Lugu Landmark Analysis
Manja Hethke, Kai Hartmann and Robert Wiese
22.07.2021
Most analyses based on package ‘geomorph’ (Adams et al., 2020), in parts following routine outlined by Theska et al. (2020).
1 Read landmark data from tps file and definition of groupings
99 individuals, 49 landmarks each
## [1] "1-113674_A" "1-121321_2_1" "1-121321_3" "1-121322_2_2"
## [5] "1-121322_2_3" "1-121322_2_4" "1-121324_1" "1-121328a_3"
## [9] "1-121328b_1" "1-121328b_2_1" "1-121328b_2_4" "1-121328b_3"
## [13] "1-121329a_2_1" "1-121329a_2_2" "1-121329b_1" "1-121329b_3"
## [17] "1-121330_2_1" "1-121330_2_3" "1-121330_A" "1-121331_X"
## [21] "1-121335_2_1" "1-121335_B" "1-121338_2_1" "1-121338_A"
## [25] "1-121340_1" "1-121341_2_6" "1-121342_2_3" "1-121342_2_4"
## [29] "1-121342_2_8" "1-121344_A" "1-121344_B" "1-121344_C"
## [33] "1-OUT_MARG" "1-OUT_CIP" "1-121321_1" "1-121321_2_2"
## [37] "1-121321_2" "1-121322_2_1" "1-121322_A" "1-121322_B"
## [41] "1-121322_C" "1-121323_2_1" "1-121323_2_2" "1-121323_2_3"
## [45] "1-121323_2_4" "1-121323_2_5" "1-121323_A" "1-121323_B"
## [49] "1-121328a_1" "1-121328a_2" "1-121328b_2_2" "1-121328b_2_3"
## [53] "1-121328b_2_5" "1-121328b_2_6" "1-121328b_2" "1-121329a_1"
## [57] "1-121329b_2" "1-121330_2_2" "1-121330_2_4" "1-121330_B"
## [61] "1-121331_A" "1-121331_B" "1-121335_2_2" "1-121335_2_3"
## [65] "1-121335_2_4" "1-121335_2_5" "1-121335_A" "1-121335_C"
## [69] "1-121337_1" "1-121338_2_2" "1-121338_2_3" "1-121338_2_4"
## [73] "1-121338_2_5" "1-121340_2" "1-121340_3" "1-121340_4"
## [77] "1-121341_2_1" "1-121341_2_2" "1-121341_2_3" "1-121341_2_4"
## [81] "1-121341_2_5" "1-121341_2_7" "1-121341_A" "1-121342_1"
## [85] "1-121342_2_1" "1-121342_2_2" "1-121342_2_5" "1-121342_2_6"
## [89] "1-121342_2_7" "1-121342_2" "1-121342_A" "1-121344_2_1"
## [93] "1-121438_A" "1-127438_2_1" "1-127438_2_2" "1-127438_2_3"
## [97] "1-127438_2_4" "1-127438_2_5" "1-127438_B"## [1] 49 2 99## [1] "Sculpture" "Sequenced"## [1] L S I I L S L I I L L I I S S S L L L S L L I S I I S L I L I I S L S S I I
