape | 威布尔-3模型 Weibull-3 | S = d × (1 − exp(−c × A^z)) | 3 |
| “S”形 Sigmoidal shape | 威布尔-4模型 Weibull-4 | S = d × (1 − exp(−c × A^z))^f | 4 |
| “S”形 Sigmoidal shape | Beta-P模型 Beta-P | S = d × (1 − (1 + (A/c)^z)^(−f)) | 4 |
| “S”形 Sigmoidal shape | 查普曼-理查兹模型 Chapman-Richards | S = d × (1 − exp(−z × A)^c) | 3 |
| “C”形或“S”形 Convex or sigmoidal shape | 扩展幂函数1模型 Extended power 1 | S = c × A^(z × A^(−d)) | 3 |
表1 sars程序包中提供的20种种-面积关系模型(修改自Matthews等, 2019)
Table 1 The 20 species-area relationship models available in the sars package (modified from Matthews et al, 2019)
| 模型形状 Model shape | 模型 Model | 公式 Equation1 | 参数数量 Number of parameters |
|---|---|---|---|
| 直线形 Linear shape | 线性模型 Linear | S = c + z × A | 2 |
| “C”形 Convex shape | 渐近模型 Asymptotic | S = d − c × z^A | 3 |
| “C”形 Convex shape | 对数模型 Logarithmic | S = c + z × log(A) | 2 |
| “C”形 Convex shape | 小林模型 Kobayashi | S = c × log(1 + A/z) | 2 |
| “C”形 Convex shape | 莫诺模型 Monod | S = d/(1 + c × A^(−1)) | 2 |
| “C”形 Convex shape | 负指数模型 Negative exponential | S = d × (1 − exp(−z × A)) | 2 |
| “C”形 Convex shape | 持久性函数1模型 Persistence function 1 | S = c × A^z × exp(−d × A) | 3 |
| “C”形 Convex shape | 幂函数模型 Power | S = c × A^z | 2 |
| “C”形 Convex shape | 罗森茨魏格幂函数模型 Power Rosenzweig | S = f + c × A^z | 3 |
| “C”形 Convex shape | 有理函数模型 Rational | S = (c + z × A)/(1 + d × A) | 3 |
| “S”形 Sigmoidal shape | 扩展幂函数2模型 Extended power 2 | S = c × A^(z − (d/A)) | 3 |
| “S”形 Sigmoidal shape | 冈珀茨模型 Gompertz | S = d × exp(−exp(−z × (A − c))) | 3 |
| “S”形 Sigmoidal shape | 逻辑斯蒂模型 Logistic | S = c/(f + A^(−z)) | 3 |
| “S”形 Sigmoidal shape | 摩根-默瑟-弗洛丁模型 Morgan-Mercer-Flodin | S = d/(1 + c × A^(−z)) | 3 |
| “S”形 Sigmoidal shape | 持久性函数2模型 Persistence function 2 | S = c × A^z × exp(−d/A) | 3 |
| “S”形 Sigmoidal shape | 威布尔-3模型 Weibull-3 | S = d × (1 − exp(−c × A^z)) | 3 |
| “S”形 Sigmoidal shape | 威布尔-4模型 Weibull-4 | S = d × (1 − exp(−c × A^z))^f | 4 |
| “S”形 Sigmoidal shape | Beta-P模型 Beta-P | S = d × (1 − (1 + (A/c)^z)^(−f)) | 4 |
| “S”形 Sigmoidal shape | 查普曼-理查兹模型 Chapman-Richards | S = d × (1 − exp(−z × A)^c) | 3 |
| “C”形或“S”形 Convex or sigmoidal shape | 扩展幂函数1模型 Extended power 1 | S = c × A^(z × A^(−d)) | 3 |
图1 种-面积关系模型的三种可能形状
Fig. 1 Three possible shapes of the species-area relationships (SARs)
图2 使用Gao和Wang (2022)中第4个断点回归模型拟合西印度群岛两栖动物种-面积关系。(a)总的残差平方和随着面积阈值的迭代而变化; (b)种-面积关系拟合结果。数据来源于附录1。
Fig. 2 Fitting the species-area relationship of amphibians of the West Indies using a two-segmented piecewise regression models with a flat slope within the area threshold (Model 4 in Gao & Wang, 2022). (a) The residual sum of squares varies with the iteration of the area threshold; (b) Fitting results of the species-area relationship. The data used for analysis are from Appendix 1.
