冗余分析验证_canoco5冗余分析步骤

群落排序RDA验证

典范分析结合了排序和回归的思想，其包含一个响应变量矩阵Y和解释变量矩阵X，是与多元回归密切相关的：

多元回归模型预测$\widehat{Y_i}$与Y的排序是不同的，二者相关系数的平方根就是多元回归模型的决定系数。因此，多元回归模型建立了$\widehat{Y_i}$排序与Y排序之间的对应，因为回归拟合值排序受限于X，并且与X是最优的且线性相关的。这个特性在典范分析中也很重要。这种限制是在最小均方（least-square）意义上最优的，意味着多元线性回归模型得到了最大的$R^2$（决定系数）。因此，典范分析结合了排序和回归的方法，在X的约束下，形成与X密切相关的Y排序。

vagan包进行RDA分析

library(vegan) library(magrittr) 

## Loading required package: permute ## Loading required package: lattice ## This is vegan 2.5-6 

spe <- read.csv("2020otuabund.csv",header=T,row.names = 1) %$% .[,-10] spe <- t(spe)[,1:16] env <- read.csv("waterc.csv",header=T,row.names = NULL) %$% .[,-(1:2)] sp <- scale(spe, center = TRUE) water <- scale(env, center = TRUE) water <- water[,c(1,2,7,8)] mod11<-rda(sp ~ TotalC+TotalN+SAL+pH, env) summary(mod11) 