## [39] S S S S I S S S S I L S L L L I I S S L L L S L L I L L L L L S I S I S I L
## [77] L I L L L I S I I I S L I S L I S I L I S L S
## Levels: I L SSculpture groupings based on visual assessment.
## [1] YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES
## [20] YES YES YES YES YES YES YES YES YES YES YES YES YES NO NO NO NO NO NO
## [39] NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO
## [58] NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO
## [77] NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO
## [96] NO NO NO NO
## Levels: NO YES2 Data subsets
Example: 34 2 99 = 34 landmarks, 2 dimensions (two coordinates per landmark), 99 gastropods
## [1] 13 2 99## [1] 10 2 99## [1] 34 2 993 Analysis 1: Overall_shape
3.1 Raw data plot
3.2 General Procrustes Analysis
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
3.3 Landmark space
3.4 Outliers
3.4.1 tps grid deformation from mean shape (specimen 96 = 127438_2_3)
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
3.4.2 tps grid deformation from mean shape (specimen 92 = 1-121344_2_1)
3.4.3 tps grid deformation from mean shape (specimen 34 = 1-OUT_CIP)
3.4.4 tps grid deformation from mean shape (specimen 33 = 1-OUT_MARG)
3.5 Shape space
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 0.02757 0.01589 0.01324 0.01063 0.008798 0.007764
## Proportion of Variance 0.44382 0.14738 0.10228 0.06600 0.045190 0.035200
## Cumulative Proportion 0.44382 0.59120 0.69348 0.75948 0.804670 0.839860
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.007353 0.006607 0.006207 0.005415 0.004972 0.004584
## Proportion of Variance 0.031570 0.025480 0.022490 0.017120 0.014430 0.012270
## Cumulative Proportion 0.871430 0.896910 0.919410 0.936520 0.950950 0.963220
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 0.003968 0.003444 0.002934 0.002555 0.002375 0.002035
## Proportion of Variance 0.009190 0.006930 0.005030 0.003810 0.003290 0.002420
## Cumulative Proportion 0.972410 0.979340 0.984370 0.988180 0.991470 0.993890
## PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 0.001901 0.001764 0.001482 0.001242 1.977e-16 1.389e-16
## Proportion of Variance 0.002110 0.001820 0.001280 0.000900 0.000e+00 0.000e+00
## Cumulative Proportion 0.996000 0.997820 0.999100 1.000000 1.000e+00 1.000e+00
## PC25 PC26
## Standard deviation 8.612e-17 3.261e-17
## Proportion of Variance 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+003.5.1 Barplot indicating the variation described by principal components
red line = mean variation 
3.5.2 Identification of number of meaningful principal components
## [1] 4.438183e+01 1.473786e+01 1.022835e+01 6.600023e+00 4.518810e+00
## [6] 3.519593e+00 3.156649e+00 2.548275e+00 2.249285e+00 1.711715e+00
## [11] 1.443021e+00 1.226959e+00 9.190360e-01 6.925796e-01 5.027501e-01
## [16] 3.810783e-01 3.292884e-01 2.418634e-01 2.110565e-01 1.815711e-01
## [21] 1.283034e-01 9.009796e-02 2.280912e-27 1.125983e-27 4.329813e-28
## [26] 6.207927e-29## $tol
## [1] 1.329425
##
## $good
## [1] 1 2 3 4number of meaningful principal components = 4
3.5.3 PCA of shape variables
Sculpture groups L, I, S 
DNA sequenced yes/no 
3.5.4 Lollipop plot of superimposed extreme shapes on PC1 and PC2
3.5.5 Contribution of landmarks on principal components (%)
