multivariate_test.Rに対応したR Notebook

第9章の内容

データの準備

まずは第8章までと同じデータを読み込む

###For chapter 09
####Preparation#####
library(vegan)

 警告:   パッケージ ‘vegan’ はバージョン 4.2.2 の R の下で造られました  要求されたパッケージ permute をロード中です 
 警告:   パッケージ ‘permute’ はバージョン 4.2.2 の R の下で造られました  要求されたパッケージ lattice をロード中です 
This is vegan 2.6-4

phyto_metadata <- readRDS("phyto_metadata.obj")
species_ryuko_data <- readRDS("phyto_ryuko_data.obj")
metadata_ecoplate <- readRDS("metadata_ecopl.obj")
summary_ecoplate <- readRDS("summary_ecopl.obj")
species_richness <- apply(species_ryuko_data > 0, 1, sum)
total_abundance <- apply(species_ryuko_data, 1, sum)

substrate_name <- c("Pyruvic-Acid-Methyl-Ester", "Tween-40", "Tween-80","alpha-Cyclodextrin", "Glycogen", "D-Cellobiose","alpha-D-Lactose", "beta-Methyl-D-Glucoside", "D-Xylose", "i-Erythritol", "D-Mannitol","N-Acetyl-D-Glucosamine", "D-Glucosaminic-Acid", "Glucose-1-Phosphate","alpha-Glycerol-Phosphate","D-Galactonic-Acid-gamma-Lactone", "D-Galacturonic-Acid", "2-Hydroxy-Benzoic-Acid", "4-Hydroxy-Benzoic-Acid", "gamma-Hydroxybutyric-Acid", "Itaconic-Acid", "alpha-Ketobutyric-Acid", "D-Malic-Acid", "L-Arginine", "L-Asparagine", "L-Phenylalanine", "L-Serine", "L-Threonine", "Glycyl-L-Glutamic-Acid", "Phenylethyl-amine", "Putrescine")

substrate_jpn <- c("Pyruvic-Acid-Methyl-Ester", "Tween-40", "Tween-80","alpha-Cyclodextrin", "Glycogen", "D-Cellobiose","alpha-D-Lactose", "beta-Methyl-D-Glucoside", "D-Xylose", "i-Erythritol", "D-Mannitol","N-Acetyl-D-Glucosamine", "D-Glucosaminic-Acid", "Glucose-1-Phosphate","alpha-Glycerol-Phosphate","D-Galactonic-Acid-gamma-Lactone", "D-Galacturonic-Acid", "2-Hydroxy-Benzoic-Acid", "4-Hydroxy-Benzoic-Acid", "gamma-Aminobutyric-acid", "Itaconic-Acid", "alpha-Ketobutyric-Acid", "D-Malic-Acid", "L-Arginine", "L-Asparagine", "L-Phenylalanine", "L-Serine", "L-Threonine", "Glycyl-L-Glutamic-Acid", "Phenylethyl-amine", "Putrescine")

9.1 一般線形モデルの多変量への拡張１：分散分析的状況

9.1.1 主座標分析による可視化の復習

####PCoA plot for ecoplate####
#With Bray-Curtis
PCoA_ecoplate_BC <- summary(capscale(summary_ecoplate ~ 1, distance = "bray"))
PCoA_ecoplate_BC

Call:
capscale(formula = summary_ecoplate ~ 1, distance = "bray") 

Partitioning of squared Bray distance:
              Inertia Proportion
Total          0.2013          1
Unconstrained  0.2013          1

Eigenvalues, and their contribution to the squared Bray distance 

Importance of components:
                         MDS1    MDS2    MDS3    MDS4
Eigenvalue            0.04957 0.02486 0.02252 0.02129
Proportion Explained  0.24622 0.12351 0.11186 0.10578
Cumulative Proportion 0.24622 0.36974 0.48159 0.58737
                         MDS5    MDS6    MDS7
Eigenvalue            0.01602 0.01508 0.01234
Proportion Explained  0.07959 0.07493 0.06129
Cumulative Proportion 0.66696 0.74189 0.80318
                          MDS8    MDS9    MDS10
Eigenvalue            0.009562 0.00738 0.006229
Proportion Explained  0.047497 0.03666 0.030940
Cumulative Proportion 0.850680 0.88734 0.918279
                         MDS11    MDS12    MDS13
Eigenvalue            0.004921 0.004402 0.003659
Proportion Explained  0.024444 0.021867 0.018174
Cumulative Proportion 0.942723 0.964590 0.982764
                         MDS14    MDS15
Eigenvalue            0.002326 0.001144
Proportion Explained  0.011552 0.005684
Cumulative Proportion 0.994316 1.000000

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:  1.463668 


Species scores

         MDS1      MDS2      MDS3       MDS4
s01 -0.178998  0.059270 -0.008570  0.0358861
s02 -0.004764  0.012586  0.086433 -0.0117237
s03 -0.006156  0.127548  0.049685  0.0701987
s04  0.203033  0.020152 -0.033316  0.1488373
s05  0.224240  0.150046  0.149323  0.0365577
s06 -0.134053  0.257353 -0.006203  0.0087516
s07  0.276641  0.192364 -0.118938 -0.0998767
s08  0.184200  0.140887  0.065420 -0.0747055
s09  0.131663  0.022282 -0.024132  0.2018923
s10  0.082577  0.079076  0.029778 -0.2166065
s11 -0.164319 -0.030079  0.019621 -0.0182591
s12 -0.168939  0.040648  0.074670  0.0613668
s13 -0.189913 -0.008663 -0.026181 -0.0891508
s14  0.091172  0.053281 -0.033246 -0.0994747
s15 -0.031125  0.056064 -0.003977  0.0072155
s16  0.011203  0.101154  0.038484  0.0160666
s17 -0.063688 -0.023309  0.151724 -0.0206044
s18  0.016602  0.029447 -0.099035 -0.0580788
s19 -0.053214  0.024721  0.073490 -0.1298941
s20  0.036197  0.025402 -0.030096 -0.0147933
s21  0.142441  0.173622  0.028680  0.0095226
s22 -0.187624  0.078854 -0.022196 -0.0024654
s23  0.103448 -0.033543  0.068378 -0.0352253
s24 -0.080816  0.080444  0.133667  0.0005663
s25 -0.119499  0.045996  0.140652  0.1255676
s26  0.001249  0.014854  0.003931  0.0810371
s27 -0.133254  0.136657 -0.091908  0.0450649
s28 -0.066374  0.040717 -0.064506  0.1489992
s29  0.018125  0.042297  0.060466 -0.0226867
s30  0.166352  0.025569  0.276883 -0.0049727
S31 -0.096508  0.060578  0.058621 -0.0623040
         MDS5      MDS6
s01 -0.092037  0.031492
s02  0.011185 -0.040732
s03  0.014781 -0.045760
s04  0.228557 -0.046743
s05  0.146320  0.067630
s06  0.119702 -0.043515
s07 -0.026077  0.006769
s08 -0.079652  0.116208
s09 -0.148448 -0.080106
s10 -0.083742 -0.077705
s11  0.045603 -0.130291
s12 -0.034276 -0.013856
s13  0.022147  0.134984
s14  0.087232 -0.062591
s15  0.014024 -0.005351
s16 -0.020134 -0.099202
s17  0.023454 -0.012349
s18 -0.025610 -0.123696
s19  0.077458 -0.030120
s20 -0.019340 -0.023050
s21 -0.038013 -0.085092
s22  0.001047 -0.115183
s23 -0.023821  0.030865
s24  0.010789  0.053673
s25  0.012933 -0.019250
s26  0.013667  0.055388
s27 -0.068280  0.010363
s28  0.001732  0.022431
s29 -0.068527 -0.024743
s30 -0.087611 -0.137081
S31  0.009606  0.093186


Site scores (weighted sums of species scores)

                MDS1      MDS2      MDS3      MDS4
20141216N1 -0.008592 -0.239562 -0.234868 -0.250282
20141216N2  0.040220 -0.112987  0.364480 -0.571420
20141216N3 -0.102752  0.111144  0.243789  0.237603
20141216T1 -0.286372 -0.465585 -0.021753 -0.004886
20141216T2  0.103280  0.357167  0.383144 -0.129988
20141216T3 -0.106103 -0.281880  0.102928 -0.079214
20150228N1  0.070741 -0.413943 -0.002145  0.001577
20150228N2  0.155105  0.297312  0.057945  0.479349
20150228N3  0.316271 -0.631556  0.187125  0.920506
20150228T1 -0.059089  0.050738  0.108821  0.152637
20150228T2 -0.137576 -0.226489  0.311168  0.169379
20150228T3  0.219018  0.263668  0.061716 -0.309201
20150507N1  0.480145  0.004244 -0.409402 -0.119220
20150507N2  0.408536 -0.078501 -0.298574 -0.193475
20150507N3 -0.167175 -0.115562  0.485164 -0.331387
20150507T1 -0.042580  0.337036 -0.083074  0.104061
20150507T2 -0.089546  0.540501  0.063262  0.228251
20150507T3 -0.691457 -0.041731 -0.538551  0.003740
20150703N1  0.480145  0.004244 -0.409402 -0.119220
20150703N2  0.408536 -0.078501 -0.298574 -0.193475
20150703N3 -0.167175 -0.115562  0.485164 -0.331387
20150703T1 -0.042580  0.337036 -0.083074  0.104061
20150703T2 -0.089546  0.540501  0.063262  0.228251
20150703T3 -0.691457 -0.041731 -0.538551  0.003740
                MDS5      MDS6
20141216N1 -0.467718  0.238779
20141216N2 -0.001568 -0.295310
20141216N3 -0.499205 -0.154280
20141216T1 -0.165944 -0.191017
20141216T2 -0.320431 -0.018240
20141216T3 -0.587989  0.778566
20150228N1  0.478652 -0.548364
20150228N2  0.139198 -0.007867
20150228N3  0.054892  0.287406
20150228T1  0.234918 -0.056880
20150228T2  0.219301 -0.318638
20150228T3  0.536709  0.598384
20150507N1 -0.224722 -0.350671
20150507N2  0.107807  0.153013
20150507N3  0.121903  0.009391
20150507T1  0.353286  0.233585
20150507T2 -0.260080 -0.203766
20150507T3  0.091398  0.002179
20150703N1 -0.224722 -0.350671
20150703N2  0.107807  0.153013
20150703N3  0.121903  0.009391
20150703T1  0.353286  0.233585
20150703T2 -0.260080 -0.203766
20150703T3  0.091398  0.002179