| 模型 Model | 公式 Equation1 | 片段数量 Number of segments |
|---|---|---|
| 1 | Y = c1 + (log A ≤ T1) z1 log A + (log A > T1) [z1 T1 + z2 (log A - T1)] | 2 |
| 2 | Y = c1 + (log A ≤ T1) [z1 log A + (z2 - z1) T1] + (log A > T1) z2 log A | 2 |
| 3 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1) (c2 + z2 log A) | 2 |
| 4 | Y = c1 + (log A > T1) z1 (log A - T1) | 2 |
| 5 | Y = c1 + (log A ≤ T1) z1 T1 + (log A > T1) z1 log A | 2 |
| 6 | Y = (log A ≤ T1) c1 + (log A > T1) (c2 + z1 log A) | 2 |
| 7 | Y = c1 + (log A ≤ T1) z1 log A + (log A > T1) z1 T1 | 2 |
| 8 | Y = c1 + (log A ≤ T1) z1 (log A - T1) | 2 |
| 9 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1) c2 | 2 |
| 10 | Y = (log A ≤ T2) [c1 + (log A ≤ T1) z1 T1 + (log A > T1) z1 log A] + (log A > T2) (c2 + z2 log A) | 3 |
| 11 | Y = (log A ≤ T1) c1 + (log A > T1 AND log A ≤ T2) (c2 + z1 log A) + (log A > T2) (c3 + z2 log A) | 3 |
| 12 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) (c2 + z2 log A) + (log A > T2) (c3 + z3 log A) | 3 |
| 13 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) (c2 + z2 log A) + (log A > T2) c3 | 3 |
| 14 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) [(c1 - c2 + z1 T1 - z2 T2) (log A - T1) / (T1 -T2) + c1 + z1 T1] + (log A > T2) (c2 + z2 log A) | 3 |
表2 14种用来检验小岛屿效应的断点回归模型(整理自Gao等, 2019)
Table 2 The 14 piecewise models for the detection of the small-island effect (organized from Gao et al, 2019)
| 模型 Model | 公式 Equation1 | 片段数量 Number of segments |
|---|---|---|
| 1 | Y = c1 + (log A ≤ T1) z1 log A + (log A > T1) [z1 T1 + z2 (log A - T1)] | 2 |
| 2 | Y = c1 + (log A ≤ T1) [z1 log A + (z2 - z1) T1] + (log A > T1) z2 log A | 2 |
| 3 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1) (c2 + z2 log A) | 2 |
| 4 | Y = c1 + (log A > T1) z1 (log A - T1) | 2 |
| 5 | Y = c1 + (log A ≤ T1) z1 T1 + (log A > T1) z1 log A | 2 |
| 6 | Y = (log A ≤ T1) c1 + (log A > T1) (c2 + z1 log A) | 2 |
| 7 | Y = c1 + (log A ≤ T1) z1 log A + (log A > T1) z1 T1 | 2 |
| 8 | Y = c1 + (log A ≤ T1) z1 (log A - T1) | 2 |
| 9 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1) c2 | 2 |
| 10 | Y = (log A ≤ T2) [c1 + (log A ≤ T1) z1 T1 + (log A > T1) z1 log A] + (log A > T2) (c2 + z2 log A) | 3 |
| 11 | Y = (log A ≤ T1) c1 + (log A > T1 AND log A ≤ T2) (c2 + z1 log A) + (log A > T2) (c3 + z2 log A) | 3 |
| 12 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) (c2 + z2 log A) + (log A > T2) (c3 + z3 log A) | 3 |
| 13 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) (c2 + z2 log A) + (log A > T2) c3 | 3 |
| 14 | Y = (log A ≤ T1) (c1 + z1 log A) + (log A > T1 AND log A ≤ T2) [(c1 - c2 + z1 T1 - z2 T2) (log A - T1) / (T1 -T2) + c1 + z1 T1] + (log A > T2) (c2 + z2 log A) | 3 |
图3 使用Gao和Wang (2022)中第6个断点回归模型拟合西印度群岛两栖类种-面积关系。(a)总的残差平方和随着第二个面积阈值的迭代而变化; (b)总的残差平方和随着第一个面积阈值的迭代而变化; (c)种-面积关系拟合结果。数据来源于附录1。
Fig. 3 Fitting the species-area relationship of amphibians of the West Indies using a three-segmented piecewise regression model (Model 6 in Gao & Wang, 2022). (a) The residual sum of squares varies with the iteration of the second area threshold; (b) The residual sum of squares varies with the iteration of the first area threshold; (c) Fitting results of the species-area relationship. The data used for analysis are from Appendix 1.