## ## Call: ## rda(formula = sp ~ TotalC + TotalN + SAL + pH, data = env) ## ## Partitioning of variance: ## Inertia Proportion ## Total 16.000 1.0000 ## Constrained 9.832 0.6145 ## Unconstrained 6.168 0.3855 ## ## Eigenvalues, and their contribution to the variance ## ## Importance of components: ## RDA1 RDA2 RDA3 RDA4 PC1 PC2 PC3 ## Eigenvalue 6.5226 2.1684 0.78380 0.35745 2.7334 1.7448 1.07726 ## Proportion Explained 0.4077 0.1355 0.04899 0.02234 0.1708 0.1091 0.06733 ## Cumulative Proportion 0.4077 0.5432 0.59218 0.61452 0.7854 0.8944 0.96173 ## PC4 ## Eigenvalue 0.61228 ## Proportion Explained 0.03827 ## Cumulative Proportion 1.00000 ## ## Accumulated constrained eigenvalues ## Importance of components: ## RDA1 RDA2 RDA3 RDA4 ## Eigenvalue 6.5226 2.1684 0.78380 0.35745 ## Proportion Explained 0.6634 0.2205 0.07972 0.03635 ## Cumulative Proportion 0.6634 0.8839 0.96365 1.00000 ## ## Scaling 2 for species and site scores ## * Species are scaled proportional to eigenvalues ## * Sites are unscaled: weighted dispersion equal on all dimensions ## * General scaling constant of scores: 3. ## ## ## Species scores ## ## RDA1 RDA2 RDA3 RDA4 PC1 PC2 ## OTU72 -0.15864 -0.26192 0. -0.04309 -0. -0.02104 ## OTU401 -0.15190 0.41764 -0.070863 0.11729 0. 0.32065 ## OTU822 0.41641 -0.27951 0.074570 -0.18489 -0.0078372 0.55600 ## OTU334 -0.67922 0.07835 0.088613 0.04723 0. 0.20553 ## OTU815 0.60617 -0.41794 0. 0.09392 -0.0 0.05853 ## OTU828 0.64631 -0.10303 0. -0.02145 0. -0.29497 ## OTU461 -0.68355 -0.32370 0. 0.06208 -0.0008486 0.15978 ## OTU361 -0.70671 -0.23541 -0.055085 -0.03725 0.0061413 -0.04282 ## OTU912 0.24139 -0.18079 -0. -0.27749 -0. 0.40881 ## OTU83 0.46548 0.35236 0. 0.20873 -0. -0.44886 ## OTU638 0.52096 -0.43189 -0. 0.17608 0. -0.10085 ## OTU75 -0.78599 -0.08045 0.023342 -0.03683 -0.0086104 0.02925 ## OTU643 0.70966 0.14607 0. -0.07273 0. -0.36211 ## OTU868 0.59002 0.13248 0.001474 0.01602 -0. -0.33728 ## OTU673 0.09015 -0.67743 -0.090516 0.14908 0. -0.06191 ## OTU651 0.39161 0.11345 0.011508 -0.07418 0. -0.18163 ## ## ## Site scores (weighted sums of species scores) ## ## RDA1 RDA2 RDA3 RDA4 PC1 PC2 ## H1 -1.5505 -0.004236 -1.50882 -1.6763 -0.39559 -0.61280 ## H2 -1.6591 1. -0.59495 0.7410 0.62023 1.45094 ## H3 -1.4895 -2. 1.21685 0.9664 0.35000 0.01861 ## M1 0.2531 -0. -0.35016 -1.7639 -0.20189 0.60985 ## M2 0.7313 1.079749 2.39744 -0.2944 -2.09920 -0.98534 ## M3 0.3798 0. 0.95080 1.3976 -0.06154 -1.47745 ## N1 1.2253 -0. -1.90587 1.5087 -0.37623 0.01875 ## N2 1.2686 0. -0.28386 2.5384 2.44508 -1.06512 ## N3 0.8410 -0. 0.07857 -3.4175 -0.28087 2.04257 ## ## ## Site constraints (linear combinations of constraining variables) ## ## RDA1 RDA2 RDA3 RDA4 PC1 PC2 ## H1 -1.5880 0.3692 -1. -1.2108 -0.39559 -0.61280 ## H2 -1.3262 1.7883 -0.071104 1.1527 0.62023 1.45094 ## H3 -1.4864 -2.2507 1. 0.8040 0.35000 0.01861 ## M1 0.4777 -0.9880 -0. -1.8351 -0.20189 0.60985 ## M2 0.6579 0.8215 1. 0.4964 -2.09920 -0.98534 ## M3 -0.2408 0.5166 0.006138 -0.3785 -0.06154 -1.47745 ## N1 1.2080 -0.8749 -2.035604 1.8738 -0.37623 0.01875 ## N2 1.2022 0.4497 0. -0.1378 2.44508 -1.06512 ## N3 1.0956 0.1684 0. -0.7648 -0.28087 2.04257 ## ## ## Biplot scores for constraining variables ## ## RDA1 RDA2 RDA3 RDA4 PC1 PC2 ## TotalC -0.8196 -0.40984 0.33625 0.21740 0 0 ## TotalN -0.3354 0.35041 0.05323 0.87287 0 0 ## SAL -0.7938 -0.38601 -0.44072 0.16332 0 0 ## pH 0.9945 -0.07912 -0.02377 -0.06469 0 0 

原理验证

#计算拟合值排序矩阵、响应变量排序矩阵 XtX = t(water) %*% water invers = solve(XtX) fitY <- water %*% invers %*% t(water) %*% sp resY <- sp - fitY U <- eigen(cov(fitY))$vectors Ures <- eigen(cov(resY))$vectors FY <- sp %*% U ZY <- fitY %*% U NYres <- resY %*% Ures B = invers %*% t(water) %*% sp C = B %*% U 

var <- eigen(cov(fitY))$values #各个典范轴方差贡献 var 

## [1] 6.e+00 2.e+00 7.e-01 3.e-01 2.e-16 ## [6] 1.e-16 1.e-16 1.e-16 6.e-17 3.e-17 ## [11] 9.e-18 -1.e-17 -2.e-17 -6.e-17 -1.e-16 ## [16] -2.e-16 

varres <- eigen(cov(resY))$values varres 

## [1] 2.e+00 1.e+00 1.077257e+00 6.e-01 4.e-16 ## [6] 1.e-17 -9.e-18 -1.e-17 -1.e-17 -3.053562e-17 ## [11] -4.060141e-17 -4.e-17 -4.e-17 -6.e-17 -7.034357e-17 ## [16] -1.e-16