PC2_contrib <- fviz_contrib(lugu.pca, choice = "var", axes = 2)
LM_contrib_PC2 <- data.frame(LM = rep(NA, nrow(PC2_contrib$data)/2), PC2_contrib = rep(NA, nrow(PC2_contrib$data)/2))
for (i in 1:(nrow(PC2_contrib$data)/2)) {
LM_contrib_PC2$PC2_contrib[i] <- sum(PC2_contrib$data[(i*2-1):(i*2),]$contrib)
LM_contrib_PC2$LM[i] <- as.character(i)
}
important_LMs_PC1 <- LM_contrib_PC1[LM_contrib_PC1$PC1_contrib > 100/(nrow(PC1_contrib$data)/2),]
important_LMs_PC1[order(decreasing = TRUE, important_LMs_PC1$PC1_contrib),]## LM PC1_contrib
## 9 9 18.171720
## 12 12 16.313943
## 10 10 12.163689
## 11 11 11.770819
## 5 5 7.845882important_LMs_PC2 <- LM_contrib_PC2[LM_contrib_PC2$PC2_contrib > 100/(nrow(PC2_contrib$data)/2),]
important_LMs_PC2[order(decreasing = TRUE, important_LMs_PC2$PC2_contrib),]## LM PC2_contrib
## 12 12 64.67223
## 10 10 12.682804 Analysis 2: Sculpture_reduced
4.1 Raw data plot
4.2 General Procrustes Analysis
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
4.3 Landmark space
4.4 Outliers
## 1-OUT_MARG 1-127438_2_3 1-121321_2_1 1-121328b_1 1-121328a_1
## 33 96 2 9 49
## 1-121438_A 1-121322_2_3 1-121340_4 1-121323_2_2 1-121328b_2_5
## 93 5 76 43 53
## 1-121335_2_2 1-121328b_2_2 1-121331_B 1-121335_C 1-127438_2_2
## 63 51 62 68 95
## 1-121330_2_3 1-121331_X 1-121322_2_2 1-121335_2_5 1-121323_2_3
## 18 20 4 66 44
## 1-121321_3 1-121329a_1 1-121342_2_6 1-121323_2_1 1-121342_2_3
## 3 56 88 42 27
## 1-127438_2_4 1-121342_A 1-121329a_2_1 1-121341_2_7 1-121321_1
## 97 91 13 82 35
## 1-121323_2_5 1-121341_2_4 1-121341_A 1-121328b_2_6 1-121330_A
## 46 80 83 54 19
## 1-121330_B 1-121329b_3 1-121335_A 1-121324_1 1-121335_B
## 60 16 67 7 22
## 1-121338_2_5 1-121328b_2_3 1-121342_2_7 1-121323_A 1-121338_2_1
## 73 52 89 47 23
## 1-121342_2_1 1-121328a_2 1-121335_2_1 1-121341_2_6 1-127438_2_5
## 85 50 21 26 98
## 1-121321_2_2 1-OUT_CIP 1-121341_2_1 1-121342_2_8 1-121328b_2_4
## 36 34 77 29 11
## 1-121321_2 1-121330_2_4 1-127438_2_1 1-121342_2_5 1-121328a_3
## 37 59 94 87 8
## 1-127438_B 1-113674_A 1-121322_C 1-121344_C 1-121341_2_2
## 99 1 41 32 78
## 1-121338_2_3 1-121323_2_4 1-121322_A 1-121344_A 1-121340_3
## 71 45 39 30 75
## 1-121335_2_3 1-121337_1 1-121322_2_4 1-121329b_2 1-121340_2
## 64 69 6 57 74
## 1-121340_1 1-121335_2_4 1-121342_1 1-121328b_2 1-121341_2_3
## 25 65 84 55 79
## 1-121329b_1 1-121330_2_1 1-121330_2_2 1-121323_B 1-121342_2_2
## 15 17 58 48 86
## 1-121342_2 1-121344_2_1 1-121338_2_4 1-121322_B 1-121322_2_1
## 90 92 72 40 38
## 1-121341_2_5 1-121328b_2_1 1-121331_A 1-121344_B 1-121342_2_4
## 81 10 61 31 28
## 1-121328b_3 1-121338_2_2 1-121338_A 1-121329a_2_2
## 12 70 24 144.4.1 tps grid deformation from mean shape (specimen 96 = 127438_2_3)
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
4.4.2 tps grid deformation from mean shape (specimen 92 = 1-121344_2_1)
4.4.3 tps grid deformation from mean shape (specimen 34 = 1-OUT_CIP)
4.4.4 tps grid deformation from mean shape (specimen 33 = 1-OUT_MARG)
4.4.5 tps grid deformation from mean shape (specimen 2 = 1-121321_2_1, most neg score on PC1)
4.4.6 tps grid deformation from mean shape (specimen 5 = 1-121322_2_3, 2nd most neg score on PC2)
4.4.7 tps grid deformation from mean shape (specimen 76 = 1-121340_4, most pos score on PC2)
