Biodiv Sci ›› 2023, Vol. 31 ›› Issue (12): 23299. DOI: 10.17520/biods.2023299
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Gao De^{1}^{,}^{2}(), Wang Yanping^{1}^{,}^{*}()()
Received:
20230824
Accepted:
20231211
Online:
20231220
Published:
20231230
Contact:
Email: Gao De, Wang Yanping. A review of the smallisland effect detection methods and method advancement[J]. Biodiv Sci, 2023, 31(12): 23299.
模型形状 Model shape  模型 Model  公式 Equation^{1}  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 MorganMercerFlodin  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 Weibull3  S = d × (1 − exp(−c × A^z))  3 
“S”形 Sigmoidal shape  威布尔4模型 Weibull4  S = d × (1 − exp(−c × A^z))^f  4 
“S”形 Sigmoidal shape  BetaP模型 BetaP  S = d × (1 − (1 + (A/c)^z)^(−f))  4 
“S”形 Sigmoidal shape  查普曼理查兹模型 ChapmanRichards  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 
Table 1 The 20 speciesarea relationship models available in the sars package (modified from Matthews et al, 2019)
模型形状 Model shape  模型 Model  公式 Equation^{1}  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 MorganMercerFlodin  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 Weibull3  S = d × (1 − exp(−c × A^z))  3 
“S”形 Sigmoidal shape  威布尔4模型 Weibull4  S = d × (1 − exp(−c × A^z))^f  4 
“S”形 Sigmoidal shape  BetaP模型 BetaP  S = d × (1 − (1 + (A/c)^z)^(−f))  4 
“S”形 Sigmoidal shape  查普曼理查兹模型 ChapmanRichards  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 
Fig. 2 Fitting the speciesarea relationship of amphibians of the West Indies using a twosegmented 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 speciesarea relationship. The data used for analysis are from Appendix 1.
模型 Model  公式 Equation^{1}  片段数量 Number of segments 

1  Y = c_{1} + (log A ≤ T_{1}) z_{1} log A + (log A > T_{1}) [z_{1 }T_{1} + z_{2} (log A  T_{1})]  2 
2  Y = c_{1} + (log A ≤ T_{1}) [z_{1} log A + (z_{2}  z_{1}) T_{1}] + (log A > T_{1}) z_{2} log A  2 
3  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1}) (c_{2} + z_{2} log A)  2 
4  Y = c_{1} + (log A > T_{1}) z_{1} (log A  T_{1})  2 
5  Y = c_{1} + (log A ≤ T_{1}) z_{1} T_{1} + (log A > T_{1}) z_{1} log A  2 
6  Y = (log A ≤ T_{1}) c_{1} + (log A > T_{1}) (c_{2} + z_{1} log A)  2 
7  Y = c_{1} + (log A ≤ T_{1}) z_{1} log A + (log A > T_{1}) z_{1 }T_{1}  2 
8  Y = c_{1} + (log A ≤ T_{1}) z_{1 }(log A  T_{1})  2 
9  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1}) c_{2}  2 
10  Y = (log A ≤ T_{2}) [c_{1} + (log A ≤ T_{1}) z_{1} T_{1} + (log A > T_{1}) z_{1} log A] + (log A > T_{2}) (c_{2} + z_{2} log A)  3 
11  Y = (log A ≤ T_{1}) c_{1} + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{1} log A) + (log A > T_{2}) (c_{3} + z_{2} log A)  3 
12  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{2} log A) + (log A > T_{2}) (c_{3} + z_{3} log A)  3 
13  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{2} log A) + (log A > T_{2}) c_{3}  3 
14  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) [(c_{1 } c_{2 }+ z_{1} T_{1 } z_{2} T_{2}) (log A  T_{1}) / (T_{1 }T_{2}) + c_{1} + z_{1 }T_{1}] + (log A > T_{2}) (c_{2} + z_{2} log A)  3 
Table 2 The 14 piecewise models for the detection of the smallisland effect (organized from Gao et al, 2019)
模型 Model  公式 Equation^{1}  片段数量 Number of segments 

1  Y = c_{1} + (log A ≤ T_{1}) z_{1} log A + (log A > T_{1}) [z_{1 }T_{1} + z_{2} (log A  T_{1})]  2 
2  Y = c_{1} + (log A ≤ T_{1}) [z_{1} log A + (z_{2}  z_{1}) T_{1}] + (log A > T_{1}) z_{2} log A  2 
3  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1}) (c_{2} + z_{2} log A)  2 
4  Y = c_{1} + (log A > T_{1}) z_{1} (log A  T_{1})  2 
5  Y = c_{1} + (log A ≤ T_{1}) z_{1} T_{1} + (log A > T_{1}) z_{1} log A  2 
6  Y = (log A ≤ T_{1}) c_{1} + (log A > T_{1}) (c_{2} + z_{1} log A)  2 
7  Y = c_{1} + (log A ≤ T_{1}) z_{1} log A + (log A > T_{1}) z_{1 }T_{1}  2 
8  Y = c_{1} + (log A ≤ T_{1}) z_{1 }(log A  T_{1})  2 
9  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1}) c_{2}  2 
10  Y = (log A ≤ T_{2}) [c_{1} + (log A ≤ T_{1}) z_{1} T_{1} + (log A > T_{1}) z_{1} log A] + (log A > T_{2}) (c_{2} + z_{2} log A)  3 
11  Y = (log A ≤ T_{1}) c_{1} + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{1} log A) + (log A > T_{2}) (c_{3} + z_{2} log A)  3 
12  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{2} log A) + (log A > T_{2}) (c_{3} + z_{3} log A)  3 
13  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) (c_{2} + z_{2} log A) + (log A > T_{2}) c_{3}  3 
14  Y = (log A ≤ T_{1}) (c_{1} + z_{1} log A) + (log A > T_{1} AND log A ≤ T_{2}) [(c_{1 } c_{2 }+ z_{1} T_{1 } z_{2} T_{2}) (log A  T_{1}) / (T_{1 }T_{2}) + c_{1} + z_{1 }T_{1}] + (log A > T_{2}) (c_{2} + z_{2} log A)  3 
Fig. 3 Fitting the speciesarea relationship of amphibians of the West Indies using a threesegmented 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 speciesarea relationship. The data used for analysis are from Appendix 1.
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 nonsignificant effects at the 0.05 level respectively.
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Treebased 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 error^{1}  低 Low  高 High  低 Low  低 Low  低 Low 
犯II类错误的概率 Probability of making type II error^{2}  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 
Table 3 Attribute comparison among the five smallisland 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Treebased 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 error^{1}  低 Low  高 High  低 Low  低 Low  低 Low 
犯II类错误的概率 Probability of making type II error^{2}  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 
Fig. 7 The speciesarea relationship of amphibians of the West Indies. (a) All amphibianinhabited islands; (b) Removing the top 40% of large islands from all amphibianinhabited islands. The data used for analysis are from Appendix 1.
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