PCoA1_ecoplate_BC <- PCoA_ecoplate_BC$sites[,1]
PCoA2_ecoplate_BC <- PCoA_ecoplate_BC$sites[,2]
plot(
  PCoA2_ecoplate_BC ~ PCoA1_ecoplate_BC,
  cex = 3, pch = as.numeric(as.factor(metadata_ecoplate$treatment)),
  xlab = "PCoA1 (24.6 %)", ylab = "PCoA2 (12.4 %) ",
  asp = 1,
  main = "Ecoplate With Bray-Curtis"
)

9.1.2 分散分析的取り扱い

F値の計算をしてみる

####Calculate F-values####
#ブレイ・カーティス距離の計算
ecoplate_BC.d <- vegdist(summary_ecoplate, method = "bray") 
#PERMANOVAによるF値の計算
ecoplate_BC_F <- adonis(ecoplate_BC.d ~ metadata_ecoplate$treatment)$aov.tab$F.Model[1]

'adonis' will be deprecated: use 'adonis2' instead

#この観測データに基づくF値
ecoplate_BC_F

[1] 2.757547

9.1.3 ランダム並び替え検定の仕組み

図9.3用のコード

####Example of permutation####
set.seed(1235) #fix the random seed　疑似乱数列の初期化
leng <- length(metadata_ecoplate$treatment)
for(i in 1:3) {
  perm_treatment <- sample(metadata_ecoplate$treatment, leng, replace = FALSE) #shuffling the index
  F_perm <- round(adonis(ecoplate_BC.d ~ perm_treatment)$aov.tab$F.Model[1],4)
  plot(
   PCoA2_ecoplate_BC ~ PCoA1_ecoplate_BC,
   cex = 3, pch = as.numeric(as.factor(perm_treatment)),
   xlab = "PCoA1 (24.6 %)", ylab = "PCoA2 (12.4 %) ",
   asp = 1,
   main = paste("Permutation trial-", i, ": F value = ", F_perm, sep="")
  )
}

'adonis' will be deprecated: use 'adonis2' instead

'adonis' will be deprecated: use 'adonis2' instead

図9.4用のコード

ランダム並び替えから得られたF値の頻度(度数)分布

####1000 permutations
#999回ランダム並び替えを行なう
test_for_Fperm <- adonis(ecoplate_BC.d ~ metadata_ecoplate$treatment, perm = 999)

'adonis' will be deprecated: use 'adonis2' instead

#ランダム並び替えで得られたF値についてヒストグラムを描く
hist(test_for_Fperm$f.perms, main = "Frequency of permutational F-values")

#ランダム並び替えで得られたF値のうち、観測データから得られたF値以上になった回数
sum(test_for_Fperm$f.perms >= ecoplate_BC_F) # fraction with which permutational F is equal or greater than the observed F value. 

[1] 3

#P値の計算
(sum(test_for_Fperm$f.perms >= ecoplate_BC_F) + 1)/(999 + 1)

[1] 0.004

9.1.4 Permutational MANOVA (PERMANOVA)

####PERMANOVA for ecoplate data####
#ブレイ・カーティス距離を計算
ecoplate_BC.d <- vegdist(summary_ecoplate, method = "bray") #Bray-Curtis
#エコプレートデータに対するPERMANOVAの実行
ecoplate_BC_permanova <- adonis(ecoplate_BC.d ~ metadata_ecoplate$treatment, perm = 999)

'adonis' will be deprecated: use 'adonis2' instead

#PERMANOVAの結果のうち分散分析表のみ表示
ecoplate_BC_permanova$aov.tab

Permutation: free
Number of permutations: 999

Terms added sequentially (first to last)

                            Df SumsOfSqs  MeanSqs
metadata_ecoplate$treatment  1  0.022226 0.022226
Residuals                   22  0.177320 0.008060
Total                       23  0.199546         
                            F.Model      R2 Pr(>F)
metadata_ecoplate$treatment  2.7576 0.11138  0.001
Residuals                           0.88862       
Total                               1.00000       
                               
metadata_ecoplate$treatment ***
Residuals                      
Total                          
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

9.1.5 「分布に差がある」とは何か

PERMDISPで散布度(=水準内分散)の不均一性を評価(帰無仮説は水準内分散が均一)

####PERMDISP for ecoplate data####
#ブレイ・カーティス距離を計算
ecoplate_BC.d <- vegdist(summary_ecoplate, method = "bray") #Bray-Curtis
#PERMDISPによって水準内分散を評価
ecoplate_BC_var <- betadisper(ecoplate_BC.d, metadata_ecoplate$treatment)
#ランダム並び替え検定によって水準内分散の不均一性を評価
permutest(ecoplate_BC_var, perm = 999)

Permutation test for homogeneity of
multivariate dispersions
Permutation: free
Number of permutations: 999

Response: Distances
          Df    Sum Sq    Mean Sq      F N.Perm
Groups     1 0.0000391 0.00003908 0.0984    999
Residuals 22 0.0087390 0.00039723              
          Pr(>F)
Groups     0.766
Residuals       

水準ごとの水準内分散は可視化できる(すでに検定をしているので可視化しても差がない雰囲気が感じられるはず)

betadisper関数の出力を格納したオブジェクトecoplate_BC_varには、distanceという要素で、各データと水準の分布中心とのユークリッド距離が格納されている。これをメタデータmetadata_ecoplateに格納されている処理区情報(treatment)を説明要因として箱ひげ図と散布図を重ねて描く

#Visualization
#水準ごとに、分布中心と各データとの距離を箱ひげ図で描写
boxplot(
  ecoplate_BC_var$distances ~ metadata_ecoplate$treatment, #「距離 ~ 処理」というモデル式
  outline = FALSE,
  col = "white"
)
#水準ごとに、分布中心と各データとの距離を散布図で描写
stripchart(
  ecoplate_BC_var$distances ~ metadata_ecoplate$treatment, #「距離 ~ 処理」というモデル式
  method = "stack",
  pch = c(1,2),
  cex = 3,
  vertical = TRUE,
  add = TRUE
)

9.1.6 PERMDISP自体にも意味がある

####PERMDISP for phytoplankton####
#植物プランクトンデータに対する3月vs5月での水準内分散の比較
#ブレイ・カーティス距離を計算：3月と5月のデータのみ使用
ryuko_BC.d <- vegdist(species_ryuko_data[c(1,2,13,14,15),], method = "bray") #Bray-Curtis
#水準内分散の比較を実行
ryuko_BC_var <- betadisper(ryuko_BC.d, phyto_metadata$month[c(1,2,13,14,15)])
#ランダム並び替え検定
permutest(ryuko_BC_var)

'nperm' >= set of all permutations: complete enumeration.
Set of permutations < 'minperm'. Generating entire set.

Permutation test for homogeneity of
multivariate dispersions
Permutation: free
Number of permutations: 119

Response: Distances
          Df   Sum Sq   Mean Sq      F N.Perm
Groups     1 0.022343 0.0223434 41.046    119
Residuals  3 0.001633 0.0005443              
            Pr(>F)   
Groups    0.008333 **
Residuals            
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

水準内分散の可視化

#Visualization
boxplot(
  ryuko_BC_var$distances ~ phyto_metadata$month[c(1,2,13,14,15)], #3月と5月のデータのみ使用
  outline = FALSE,
  col = "white",
  xlab = "Month(月)", ylab = "distance to center(分布中心への距離)"
)
stripchart(
  ryuko_BC_var$distances ~ phyto_metadata$month[c(1,2,13,14,15)],
  method = "stack",
  pch = c(1,2),
  cex = 3,
  vertical = TRUE,
  add = TRUE
)

9.2 一般線形モデルの多変量への拡張２：回帰分析的状況

9.2.2 冗長性分析（RDA）のためのＲコーディング

植物プランクトンデータに対する冗長性分析

####RDA for phytoplankton
#説明要因はメタデータから持ってくる。温度・総個体数・種数
phyto.rda <- rda(species_ryuko_data ~ phyto_metadata$temp + total_abundance + species_richness)
#結果の表示
summary(phyto.rda)

Call:
rda(formula = species_ryuko_data ~ phyto_metadata$temp + total_abundance +      species_richness) 

Partitioning of variance:
              Inertia Proportion
Total           32768     1.0000
Constrained     17548     0.5355
Unconstrained   15220     0.4645