4.5 Shape space
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 0.02777 0.01903 0.01551 0.01132 0.009336 0.008187
## Proportion of Variance 0.41788 0.19622 0.13040 0.06942 0.047230 0.036320
## Cumulative Proportion 0.41788 0.61410 0.74450 0.81392 0.861160 0.897480
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.006958 0.005646 0.005349 0.004835 0.003649 0.003618
## Proportion of Variance 0.026230 0.017280 0.015500 0.012670 0.007220 0.007090
## Cumulative Proportion 0.923720 0.940990 0.956500 0.969170 0.976380 0.983470
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 0.003396 0.002903 0.002433 0.002149 1.785e-16 1.131e-16
## Proportion of Variance 0.006250 0.004570 0.003210 0.002500 0.000e+00 0.000e+00
## Cumulative Proportion 0.989720 0.994290 0.997500 1.000000 1.000e+00 1.000e+00
## PC19 PC20
## Standard deviation 7.32e-17 3.28e-17
## Proportion of Variance 0.00e+00 0.00e+00
## Cumulative Proportion 1.00e+00 1.00e+004.5.1 Barplot indicating the variation described by principal components
red line = mean variation 
4.5.2 Identification of number of meaningful principal components
## [1] 4.178762e+01 1.962207e+01 1.304049e+01 6.942267e+00 4.723403e+00
## [6] 3.632295e+00 2.623479e+00 1.727562e+00 1.550380e+00 1.266946e+00
## [11] 7.216820e-01 7.092099e-01 6.249361e-01 4.567144e-01 3.206373e-01
## [16] 2.503160e-01 1.726056e-27 6.933844e-28 2.903404e-28 5.828669e-29## $tol
## [1] 1.329425
##
## $good
## [1] 1 2 3 4number of meaningful principal components = 4
4.5.3 PCA of shape variables
Sculpture groups L, I, S 
DNA sequenced yes/no 
Little discrimination between the three visual sculpture groups I, L and S. That’s quite unexpected.
4.5.4 Lollipop plot of superimposed extreme shapes on PC1 and PC2
4.5.5 Contribution of landmarks on principal components (%)
## LM PC1_contrib
## 6 6 19.35918
## 7 7 13.80565
## 1 1 11.59666
## 2 2 10.00430## LM PC2_contrib
## 7 7 24.60152
## 6 6 22.80727
## 5 5 15.99569
## 4 4 14.34012
## 10 10 10.766055 Analysis 3: Full_set
5.1 Raw data plot
5.2 General Procrustes Analysis
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
5.3 Landmark space
5.4 Outliers
## 1-OUT_MARG 1-127438_2_3 1-121321_2_1 1-121338_2_5 1-121335_C
## 33 96 2 73 68
## 1-121322_2_2 1-121324_1 1-121438_A 1-121331_B 1-127438_2_4
## 4 7 93 62 97
## 1-121328a_1 1-121340_4 1-121329a_2_1 1-121344_2_1 1-121328b_2_5
## 49 76 13 92 53
## 1-121335_B 1-121322_2_3 1-121335_2_5 1-121323_2_3 1-121331_X
## 22 5 66 44 20
## 1-127438_2_2 1-121323_2_2 1-121342_A 1-121323_2_5 1-121338_2_1
## 95 43 91 46 23
## 1-121342_2_6 1-121341_2_4 1-121342_2_8 1-121328b_1 1-121330_2_1
## 88 80 29 9 17
## 1-OUT_CIP 1-121321_2 1-121341_A 1-121341_2_6 1-121321_3
## 34 37 83 26 3
## 1-121329a_1 1-121321_1 1-121323_A 1-121328a_3 1-127438_2_1
## 56 35 47 8 94
## 1-121335_2_2 1-121342_2_1 1-121323_2_1 1-121328b_2_2 1-121341_2_1
## 63 85 42 51 77
## 1-121344_C 1-121330_B 1-121323_B 1-121340_1 1-121328b_2_6
## 32 60 48 25 54
## 1-113674_A 1-127438_2_5 1-121330_2_3 1-121342_2_7 1-121335_2_1
## 1 98 18 89 21
## 1-121338_2_2 1-121340_3 1-121321_2_2 1-127438_B 1-121338_2_3
## 70 75 36 99 71
## 1-121342_2_2 1-121328a_2 1-121330_A 1-121341_2_2 1-121330_2_4
## 86 50 19 78 59
## 1-121328b_2_3 1-121344_A 1-121329b_1 1-121335_2_3 