北京东灵山地区植物群落多样性研究——种-面积曲线的拟合与评价

PLANT COMMUNITY DIVERSITY IN DONGLING MOUNTAIN, BEIJING,CHINA —— THE FITTING AND ASSESSMENT OF SPECIES AREA CURVES

本文选择了 1 0条曲线作为种 -面积曲线的拟合模型 ,它们分别是S=b +a A (1 )S=b +aln A (2 )S=(b +aln A) c (3)S=aln(A +1 ) (4)S=aln(b A +1 ) (5)S=a Ab (6)S=a A/ (1 +b A) (7)S=c/ (1 +ae-b A ) (8)S=c - ae-b A (9)S=a(1 - e-b A ) (1 0 )对其中的 7个非线性模型给出了参数初值的计算方法 ,并用 Gauss- Newton或 Marquardt方法计算非线性最优解。又选择了剩余标准差 (RSE)、相关指数 (CRI)、偏差绝对值的平均值 (AAD)和相对偏差绝对值的平均值 (AARD)作为模型拟合优劣的 4个评价指标。研究结果表明 :1 ) 7个非线性模型中参数初值的计算方法是可行的。从 4个评价指标来看 ,它们的非线性最小二乘解都明显优于线性最小二乘解 ;2 ) 1 0个模型的拟合效果都相当好 ,对 5个样地及其各层拟合的共 2 0 0个 CRI中有 71 .5%大于 0 .9,89%大于0 .8,其中曲线 (3)和 (9)最好 ,其次是 (5)、(6)、(2 ) ,(1 )和 (1 0 )最差 ;3)秩相关分析表明 ,3个评价指标RSE、AAD和 AARD相互之间存在极强的正秩相关 ,因此在本研究中 ,它们的评价结果具很强的一致性。

The following 10 curves were chosen as the models for species area curves:S=b+aA(1) S=b+a ln A(2) S=(b+a ln A) c(3) S=a ln (A+1)(4) S=a ln (bA+1)(5) S=aA b(6) S=aA/(1+bA)(7) S=c/(1+a e -bA )(8) S=c-a e -bA (9) S=a(1- e -bA )(10)The algorithms were given to calculate the initial values of the parameters in the 7 nonlinear models, and Gauss Newton and Marquardt algorithms were used to solve the nonlinear problems.Four indices were chosen to assess the fittness of the models,which are residual standard error( RSE ),correlation index( CRI ),average of absolute deviation( AAD ),and average of absolute relative deviation( AARD ).The results show that:1) the algorithms of calculating the initial values of the parameters in the 7 nonlinear models were suitable,and the solutions from nonlinear least squares were better than those from linear least squares according to the 4 assessment indices; 2) the fittness of the 10 models were high because 71.5% of the 200 values of CRI were greater than 0.9 and 89% were greater than 0.8.The calculation results of curves (3) and (9) were the best two;the next three were (5),(6),and (2);and the worst two were (1) and (10); 3) rank correlation analyses show that there existed extremely strong positive rank correlations between any two of the three indices of RSE,AAD ,and AARD .