Eigenvalues, and their contribution to the variance 

Importance of components:
                           RDA1      RDA2      RDA3
Eigenvalue            1.511e+04 2.202e+03 2.378e+02
Proportion Explained  4.611e-01 6.721e-02 7.256e-03
Cumulative Proportion 4.611e-01 5.283e-01 5.355e-01
                            PC1       PC2       PC3
Eigenvalue            1.229e+04 1.444e+03 373.27542
Proportion Explained  3.752e-01 4.406e-02   0.01139
Cumulative Proportion 9.107e-01 9.548e-01   0.96617
                            PC4       PC5       PC6
Eigenvalue            3.214e+02 2.185e+02 1.693e+02
Proportion Explained  9.809e-03 6.669e-03 5.166e-03
Cumulative Proportion 9.760e-01 9.826e-01 9.878e-01
                            PC7       PC8       PC9
Eigenvalue            1.438e+02 1.175e+02 77.376067
Proportion Explained  4.387e-03 3.586e-03  0.002361
Cumulative Proportion 9.922e-01 9.958e-01  0.998145
                           PC10      PC11
Eigenvalue            34.692727 2.609e+01
Proportion Explained   0.001059 7.962e-04
Cumulative Proportion  0.999204 1.000e+00

Accumulated constrained eigenvalues
Importance of components:
                           RDA1      RDA2      RDA3
Eigenvalue            15108.403 2202.2966 237.75500
Proportion Explained      0.861    0.1255   0.01355
Cumulative Proportion     0.861    0.9865   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:  26.02529 