图4 参考Triantis等(2006)构建的面积和生境多样性对物种丰富度影响的结构方程模型。(a)在大岛屿上, 面积对物种丰富度既有直接影响又有间接影响; (b)在小岛屿上, 面积对物种丰富度的直接影响消失。a, bA, bH和SIE为标准回归系数。实线和虚线分别表示0.05水平下的显著效果和非显著效果。
Fig. 4 A structural equation model for the effects of area and habitat diversity on species richness according to Triantis et al, 2006. (a) On large islands, area has both direct and indirect impacts on species richness; (b) On small islands, the direct impact of area on species richness disappears. a, bA, bH, and SIE are standardized regression coefficients. Solid and dashed lines represent the significant and non-significant effects at the 0.05 level respectively.
图5 使用岛屿面积和岛屿隔离度两个自变量来预测物种丰富度并绘制散点图
Fig. 5 Using two independent variables, island area and island isolation, to predict species richness and make scatter plot
图6 通过分类树模型对图5的例子进行分析
Fig. 6 Using the classification tree model to analyze the example in Fig. 5
| 属性 Attribute | 种-面积关系形状比较法 SAR shape comparison | 断点回归法Breakpoint/piecewise regression | 零模型法Null model | 路径分析法Path analysis | 树模型法Tree-based model |
|---|---|---|---|---|---|
| 能否计算SIE面积阈值 Whether being able to calculate the SIE area threshold | 否 No | 是 Yes | 否 No | 是 Yes | 是 Yes |
| 能否判断SIE区间内SAR具有斜率 Whether being able to determine SAR slope within the limit of the SIE | 否 No | 是 Yes | 否 No | 否 No | 否 No |
| 是否只依赖岛屿面积和物种丰富度数据 Whether only relying on island area and species richness data | 是 Yes | 是 Yes | 是 Yes | 否 No | 否 No |
| 是否必须将岛屿面积对数转化 Whether logarithmic transformation is required for island area | 否 No | 是 Yes | 否 No | 否 No | 否 No |
| 犯I类错误的概率 Probability of making type I error1 | 低 Low | 高 High | 低 Low | 低 Low | 低 Low |
| 犯II类错误的概率 Probability of making type II error2 | 高 High | 低 Low | 低 Low | 高 High | 高 High |
| 使用这5种SIE检测方法的论文数 Number of publications using the five SIE detection methods | 5 | 45 | 4 | 9 | 1 |
表3 5种小岛屿效应检测方法的属性比较
Table 3 Attribute comparison among the five small-island effect (SIE) detection methods
| 属性 Attribute | 种-面积关系形状比较法 SAR shape comparison | 断点回归法Breakpoint/piecewise regression | 零模型法Null model | 路径分析法Path analysis | 树模型法Tree-based model |
|---|---|---|---|---|---|
| 能否计算SIE面积阈值 Whether being able to calculate the SIE area threshold | 否 No | 是 Yes | 否 No | 是 Yes | 是 Yes |
| 能否判断SIE区间内SAR具有斜率 Whether being able to determine SAR slope within the limit of the SIE | 否 No | 是 Yes | 否 No | 否 No | 否 No |
| 是否只依赖岛屿面积和物种丰富度数据 Whether only relying on island area and species richness data | 是 Yes | 是 Yes | 是 Yes | 否 No | 否 No |
| 是否必须将岛屿面积对数转化 Whether logarithmic transformation is required for island area | 否 No | 是 Yes | 否 No | 否 No | 否 No |
| 犯I类错误的概率 Probability of making type I error1 | 低 Low | 高 High | 低 Low | 低 Low | 低 Low |
| 犯II类错误的概率 Probability of making type II error2 | 高 High | 低 Low | 低 Low | 高 High | 高 High |
| 使用这5种SIE检测方法的论文数 Number of publications using the five SIE detection methods | 5 | 45 | 4 | 9 | 1 |
图7 西印度群岛两栖动物种-面积关系。(a)全部166个两栖类出现的岛屿; (b)从全部两栖类出现的岛屿中删除了前40%的大岛屿。数据来源于附录1。
Fig. 7 The species-area relationship of amphibians of the West Indies. (a) All amphibian-inhabited islands; (b) Removing the top 40% of large islands from all amphibian-inhabited islands. The data used for analysis are from Appendix 1.
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