Species scores

                                             RDA1
Acanthoceras sp.                        0.0810808
Acanthoceras zachariasii               -0.0874744
Actinastrum hantzschii                  0.0218192
Anabaena affinis                        0.1533640
Anabaena flos-aquae                     0.0183610
Anabaena macrospora                     0.0457854
Anabaena spiroides                      0.0679164
Ankistrodesmus sp.                      0.0204222
Aphanizomenon flos-aquae                0.0464171
Aphanocapsa sp.                         0.0454530
Aphanothece sp.                        -0.0062952
Asterionella formosa                   -1.9771577
Asterionella sp.                       -0.0550005
Aulacoseira ambigua                     0.5995809
Aulacoseira distans                    -0.0517502
Aulacoseira granulata                   1.1083039
Aulacoseira nipponica                  -0.0058615
Aulacoseira sp.                        -0.4337952
Botryococcus braunii                    0.2545611
Botryococcus sp.                        0.0576836
Ceratium hirundinella                  -0.0785802
Ceratium sp.                            0.0647994
Chlamydomonas sp.                      -0.0165599
Chlorogonium elongatum                  0.0678302
Chroococcus dispersus                  -0.2608089
Chroococcus sp.                        -0.1249244
Cladophora glomerata                   -0.0829065
Cladophora sp.                         -0.0085605
Closterium aciculare                   -0.1313103
Closterium aciculare var.subponum       0.0721045
Closterium moniliferum                 -0.0315432
Cocconeis placentula                   -0.0846041
Coelastrum cambricum                    0.3387965
Coelastrum microporum                   0.2932924
Coelosphaerium kuetzingianum            0.0140617
Coelosphaerium sp.                     -0.0610253
Cosmarium sp.                           0.1320981
Cosmocladium constrictum                0.1572699
Crucigenia lauterbornei                 0.3605225
Crucigenia lauterbornii                -0.0062952
Cryptomonas sp.                         0.0934310
Cyclotella meneghiniana                 0.0461326
Cyclotella sp.                          0.0203337
Cymbella sp.                            0.0160194
Diatoma vulgare                        -0.0055987
Dictyosphaerium sp.                    -0.0075953
Dinobryon cylindricum                  -0.1826741
Dinobryon sp.                          -0.0075953
Diploneis sp.                           0.5466149
Elakatothrix gelatinosa                 0.0400990
Eudorina sp.                           -0.0082800
Euglena proxima                         0.1582888
Euglena sp.                            -0.0200224
Fragilaria crotonensis                 -0.2503452
Frustulia sp.                          -0.0029356
Gloeocystis sp.                        -0.0085605
Gonium sp.                              0.0091571
Gyrosigma sp.                          -0.0171211
Hydrodictyon sp.                        0.0185141
Lyngbya limnetica                      -0.0428219
Melosira sp.                           -0.0510537
Melosira varians                       -0.1543423
Merismopedia sp.                       -0.0029356
Micrasterias hardyi                     2.8581305
Micrasterias mahabuleshwarensis         0.4322486
Microcystis aeruginosa                  0.7652747
Microcystis ichthyoblabe                0.3293312
Microcystis novacekii                   0.4941288
Microcystis sp.                        -0.1682716
Microcystis viridis                     0.0992466
Microcystis wesenbergii                -0.2230455
Mougeotia sp.                           0.3042563
Navicula sp.                           -0.0143459
Nitzschia sp.                          -0.1488285
Oedogonium sp.                          1.0141856
Oocystis lacustris                      0.0184141
Oscillatoria kawamurae                 -0.0099936
Oscillatoria sp.                       -0.0428027
Oscillatoria tenuis                     0.0824136
Paulschulzia pseudovolvox               0.3936393
Pediastrum biwae                        0.1960263
Pediastrum boryanum                     0.0114853
Pediastrum duplex                       0.0379989
Peridinium sp.                          0.0947093
Phormidium tenue                       -0.0306223
Pleodorina californica                  0.1166996
Pleurotaenium sp.                       0.0915707
Rhoicosphenia abbreviata               -0.0049968
Scenedesmus opoliensis                 -0.0382357
Schroederia ancora                      0.0183141
Sphaerocystis schroeteri                0.3475554
Spirogyra sp.                           0.4740448
Spondylosium moniliforme                0.1260458
Staurastrum arctiscon                   0.0017542
Staurastrum dorsidentiferum            16.3074957
Staurastrum dorsidentiferum var.ornatu  5.1771037
Staurastrum sebaldi                     0.3873828
Staurastrum sp.                        -0.0657092
Stauroneis sp.                         -0.0125905
Stephanodiscus sp.                     -0.0293077
Stephanodiscus suzukii                  0.9467457
Surirella sp.                           0.0140395
Synedra sp.                            -0.4554816
Synedra ulna                            0.3507234
Tabellaria sp.                          0.0721045
Tetraedron gracile                     -0.0009774
Tetraedron sp.                          0.1007278
Tetraselmis cordiformis                 0.0185141
Tetraspora lacustris                    0.1365863
Tetraspora sp.                          0.0144209
Trachelomonas hispida                  -0.1291417
Trachelomonas sp.                       0.2509616
Treubaria setigerum                    -0.0049968
Ulothrix zonata                         0.2569976
Uroglena americana                      0.0690937
Uroglena sp.                           -0.2653769
Xanthidium hastiferum                   0.0600797
Xanthidium sp.                          0.0144209
                                            RDA2
Acanthoceras sp.                        0.124280
Acanthoceras zachariasii               -0.003359
Actinastrum hantzschii                  0.119696
Anabaena affinis                        0.088270
Anabaena flos-aquae                    -0.004012
Anabaena macrospora                     0.060085
Anabaena spiroides                      0.045520
Ankistrodesmus sp.                     -0.021031
Aphanizomenon flos-aquae                0.011820
Aphanocapsa sp.                        -0.027985
Aphanothece sp.                         0.001277
Asterionella formosa                   -2.532434
Asterionella sp.                       -0.020758
Aulacoseira ambigua                     0.388171
Aulacoseira distans                     0.066733
Aulacoseira granulata                  -0.720479
Aulacoseira nipponica                  -0.006245
Aulacoseira sp.                        -0.303675
Botryococcus braunii                    0.387385
Botryococcus sp.                       -0.059501
Ceratium hirundinella                   0.135690
Ceratium sp.                            0.161839
Chlamydomonas sp.                      -0.004822
Chlorogonium elongatum                  0.028361
Chroococcus dispersus                   0.005372
Chroococcus sp.                        -0.042459
Cladophora glomerata                   -0.114532
Cladophora sp.                         -0.012032
Closterium aciculare                   -0.058631
Closterium aciculare var.subponum      -0.074376
Closterium moniliferum                 -0.042340
Cocconeis placentula                   -0.037908
Coelastrum cambricum                   -0.120791
Coelastrum microporum                  -0.202688
Coelosphaerium kuetzingianum           -0.071521
Coelosphaerium sp.                     -0.065762
Cosmarium sp.                           0.029894
Cosmocladium constrictum                0.381936
Crucigenia lauterbornei                -0.371882
Crucigenia lauterbornii                 0.001277
Cryptomonas sp.                        -0.039320
Cyclotella meneghiniana                 0.003602
Cyclotella sp.                         -0.055839
Cymbella sp.                            0.107382
Diatoma vulgare                         0.012365
Dictyosphaerium sp.                     0.004497
Dinobryon cylindricum                  -0.220281
Dinobryon sp.                           0.004497
Diploneis sp.                          -0.456403
Elakatothrix gelatinosa                -0.078235
Eudorina sp.                           -0.002411
Euglena proxima                        -0.130327
Euglena sp.                            -0.047213
Fragilaria crotonensis                 -0.100090
Frustulia sp.                          -0.011201
Gloeocystis sp.                        -0.012032
Gonium sp.                              0.012017
Gyrosigma sp.                          -0.024064
Hydrodictyon sp.                        0.046240
Lyngbya limnetica                       0.059427
Melosira sp.                           -0.009153
Melosira varians                        0.108879
Merismopedia sp.                       -0.011201
Micrasterias hardyi                    -1.466713
Micrasterias mahabuleshwarensis         0.592610
Microcystis aeruginosa                 -0.763646
Microcystis ichthyoblabe               -0.179492
Microcystis novacekii                  -0.308023
Microcystis sp.                        -0.105136
Microcystis viridis                     0.412991
Microcystis wesenbergii                -0.160981
Mougeotia sp.                          -0.199156
Navicula sp.                            0.004182
Nitzschia sp.                          -0.037117
Oedogonium sp.                         -0.369360
Oocystis lacustris                      0.035137
Oscillatoria kawamurae                  0.011635
Oscillatoria sp.                       -0.060160
Oscillatoria tenuis                     0.108154
Paulschulzia pseudovolvox              -0.106667
Pediastrum biwae                       -0.002654
Pediastrum boryanum                    -0.026076
Pediastrum duplex                      -0.017733
Peridinium sp.                          0.263447
Phormidium tenue                       -0.024693
Pleodorina californica                  0.280702
Pleurotaenium sp.                       0.120171
Rhoicosphenia abbreviata                0.005818
Scenedesmus opoliensis                 -0.014415
Schroederia ancora                      0.024034
Sphaerocystis schroeteri                0.268200
Spirogyra sp.                          -0.493633
Spondylosium moniliforme               -0.026030
Staurastrum arctiscon                   0.019212
Staurastrum dorsidentiferum             1.736743
Staurastrum dorsidentiferum var.ornatu -5.340223
Staurastrum sebaldi                     1.106543
Staurastrum sp.                        -0.068009
Stauroneis sp.                          0.002555
Stephanodiscus sp.                     -0.031223
Stephanodiscus suzukii                 -0.391459
Surirella sp.                           0.009429
Synedra sp.                             0.194643
Synedra ulna                            0.223901
Tabellaria sp.                         -0.074376
Tetraedron gracile                     -0.008158
Tetraedron sp.                          0.132188
Tetraselmis cordiformis                 0.046240
Tetraspora lacustris                    0.234824
Tetraspora sp.                         -0.014875
Trachelomonas hispida                  -0.178106
Trachelomonas sp.                       0.005479
Treubaria setigerum                     0.005818
Ulothrix zonata                        -0.154116
Uroglena americana                     -0.059928
Uroglena sp.                           -0.372991
Xanthidium hastiferum                  -0.017855
Xanthidium sp.                         -0.014875
                                             RDA3
Acanthoceras sp.                       -0.1967463
Acanthoceras zachariasii                0.1467576
Actinastrum hantzschii                 -0.0235380
Anabaena affinis                       -0.1663991
Anabaena flos-aquae                     0.0019476
Anabaena macrospora                    -0.0903388
Anabaena spiroides                     -0.1725394
Ankistrodesmus sp.                      0.0024588
Aphanizomenon flos-aquae                0.0767387
Aphanocapsa sp.                        -0.0658231
Aphanothece sp.                        -0.0112763
Asterionella formosa                   -1.2401428
Asterionella sp.                       -0.1303575
Aulacoseira ambigua                    -0.1094193
Aulacoseira distans                    -0.0202574
Aulacoseira granulata                   0.0221898
Aulacoseira nipponica                  -0.0019006
Aulacoseira sp.                         0.3898260
Botryococcus braunii                   -0.0499241
Botryococcus sp.                        0.0055406
Ceratium hirundinella                  -0.1718021
Ceratium sp.                           -0.0008463
Chlamydomonas sp.                       0.0218107
Chlorogonium elongatum                  0.0939633
Chroococcus dispersus                  -0.2264094
Chroococcus sp.                         0.1719481
Cladophora glomerata                   -0.1933865
Cladophora sp.                         -0.0212762
Closterium aciculare                   -0.8180448
Closterium aciculare var.subponum       0.0069258
Closterium moniliferum                 -0.0657292
Cocconeis placentula                   -0.1753156
Coelastrum cambricum                    0.0254716
Coelastrum microporum                   0.0203372
Coelosphaerium kuetzingianum           -0.0492130
Coelosphaerium sp.                      0.1583709
Cosmarium sp.                          -0.0878108
Cosmocladium constrictum               -0.0200022
Crucigenia lauterbornei                 0.0346288
Crucigenia lauterbornii                -0.0112763
Cryptomonas sp.                         0.0044976
Cyclotella meneghiniana                 0.0301180
Cyclotella sp.                         -0.0040192
Cymbella sp.                           -0.0051974
Diatoma vulgare                        -0.0326734
Dictyosphaerium sp.                     0.0085321
Dinobryon cylindricum                  -0.0315180
Dinobryon sp.                           0.0085321
Diploneis sp.                           0.0620733
Elakatothrix gelatinosa                -0.0001612
Eudorina sp.                            0.0109053
Euglena proxima                        -0.0202597
Euglena sp.                             0.0162429
Fragilaria crotonensis                 -0.1560006
Frustulia sp.                           0.0013344
Gloeocystis sp.                        -0.0212762
Gonium sp.                             -0.0180678
Gyrosigma sp.                          -0.0425524
Hydrodictyon sp.                       -0.0002418
Lyngbya limnetica                       0.0258592
Melosira sp.                            0.0572307
Melosira varians                       -0.2276395
Merismopedia sp.                        0.0013344
Micrasterias hardyi                     0.1700538
Micrasterias mahabuleshwarensis         0.2945234
Microcystis aeruginosa                  0.1316849
Microcystis ichthyoblabe                0.5159448
Microcystis novacekii                  -0.3447477
Microcystis sp.                         0.2687888
Microcystis viridis                    -0.3784125
Microcystis wesenbergii                -0.1437617
Mougeotia sp.                          -0.0070603
Navicula sp.                            0.0126489
Nitzschia sp.                           0.1220070
Oedogonium sp.                         -0.1839184
Oocystis lacustris                     -0.0181887
Oscillatoria kawamurae                  0.0016464
Oscillatoria sp.                       -0.1063810
Oscillatoria tenuis                    -0.1626099
Paulschulzia pseudovolvox               0.0248616
Pediastrum biwae                        0.0063370
Pediastrum boryanum                     0.0027195
Pediastrum duplex                      -0.0152975
Peridinium sp.                         -0.0032995
Phormidium tenue                       -0.0343188
Pleodorina californica                 -0.1499478
Pleurotaenium sp.                      -0.1806777
Rhoicosphenia abbreviata                0.0008232
Scenedesmus opoliensis                  0.0627722
Schroederia ancora                     -0.0361355
Sphaerocystis schroeteri                0.3234352
Spirogyra sp.                          -0.0716592
Spondylosium moniliforme                0.0055011
Staurastrum arctiscon                  -0.0143249
Staurastrum dorsidentiferum            -0.3540036
Staurastrum dorsidentiferum var.ornatu  0.4972689
Staurastrum sebaldi                     0.2380237
Staurastrum sp.                        -0.1150084
Stauroneis sp.                         -0.0225527
Stephanodiscus sp.                     -0.0095030
Stephanodiscus suzukii                  0.0184469
Surirella sp.                           0.0552921
Synedra sp.                             0.0890496
Synedra ulna                            0.0717135
Tabellaria sp.                          0.0069258
Tetraedron gracile                      0.0103209
Tetraedron sp.                         -0.1987454
Tetraselmis cordiformis                -0.0002418
Tetraspora lacustris                    0.1088890
Tetraspora sp.                          0.0013852
Trachelomonas hispida                  -0.2141867
Trachelomonas sp.                      -0.1174791
Treubaria setigerum                     0.0008232
Ulothrix zonata                        -0.2077116
Uroglena americana                      0.0488723
Uroglena sp.                           -0.6595624
Xanthidium hastiferum                   0.0050196
Xanthidium sp.                          0.0013852
                                              PC1
Acanthoceras sp.                       -7.666e-02
Acanthoceras zachariasii               -5.338e-02
Actinastrum hantzschii                  1.531e-02
Anabaena affinis                       -9.311e-02
Anabaena flos-aquae                    -1.710e-02
Anabaena macrospora                    -1.490e-02
Anabaena spiroides                     -5.755e-02
Ankistrodesmus sp.                     -2.298e-02
Aphanizomenon flos-aquae               -4.410e-02
Aphanocapsa sp.                        -7.367e-02
Aphanothece sp.                         1.082e-03
Asterionella formosa                   -8.099e-01
Asterionella sp.                       -1.501e-02
Aulacoseira ambigua                    -3.611e-01
Aulacoseira distans                    -3.507e-02
Aulacoseira granulata                  -9.654e-01
Aulacoseira nipponica                  -2.109e-03
Aulacoseira sp.                        -1.143e-01
Botryococcus braunii                   -2.083e-01
Botryococcus sp.                        1.210e-01
Ceratium hirundinella                   5.278e-01
Ceratium sp.                            4.879e-02
Chlamydomonas sp.                      -7.087e-03
Chlorogonium elongatum                 -4.653e-02
Chroococcus dispersus                  -5.015e-02
Chroococcus sp.                        -1.789e-02
Cladophora glomerata                   -3.950e-02
Cladophora sp.                         -4.155e-03
Closterium aciculare                   -1.080e-01
Closterium aciculare var.subponum       1.512e-01
Closterium moniliferum                 -1.457e-02
Cocconeis placentula                   -7.965e-03
Coelastrum cambricum                    6.234e-01
Coelastrum microporum                   1.328e-01
Coelosphaerium kuetzingianum           -1.395e-01
Coelosphaerium sp.                      4.444e-02
Cosmarium sp.                          -9.166e-02
Cosmocladium constrictum                1.085e-01
Crucigenia lauterbornei                 7.561e-01
Crucigenia lauterbornii                 1.082e-03
Cryptomonas sp.                        -7.967e-02
Cyclotella meneghiniana                -3.878e-02
Cyclotella sp.                         -5.133e-02
Cymbella sp.                            3.214e-02
Diatoma vulgare                         3.898e-03
Dictyosphaerium sp.                     2.592e-04
Dinobryon cylindricum                  -8.512e-02
Dinobryon sp.                           2.592e-04
Diploneis sp.                           6.275e-01
Elakatothrix gelatinosa                 1.146e-01
Eudorina sp.                           -3.543e-03
Euglena proxima                         9.266e-02
Euglena sp.                            -1.578e-02
Fragilaria crotonensis                 -3.558e-02
Frustulia sp.                          -3.058e-03
Gloeocystis sp.                        -4.155e-03
Gonium sp.                             -2.981e-03
Gyrosigma sp.                          -8.309e-03
Hydrodictyon sp.                        1.394e-02
Lyngbya limnetica                       2.160e-01
Melosira sp.                           -2.704e-02
Melosira varians                        8.026e-03
Merismopedia sp.                       -3.058e-03
Micrasterias hardyi                     1.504e+00
Micrasterias mahabuleshwarensis        -2.412e-02
Microcystis aeruginosa                 -1.255e+00
Microcystis ichthyoblabe               -6.944e-01
Microcystis novacekii                  -6.047e-01
Microcystis sp.                        -3.951e-02
Microcystis viridis                    -1.199e-01
Microcystis wesenbergii                -1.128e-01
Mougeotia sp.                           5.212e-01
Navicula sp.                           -2.792e-04
Nitzschia sp.                          -1.620e-02
Oedogonium sp.                          3.003e-01
Oocystis lacustris                      3.990e-03
Oscillatoria kawamurae                  5.634e-03
Oscillatoria sp.                       -2.077e-02
Oscillatoria tenuis                    -2.683e-02
Paulschulzia pseudovolvox               7.671e-01
Pediastrum biwae                       -6.760e-02
Pediastrum boryanum                     2.719e-02
Pediastrum duplex                       5.751e-02
Peridinium sp.                          7.959e-02
Phormidium tenue                       -9.386e-03
Pleodorina californica                  9.920e-02
Pleurotaenium sp.                      -2.981e-02
Rhoicosphenia abbreviata                2.817e-03
Scenedesmus opoliensis                 -8.891e-03
Schroederia ancora                     -5.962e-03
Sphaerocystis schroeteri               -5.346e-02
Spirogyra sp.                           1.075e+00
Spondylosium moniliforme               -9.262e-02
Staurastrum arctiscon                  -1.305e-02
Staurastrum dorsidentiferum            -1.117e+01
Staurastrum dorsidentiferum var.ornatu  1.086e+01
Staurastrum sebaldi                     3.714e-01
Staurastrum sp.                        -2.521e-02
Stauroneis sp.                          2.163e-03
Stephanodiscus sp.                     -1.055e-02
Stephanodiscus suzukii                 -8.188e-01
Surirella sp.                          -2.402e-02
Synedra sp.                             1.243e-01
Synedra ulna                            2.402e-01
Tabellaria sp.                          1.512e-01
Tetraedron gracile                      2.961e-02
Tetraedron sp.                         -3.279e-02
Tetraselmis cordiformis                 1.394e-02
Tetraspora lacustris                    1.104e-02
Tetraspora sp.                          3.024e-02
Trachelomonas hispida                  -6.615e-02
Trachelomonas sp.                      -1.802e-01
Treubaria setigerum                     2.817e-03
Ulothrix zonata                        -2.800e-01
Uroglena americana                     -1.162e-01
Uroglena sp.                           -1.288e-01
Xanthidium hastiferum                  -5.412e-02
Xanthidium sp.                          3.024e-02
                                             PC2
Acanthoceras sp.                        0.024417
Acanthoceras zachariasii                0.146596
Actinastrum hantzschii                 -0.005552
Anabaena affinis                        0.099726
Anabaena flos-aquae                     0.004886
Anabaena macrospora                     0.035811
Anabaena spiroides                      0.073394
Ankistrodesmus sp.                     -0.023959
Aphanizomenon flos-aquae               -0.008119
Aphanocapsa sp.                         0.052663
Aphanothece sp.                         0.004882
Asterionella formosa                   -4.049320
Asterionella sp.                        0.033050
Aulacoseira ambigua                    -0.021426
Aulacoseira distans                    -0.131049
Aulacoseira granulata                  -1.033427
Aulacoseira nipponica                  -0.005601
Aulacoseira sp.                        -0.228051
Botryococcus braunii                    0.012727
Botryococcus sp.                        0.020591
Ceratium hirundinella                   0.244876
Ceratium sp.                           -0.100682
Chlamydomonas sp.                       0.027624
Chlorogonium elongatum                  0.003598
Chroococcus dispersus                  -0.049805
Chroococcus sp.                         0.096535
Cladophora glomerata                    0.006669
Cladophora sp.                          0.001363
Closterium aciculare                   -0.078208
Closterium aciculare var.subponum       0.025738
Closterium moniliferum                 -0.001511
Cocconeis placentula                    0.044512
Coelastrum cambricum                   -0.002876
Coelastrum microporum                   0.079679
Coelosphaerium kuetzingianum            0.083504
Coelosphaerium sp.                      0.079712
Cosmarium sp.                           0.061225
Cosmocladium constrictum               -0.222968
Crucigenia lauterbornei                 0.128692
Crucigenia lauterbornii                 0.004882
Cryptomonas sp.                         0.019057
Cyclotella meneghiniana                 0.011189
Cyclotella sp.                         -0.041600
Cymbella sp.                           -0.043631
Diatoma vulgare                        -0.008137
Dictyosphaerium sp.                     0.002662
Dinobryon cylindricum                  -0.427910
Dinobryon sp.                           0.002662
Diploneis sp.                           0.177278
Elakatothrix gelatinosa                 0.003787
Eudorina sp.                            0.013812
Euglena proxima                         0.065898
Euglena sp.                            -0.101081
Fragilaria crotonensis                 -0.086013
Frustulia sp.                          -0.028723
Gloeocystis sp.                         0.001363
Gonium sp.                              0.007162
Gyrosigma sp.                           0.002727
Hydrodictyon sp.                       -0.028766
Lyngbya limnetica                       0.028545
Melosira sp.                            0.063974
Melosira varians                        0.034337
Merismopedia sp.                       -0.028723
Micrasterias hardyi                     0.504731
Micrasterias mahabuleshwarensis        -0.280548
Microcystis aeruginosa                 -1.039876
Microcystis ichthyoblabe                0.713614
Microcystis novacekii                   0.238273
Microcystis sp.                        -0.003063
Microcystis viridis                     0.222197
Microcystis wesenbergii                -0.030829
Mougeotia sp.                           0.218846
Navicula sp.                           -0.001202
Nitzschia sp.                           0.234353
Oedogonium sp.                          0.227804
Oocystis lacustris                     -0.007221
Oscillatoria kawamurae                  0.000244
Oscillatoria sp.                        0.006817
Oscillatoria tenuis                     0.064459
Paulschulzia pseudovolvox               0.008019
Pediastrum biwae                        0.052319
Pediastrum boryanum                    -0.023576
Pediastrum duplex                       0.017457
Peridinium sp.                         -0.151857
Phormidium tenue                       -0.005001
Pleodorina californica                 -0.149888
Pleurotaenium sp.                       0.071621
Rhoicosphenia abbreviata                0.000122
Scenedesmus opoliensis                  0.036951
Schroederia ancora                      0.014324
Sphaerocystis schroeteri               -0.088621
Spirogyra sp.                           0.212981
Spondylosium moniliforme                0.009438
Staurastrum arctiscon                   0.041949
Staurastrum dorsidentiferum             2.329495
Staurastrum dorsidentiferum var.ornatu  1.848012
Staurastrum sebaldi                    -0.724072
Staurastrum sp.                         0.006979
Stauroneis sp.                          0.009765
Stephanodiscus sp.                     -0.028007
Stephanodiscus suzukii                  0.218046
Surirella sp.                           0.011490
Synedra sp.                             0.103689
Synedra ulna                           -0.083244
Tabellaria sp.                          0.025738
Tetraedron gracile                      0.025317
Tetraedron sp.                          0.078783
Tetraselmis cordiformis                -0.028766
Tetraspora lacustris                   -0.110587
Tetraspora sp.                          0.005148
Trachelomonas hispida                  -0.220740
Trachelomonas sp.                       0.088249
Treubaria setigerum                     0.000122
Ulothrix zonata                         0.095364
Uroglena americana                      0.097765
Uroglena sp.                            0.042266
Xanthidium hastiferum                   0.014537
Xanthidium sp.                          0.005148
                                              PC3
Acanthoceras sp.                       -0.2603377
Acanthoceras zachariasii               -0.0126215
Actinastrum hantzschii                  0.0378594
Anabaena affinis                       -0.1398848
Anabaena flos-aquae                     0.0123645
Anabaena macrospora                    -0.0884272
Anabaena spiroides                     -0.0229862
Ankistrodesmus sp.                      0.0051128
Aphanizomenon flos-aquae               -0.0831929
Aphanocapsa sp.                         0.1010231
Aphanothece sp.                         0.0157049
Asterionella formosa                   -0.9700877
Asterionella sp.                       -0.0268756
Aulacoseira ambigua                     0.1922222
Aulacoseira distans                     0.0569687
Aulacoseira granulata                  -0.1884073
Aulacoseira nipponica                   0.0030606
Aulacoseira sp.                         0.1311848
Botryococcus braunii                   -0.1734092
Botryococcus sp.                       -0.0071872
Ceratium hirundinella                   0.1317886
Ceratium sp.                            0.1118446
Chlamydomonas sp.                       0.0104458
Chlorogonium elongatum                 -0.1041998
Chroococcus dispersus                  -0.0397579
Chroococcus sp.                         0.1582752
Cladophora glomerata                   -0.0046590
Cladophora sp.                         -0.0008577
Closterium aciculare                   -0.0325166
Closterium aciculare var.subponum      -0.0089840
Closterium moniliferum                  0.0004874
Cocconeis placentula                    0.1222086
Coelastrum cambricum                    0.0777053
Coelastrum microporum                   0.0579042
Coelosphaerium kuetzingianum            0.2018743
Coelosphaerium sp.                      0.0978987
Cosmarium sp.                          -0.0477322
Cosmocladium constrictum                0.2379593
Crucigenia lauterbornei                -0.0449201
Crucigenia lauterbornii                 0.0157049
Cryptomonas sp.                         0.0423288
Cyclotella meneghiniana                -0.0183699
Cyclotella sp.                          0.0279374
Cymbella sp.                            0.0665321
Diatoma vulgare                         0.0308250
Dictyosphaerium sp.                    -0.0114501
Dinobryon cylindricum                  -0.0867596
Dinobryon sp.                          -0.0114501
Diploneis sp.                           0.0150405
Elakatothrix gelatinosa                 0.0019946
Eudorina sp.                            0.0052229
Euglena proxima                         0.0116791
Euglena sp.                            -0.0166546
Fragilaria crotonensis                 -0.0375323
Frustulia sp.                          -0.0054694
Gloeocystis sp.                        -0.0008577
Gonium sp.                             -0.0176854
Gyrosigma sp.                          -0.0017155
Hydrodictyon sp.                        0.0319556
Lyngbya limnetica                       0.0320094
Melosira sp.                           -0.0032676
Melosira varians                        0.2845981
Merismopedia sp.                       -0.0054694
Micrasterias hardyi                    -1.3585825
Micrasterias mahabuleshwarensis        -0.0533693
Microcystis aeruginosa                  0.3546586
Microcystis ichthyoblabe                0.8632504
Microcystis novacekii                   0.8131706
Microcystis sp.                         0.1402668
Microcystis viridis                    -0.4579031
Microcystis wesenbergii                -0.0468157
Mougeotia sp.                          -0.0865642
Navicula sp.                           -0.0184596
Nitzschia sp.                           0.1307230
Oedogonium sp.                          0.1166921
Oocystis lacustris                     -0.0017076
Oscillatoria kawamurae                  0.0035646
Oscillatoria sp.                       -0.0042887
Oscillatoria tenuis                    -0.1591689
Paulschulzia pseudovolvox               0.0975721
Pediastrum biwae                        0.0776398
Pediastrum boryanum                    -0.0072662
Pediastrum duplex                      -0.0212790
Peridinium sp.                          0.1741219
Phormidium tenue                       -0.0157343
Pleodorina californica                  0.1669146
Pleurotaenium sp.                      -0.1768543
Rhoicosphenia abbreviata                0.0017823
Scenedesmus opoliensis                  0.0390537
Schroederia ancora                     -0.0353709
Sphaerocystis schroeteri               -0.2726082
Spirogyra sp.                          -0.1043130
Spondylosium moniliforme                0.0688888
Staurastrum arctiscon                  -0.0249251
Staurastrum dorsidentiferum            -0.8482534
Staurastrum dorsidentiferum var.ornatu -0.6450525
Staurastrum sebaldi                     0.9663954
Staurastrum sp.                        -0.0236059
Stauroneis sp.                          0.0314099
Stephanodiscus sp.                      0.0153030
Stephanodiscus suzukii                  0.4560524
Surirella sp.                          -0.0464436
Synedra sp.                             0.1236644
Synedra ulna                           -0.0582173
Tabellaria sp.                         -0.0089840
Tetraedron gracile                      0.0017922
Tetraedron sp.                         -0.1945397
Tetraselmis cordiformis                 0.0319556
Tetraspora lacustris                    0.0140838
Tetraspora sp.                         -0.0017968
Trachelomonas hispida                   0.0126148
Trachelomonas sp.                      -0.0391404
Treubaria setigerum                     0.0017823
Ulothrix zonata                         0.0502406
Uroglena americana                      0.0947304
Uroglena sp.                           -0.0265896
Xanthidium hastiferum                   0.0353113
Xanthidium sp.                         -0.0017968


Site scores (weighted sums of species scores)

                       RDA1     RDA2    RDA3      PC1
20180316_1_ryuko.csv -4.687   2.2969  13.612  -0.9055
20180316_2_ryuko.csv -3.061   2.9228  13.046  -2.4000
20181004_1_ryuko.csv  8.422  10.2952 -14.160  -2.0190
20181004_2_ryuko.csv  2.152   8.7569   3.112   4.7213
20181004_3_ryuko.csv 21.436  16.2893 -23.449 -13.4908
20181025_1_ryuko.csv  8.618  10.4983  -3.611  -4.5025
20181025_2_ryuko.csv  2.540 -44.4094  48.290  20.4843
20190425_1_ryuko.csv -4.558  -2.3752 -22.362  -2.8140
20190425_2_ryuko.csv -4.386  -6.8553 -22.802  -2.0713
20190425_3_ryuko.csv -4.424  -1.3355  -3.859  -0.3647
20190425_4_ryuko.csv -4.398  -1.2240  -5.885  -1.4285
20190425_5_ryuko.csv -4.029   0.4231   4.521   0.1756
20190520_1_ryuko.csv -4.548   1.0262   2.953   0.7326
20190520_2_ryuko.csv -4.503   2.0061   7.498   1.9744
20190520_3_ryuko.csv -4.575   1.6845   3.096   1.9080
                           PC2     PC3
20180316_1_ryuko.csv   3.91808   5.729
20180316_2_ryuko.csv   9.35525   3.538
20181004_1_ryuko.csv   4.85103 -11.979
20181004_2_ryuko.csv  -9.74191  10.822
20181004_3_ryuko.csv   3.22690   7.167
20181025_1_ryuko.csv   0.34815 -10.082
20181025_2_ryuko.csv   3.48660  -1.217
20190425_1_ryuko.csv   0.92347  -0.581
20190425_2_ryuko.csv -19.45477  -3.704
20190425_3_ryuko.csv  -2.61717  -4.748
20190425_4_ryuko.csv  -3.79391   2.073
20190425_5_ryuko.csv   1.80318  -7.755
20190520_1_ryuko.csv   3.30687  10.637
20190520_2_ryuko.csv   4.30560  -1.107
20190520_3_ryuko.csv   0.08264   1.207


Site constraints (linear combinations of constraining variables)

                       RDA1     RDA2      RDA3
20180316_1_ryuko.csv -5.072  -2.0326   8.78256
20180316_2_ryuko.csv -5.608  -1.6331   7.38635
20181004_1_ryuko.csv  6.202   8.1393 -12.23758
20181004_2_ryuko.csv  6.270  15.6595  -0.08189
20181004_3_ryuko.csv 15.821  -6.6580   0.76158
20181025_1_ryuko.csv  6.563   2.7442   9.09183
20181025_2_ryuko.csv  9.768 -10.0753   0.93818
20190425_1_ryuko.csv -5.798  -8.1494 -14.41071
20190425_2_ryuko.csv -1.988  -7.5863   0.90380
20190425_3_ryuko.csv -4.572  -0.2130   2.78838
20190425_4_ryuko.csv -3.970  -4.2295  -1.28731
20190425_5_ryuko.csv -5.144   3.0458   5.77891
20190520_1_ryuko.csv -4.264   0.8653  -7.63764
20190520_2_ryuko.csv -4.821   6.1828  -1.33402
20190520_3_ryuko.csv -3.384   3.9403   0.55756
                          PC1       PC2     PC3
20180316_1_ryuko.csv  -0.9055   3.91808   5.729
20180316_2_ryuko.csv  -2.4000   9.35525   3.538
20181004_1_ryuko.csv  -2.0190   4.85103 -11.979
20181004_2_ryuko.csv   4.7213  -9.74191  10.822
20181004_3_ryuko.csv -13.4908   3.22690   7.167
20181025_1_ryuko.csv  -4.5025   0.34815 -10.082
20181025_2_ryuko.csv  20.4843   3.48660  -1.217
20190425_1_ryuko.csv  -2.8140   0.92347  -0.581
20190425_2_ryuko.csv  -2.0713 -19.45477  -3.704
20190425_3_ryuko.csv  -0.3647  -2.61717  -4.748
20190425_4_ryuko.csv  -1.4285  -3.79391   2.073
20190425_5_ryuko.csv   0.1756   1.80318  -7.755
20190520_1_ryuko.csv   0.7326   3.30687  10.637
20190520_2_ryuko.csv   1.9744   4.30560  -1.107
20190520_3_ryuko.csv   1.9080   0.08264   1.207


Biplot scores for constraining variables

                      RDA1     RDA2    RDA3 PC1 PC2
phyto_metadata$temp 0.8964  0.37467 -0.2368   0   0
total_abundance     0.9551 -0.27141 -0.1189   0   0
species_richness    0.5440  0.04071 -0.8381   0   0
                    PC3
phyto_metadata$temp   0
total_abundance       0
species_richness      0

#可視化：スケーリング１
plot(phyto.rda, scaling = 1, type = "text")

#可視化：スケーリング２
plot(phyto.rda, scaling = 2, type = "text")

冗長性解析に対するランダム並び替え検定

permutest(phyto.rda, by = "terms", perm = 1999)

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 1999
 
Model: rda(formula = species_ryuko_data ~
phyto_metadata$temp + total_abundance +
species_richness)
Permutation test for sequential contrasts
                    Df Inertia      F Pr(>F)   
phyto_metadata$temp  1 12463.0 9.0075 0.0015 **
total_abundance      1  4320.9 3.1229 0.0585 . 
species_richness     1   764.6 0.5526 0.5985   
Residual            11 15219.9                 
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

9.2.4 CAP/dbRDAのためのRコーディング

CAP-capscale()とdbRDA-dbrda()の比較

####CAP/dbRDA for phytoplankton#### 
#まずは共通部分 ブレイ・カーティス距離を計算
ryuko_BC.d <- vegdist(species_ryuko_data, method = "bray") #Bray-Curtis
#メタデータ中の温度情報を新しいオブジェクトtemperatureに格納
temperature <- phyto_metadata$temp

#CAPを使う場合
ryuko_CAP <- capscale(ryuko_BC.d ~ temperature + total_abundance + species_richness)
#dbRDAを使う場合
ryuko_dbRDA <- dbrda(ryuko_BC.d ~ temperature + total_abundance + species_richness)

#CAPの結果
summary(ryuko_CAP)

Call:
capscale(formula = ryuko_BC.d ~ temperature + total_abundance +      species_richness) 

Partitioning of squared Bray distance:
              Inertia Proportion
Total           4.626     1.0000
Constrained     1.604     0.3469
Unconstrained   3.021     0.6531

Eigenvalues, and their contribution to the squared Bray distance 

Importance of components:
                        CAP1    CAP2    CAP3   MDS1
Eigenvalue            0.9839 0.40136 0.21917 0.6525
Proportion Explained  0.2127 0.08677 0.04738 0.1411
Cumulative Proportion 0.2127 0.29947 0.34685 0.4879
                        MDS2    MDS3    MDS4    MDS5
Eigenvalue            0.6098 0.41834 0.38170 0.23093
Proportion Explained  0.1318 0.09044 0.08252 0.04992
Cumulative Proportion 0.6197 0.71018 0.79269 0.84261
                         MDS6    MDS7    MDS8    MDS9
Eigenvalue            0.18784 0.14099 0.13098 0.11754
Proportion Explained  0.04061 0.03048 0.02831 0.02541
Cumulative Proportion 0.88322 0.91370 0.94202 0.96743
                        MDS10   MDS11
Eigenvalue            0.08431 0.06637
Proportion Explained  0.01823 0.01435
Cumulative Proportion 0.98565 1.00000

Accumulated constrained eigenvalues
Importance of components:
                        CAP1   CAP2   CAP3
Eigenvalue            0.9839 0.4014 0.2192
Proportion Explained  0.6132 0.2502 0.1366
Cumulative Proportion 0.6132 0.8634 1.0000

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:  2.836793 


Species scores

      CAP1 CAP2 CAP3 MDS1 MDS2 MDS3
Dim1                               
Dim2                               
Dim3                               
Dim4                               
Dim5                               
Dim6                               
Dim7                               
Dim8                               
Dim9                               
Dim10                              
Dim11                              
Dim12                              
Dim13                              
Dim14                              


Site scores (weighted sums of species scores)

                         CAP1     CAP2     CAP3
20180316_1_ryuko.csv -0.42120 -0.35959  1.95847
20180316_2_ryuko.csv -0.02415 -0.05533  1.94221
20181004_1_ryuko.csv  1.21021 -0.18051 -0.53492
20181004_2_ryuko.csv  0.99646 -1.15705 -0.22117
20181004_3_ryuko.csv  1.20142  0.83172 -0.04415
20181025_1_ryuko.csv  1.25625 -0.44962 -0.10922
20181025_2_ryuko.csv  0.59240  1.73241  0.77335
20190425_1_ryuko.csv -0.76586  0.71349 -2.05370
20190425_2_ryuko.csv -0.60632  1.10140  0.12627
20190425_3_ryuko.csv -0.82872  0.23417 -0.54261
20190425_4_ryuko.csv -0.77441  0.22262 -0.26936
20190425_5_ryuko.csv -0.62803 -0.21920  0.30625
20190520_1_ryuko.csv -0.38938 -0.46209 -0.59980
20190520_2_ryuko.csv -0.44168 -1.06882 -0.49810
20190520_3_ryuko.csv -0.37697 -0.88361 -0.23354
                        MDS1     MDS2    MDS3
20180316_1_ryuko.csv  1.1182  0.63551 -1.9833
20180316_2_ryuko.csv -0.8661  2.09775  0.8905
20181004_1_ryuko.csv -0.2580  0.41380 -0.6316
20181004_2_ryuko.csv -0.3084  0.30305 -0.1197
20181004_3_ryuko.csv -0.3166 -0.11251 -0.2231
20181025_1_ryuko.csv -0.5612 -0.31431 -0.1574
20181025_2_ryuko.csv  1.2932  0.20006  1.0924
20190425_1_ryuko.csv -0.4991  0.44392 -0.2717
20190425_2_ryuko.csv -0.7428 -0.56126 -0.5095
20190425_3_ryuko.csv -0.4786 -0.93514  0.2432
20190425_4_ryuko.csv -0.3815 -0.73015 -0.3291
20190425_5_ryuko.csv -0.5555 -0.86470  0.6760
20190520_1_ryuko.csv  0.5551 -0.03825  0.5356
20190520_2_ryuko.csv  0.9618 -0.18238  0.5996
20190520_3_ryuko.csv  1.0395 -0.35538  0.1882


Site constraints (linear combinations of constraining variables)

                        CAP1     CAP2      CAP3
20180316_1_ryuko.csv -0.5551 -0.08492  0.977708
20180316_2_ryuko.csv -0.6026 -0.12650  0.821248
20181004_1_ryuko.csv  0.8695 -0.45524 -1.435345
20181004_2_ryuko.csv  1.1934 -1.38065 -0.224435
20181004_3_ryuko.csv  1.4029  1.22848  0.173695
20181025_1_ryuko.csv  0.8134 -0.16807  0.945222
20181025_2_ryuko.csv  0.6599  1.36274  0.239915
20190425_1_ryuko.csv -0.9470  0.81738 -1.445987
20190425_2_ryuko.csv -0.4660  0.69456  0.202149
20190425_3_ryuko.csv -0.4667 -0.17549  0.304515
20190425_4_ryuko.csv -0.5630  0.30978 -0.080931
20190425_5_ryuko.csv -0.3985 -0.56805  0.583047
20190520_1_ryuko.csv -0.4437 -0.13926 -0.837687
20190520_2_ryuko.csv -0.2874 -0.78510 -0.229240
20190520_3_ryuko.csv -0.2090 -0.52965  0.006127
                        MDS1     MDS2    MDS3
20180316_1_ryuko.csv  1.1182  0.63551 -1.9833
20180316_2_ryuko.csv -0.8661  2.09775  0.8905
20181004_1_ryuko.csv -0.2580  0.41380 -0.6316
20181004_2_ryuko.csv -0.3084  0.30305 -0.1197
20181004_3_ryuko.csv -0.3166 -0.11251 -0.2231
20181025_1_ryuko.csv -0.5612 -0.31431 -0.1574
20181025_2_ryuko.csv  1.2932  0.20006  1.0924
20190425_1_ryuko.csv -0.4991  0.44392 -0.2717
20190425_2_ryuko.csv -0.7428 -0.56126 -0.5095
20190425_3_ryuko.csv -0.4786 -0.93514  0.2432
20190425_4_ryuko.csv -0.3815 -0.73015 -0.3291
20190425_5_ryuko.csv -0.5555 -0.86470  0.6760
20190520_1_ryuko.csv  0.5551 -0.03825  0.5356
20190520_2_ryuko.csv  0.9618 -0.18238  0.5996
20190520_3_ryuko.csv  1.0395 -0.35538  0.1882


Biplot scores for constraining variables

                   CAP1    CAP2     CAP3 MDS1 MDS2
temperature      0.9587 -0.0339 -0.28232    0    0
total_abundance  0.8121  0.5775 -0.08382    0    0
species_richness 0.4936  0.2376 -0.83663    0    0
                 MDS3
temperature         0
total_abundance     0
species_richness    0

#dbRDAの結果
summary(ryuko_dbRDA)

Call:
dbrda(formula = ryuko_BC.d ~ temperature + total_abundance +      species_richness) 

Partitioning of squared Bray distance:
              Inertia Proportion
Total           4.626     1.0000
Constrained     1.604     0.3469
Unconstrained   3.021     0.6531

Eigenvalues, and their contribution to the squared Bray distance 

Importance of components:
                      dbRDA1  dbRDA2  dbRDA3   MDS1
Eigenvalue            0.9839 0.40136 0.21917 0.6525
Proportion Explained  0.2127 0.08677 0.04738 0.1411
Cumulative Proportion 0.2127 0.29947 0.34685 0.4879
                        MDS2    MDS3    MDS4    MDS5
Eigenvalue            0.6098 0.41834 0.38170 0.23093
Proportion Explained  0.1318 0.09044 0.08252 0.04992
Cumulative Proportion 0.6197 0.71018 0.79269 0.84261
                         MDS6    MDS7    MDS8    MDS9
Eigenvalue            0.18784 0.14099 0.13098 0.11754
Proportion Explained  0.04061 0.03048 0.02831 0.02541
Cumulative Proportion 0.88322 0.91370 0.94202 0.96743
                        MDS10   MDS11
Eigenvalue            0.08431 0.06637
Proportion Explained  0.01823 0.01435
Cumulative Proportion 0.98565 1.00000

Accumulated constrained eigenvalues
Importance of components:
                      dbRDA1 dbRDA2 dbRDA3
Eigenvalue            0.9839 0.4014 0.2192
Proportion Explained  0.6132 0.2502 0.1366
Cumulative Proportion 0.6132 0.8634 1.0000

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:  2.836793 


Site scores (weighted sums of species scores)

                       dbRDA1   dbRDA2   dbRDA3
20180316_1_ryuko.csv -0.42120 -0.35959  1.95847
20180316_2_ryuko.csv -0.02415 -0.05533  1.94221
20181004_1_ryuko.csv  1.21021 -0.18051 -0.53492
20181004_2_ryuko.csv  0.99646 -1.15705 -0.22117
20181004_3_ryuko.csv  1.20142  0.83172 -0.04415
20181025_1_ryuko.csv  1.25625 -0.44962 -0.10922
20181025_2_ryuko.csv  0.59240  1.73241  0.77335
20190425_1_ryuko.csv -0.76586  0.71349 -2.05370
20190425_2_ryuko.csv -0.60632  1.10140  0.12627
20190425_3_ryuko.csv -0.82872  0.23417 -0.54261
20190425_4_ryuko.csv -0.77441  0.22262 -0.26936
20190425_5_ryuko.csv -0.62803 -0.21920  0.30625
20190520_1_ryuko.csv -0.38938 -0.46209 -0.59980
20190520_2_ryuko.csv -0.44168 -1.06882 -0.49810
20190520_3_ryuko.csv -0.37697 -0.88361 -0.23354
                        MDS1     MDS2    MDS3
20180316_1_ryuko.csv  1.1182 -0.63551 -1.9833
20180316_2_ryuko.csv -0.8661 -2.09775  0.8905
20181004_1_ryuko.csv -0.2580 -0.41380 -0.6316
20181004_2_ryuko.csv -0.3084 -0.30305 -0.1197
20181004_3_ryuko.csv -0.3166  0.11251 -0.2231
20181025_1_ryuko.csv -0.5612  0.31431 -0.1574
20181025_2_ryuko.csv  1.2932 -0.20006  1.0924
20190425_1_ryuko.csv -0.4991 -0.44392 -0.2717
20190425_2_ryuko.csv -0.7428  0.56126 -0.5095
20190425_3_ryuko.csv -0.4786  0.93514  0.2432
20190425_4_ryuko.csv -0.3815  0.73015 -0.3291
20190425_5_ryuko.csv -0.5555  0.86470  0.6760
20190520_1_ryuko.csv  0.5551  0.03825  0.5356
20190520_2_ryuko.csv  0.9618  0.18238  0.5996
20190520_3_ryuko.csv  1.0395  0.35538  0.1882


Site constraints (linear combinations of constraining variables)

                      dbRDA1   dbRDA2    dbRDA3
20180316_1_ryuko.csv -0.5551 -0.08492  0.977708
20180316_2_ryuko.csv -0.6026 -0.12650  0.821248
20181004_1_ryuko.csv  0.8695 -0.45524 -1.435345
20181004_2_ryuko.csv  1.1934 -1.38065 -0.224435
20181004_3_ryuko.csv  1.4029  1.22848  0.173695
20181025_1_ryuko.csv  0.8134 -0.16807  0.945222
20181025_2_ryuko.csv  0.6599  1.36274  0.239915
20190425_1_ryuko.csv -0.9470  0.81738 -1.445987
20190425_2_ryuko.csv -0.4660  0.69456  0.202149
20190425_3_ryuko.csv -0.4667 -0.17549  0.304515
20190425_4_ryuko.csv -0.5630  0.30978 -0.080931
20190425_5_ryuko.csv -0.3985 -0.56805  0.583047
20190520_1_ryuko.csv -0.4437 -0.13926 -0.837687
20190520_2_ryuko.csv -0.2874 -0.78510 -0.229240
20190520_3_ryuko.csv -0.2090 -0.52965  0.006127
                        MDS1     MDS2    MDS3
20180316_1_ryuko.csv  1.1182 -0.63551 -1.9833
20180316_2_ryuko.csv -0.8661 -2.09775  0.8905
20181004_1_ryuko.csv -0.2580 -0.41380 -0.6316
20181004_2_ryuko.csv -0.3084 -0.30305 -0.1197
20181004_3_ryuko.csv -0.3166  0.11251 -0.2231
20181025_1_ryuko.csv -0.5612  0.31431 -0.1574
20181025_2_ryuko.csv  1.2932 -0.20006  1.0924
20190425_1_ryuko.csv -0.4991 -0.44392 -0.2717
20190425_2_ryuko.csv -0.7428  0.56126 -0.5095
20190425_3_ryuko.csv -0.4786  0.93514  0.2432
20190425_4_ryuko.csv -0.3815  0.73015 -0.3291
20190425_5_ryuko.csv -0.5555  0.86470  0.6760
20190520_1_ryuko.csv  0.5551  0.03825  0.5356
20190520_2_ryuko.csv  0.9618  0.18238  0.5996
20190520_3_ryuko.csv  1.0395  0.35538  0.1882


Biplot scores for constraining variables

                 dbRDA1  dbRDA2   dbRDA3 MDS1 MDS2
temperature      0.9587 -0.0339 -0.28232    0    0
total_abundance  0.8121  0.5775 -0.08382    0    0
species_richness 0.4936  0.2376 -0.83663    0    0
                 MDS3
temperature         0
total_abundance     0
species_richness    0

#CAPの結果の可視化
plot(ryuko_CAP, scaling = 2, type = "text")

#dbRDAの結果の可視化
plot(ryuko_dbRDA, scaling = 2, type = "text")

#CAPの結果についてのランダム並び替え検定
permutest(ryuko_CAP, by = "terms", perm = 1999)

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 1999
 
Model: capscale(formula = ryuko_BC.d ~
temperature + total_abundance +
species_richness)
Permutation test for sequential contrasts
                 Df Inertia      F Pr(>F)    
temperature       1 0.92230 3.3579 0.0005 ***
total_abundance   1 0.39825 1.4499 0.1105    
species_richness  1 0.28391 1.0336 0.4195    
Residual         11 3.02130                  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#dbRDAの結果についてのランダム並び替え検定
permutest(ryuko_dbRDA, by = "terms", perm = 1999)

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 1999
 
Model: dbrda(formula = ryuko_BC.d ~ temperature
+ total_abundance + species_richness)
Permutation test for sequential contrasts
                 Df Inertia      F Pr(>F)    
temperature       1 0.92230 3.3579 0.0005 ***
total_abundance   1 0.39825 1.4499 0.1130    
species_richness  1 0.28391 1.0336 0.4150    
Residual         11 3.02130                  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

9.2.5 カテゴリー変数と量的変数も混ぜて使うことが可能

#月情報をメタデータから抜き出して新しいオブジェクトmonthに格納
month <- phyto_metadata$month
#capscaleをつかってCAPを実行
ryuko_CAP2 <- capscale(ryuko_BC.d ~ temperature + total_abundance + species_richness + month)
#ランダム並び替え検定
permutest(ryuko_CAP2, by = "terms", perm = 1999)

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 1999
 
Model: capscale(formula = ryuko_BC.d ~
temperature + total_abundance +
species_richness + month)
Permutation test for sequential contrasts
                 Df Inertia      F Pr(>F)    
temperature       1 0.92230 4.2185 0.0005 ***
total_abundance   1 0.39825 1.8215 0.0280 *  
species_richness  1 0.28391 1.2986 0.2010    
month             3 1.27225 1.9397 0.0025 ** 
Residual          8 1.74905                  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

BOX9　adonis()/capscale()/dbrda()の違い

ジャッカード距離で月間比較

####PERMANOVA, CAP, and dbRDA####
#距離行列の計算
ryuko_J.d <- vegdist(species_ryuko_data, method = "jaccard", binary = TRUE) #jaccard
#PERMANOVAによる検定
adonis(ryuko_J.d  ~ month)$aov.tab

'adonis' will be deprecated: use 'adonis2' instead

Permutation: free
Number of permutations: 999

Terms added sequentially (first to last)

          Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
month      3    1.3581 0.45269  1.6785 0.31402  0.001
Residuals 11    2.9667 0.26970         0.68598       
Total     14    4.3248                 1.00000       
             
month     ***
Residuals    
Total        
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#capscaleに対するランダム並び替え検定
permutest(capscale(ryuko_J.d ~ month), by = "terms", perm = 999)

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 999
 
Model: capscale(formula = ryuko_J.d ~ month)
Permutation test for all constrained eigenvalues
         Df Inertia      F Pr(>F)    
month     3  1.3581 1.6785  0.001 ***
Residual 11  2.9667                  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#dbrdaに対するランダム並び替え検定
permutest(dbrda(ryuko_J.d ~ month), by = "terms", perm = 999)

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 999
 
Model: dbrda(formula = ryuko_J.d ~ month)
Permutation test for all constrained eigenvalues
         Df Inertia      F Pr(>F)    
month     3  1.3581 1.6785  0.001 ***
Residual 11  2.9667                  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1