1-121341_2_7
## 52 30 15 64 82
## 1-121323_2_4 1-121328b_2_4 1-121322_2_4 1-121342_1 1-121335_A
## 45 11 6 84 67
## 1-121342_2_3 1-121329b_2 1-121330_2_2 1-121341_2_5 1-121342_2_5
## 27 57 58 81 87
## 1-121338_A 1-121328b_3 1-121329b_3 1-121335_2_4 1-121340_2
## 24 12 16 65 74
## 1-121328b_2 1-121329a_2_2 1-121322_2_1 1-121322_C 1-121341_2_3
## 55 14 38 41 79
## 1-121328b_2_1 1-121338_2_4 1-121342_2_4 1-121337_1 1-121342_2
## 10 72 28 69 90
## 1-121322_A 1-121344_B 1-121331_A 1-121322_B
## 39 31 61 405.4.1 tps grid deformation from mean shape (specimen 96 = 127438_2_3)
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
5.4.2 tps grid deformation from mean shape (specimen 92 = 1-121344_2_1)
5.4.3 tps grid deformation from mean shape (specimen 34 = 1-OUT_CIP)
5.4.4 tps grid deformation from mean shape (specimen 33 = 1-OUT_MARG)
5.5 Shape space
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 0.03146 0.01908 0.01526 0.01268 0.01122 0.01102 0.009741
## Proportion of Variance 0.35669 0.13124 0.08391 0.05795 0.04536 0.04375 0.034200
## Cumulative Proportion 0.35669 0.48793 0.57185 0.62980 0.67516 0.71891 0.753120
## PC8 PC9 PC10 PC11 PC12 PC13
## Standard deviation 0.008184 0.007989 0.007365 0.007096 0.006638 0.006455
## Proportion of Variance 0.024140 0.023000 0.019550 0.018150 0.015880 0.015020
## Cumulative Proportion 0.777250 0.800260 0.819810 0.837960 0.853840 0.868860
## PC14 PC15 PC16 PC17 PC18 PC19
## Standard deviation 0.005689 0.005575 0.00541 0.005161 0.004991 0.004506
## Proportion of Variance 0.011660 0.011200 0.01055 0.009600 0.008980 0.007320
## Cumulative Proportion 0.880520 0.891720 0.90227 0.911870 0.920850 0.928170
## PC20 PC21 PC22 PC23 PC24 PC25
## Standard deviation 0.004299 0.004119 0.003886 0.003694 0.003528 0.003448
## Proportion of Variance 0.006660 0.006110 0.005440 0.004920 0.004490 0.004290
## Cumulative Proportion 0.934830 0.940950 0.946390 0.951310 0.955790 0.960080
## PC26 PC27 PC28 PC29 PC30 PC31
## Standard deviation 0.003143 0.003061 0.003006 0.002768 0.00270 0.002519
## Proportion of Variance 0.003560 0.003380 0.003260 0.002760 0.00263 0.002290
## Cumulative Proportion 0.963640 0.967020 0.970270 0.973040 0.97566 0.977950
## PC32 PC33 PC34 PC35 PC36 PC37
## Standard deviation 0.002407 0.002324 0.002248 0.002055 0.002005 0.001864
## Proportion of Variance 0.002090 0.001950 0.001820 0.001520 0.001450 0.001250
## Cumulative Proportion 0.980040 0.981990 0.983810 0.985330 0.986780 0.988030
## PC38 PC39 PC40 PC41 PC42 PC43
## Standard deviation 0.001767 0.001658 0.001641 0.001581 0.001503 0.001423
## Proportion of Variance 0.001130 0.000990 0.000970 0.000900 0.000810 0.000730
## Cumulative Proportion 0.989160 0.990150 0.991120 0.992020 0.992830 0.993560
## PC44 PC45 PC46 PC47 PC48 PC49
## Standard deviation 0.001406 0.001329 0.001246 0.001209 0.001198 0.001147
## Proportion of Variance 0.000710 0.000640 0.000560 0.000530 0.000520 0.000470
## Cumulative Proportion 0.994280 0.994910 0.995470 0.996000 0.996520 0.996990
## PC50 PC51 PC52 PC53 PC54
## Standard deviation 0.00103 0.0009925 0.0009659 0.0009183 0.0008343
## Proportion of Variance 0.00038 0.0003600 0.0003400 0.0003000 0.0002500
## Cumulative Proportion 0.99737 0.9977300 0.9980600 0.9983700 0.9986200
## PC55 PC56 PC57 PC58 PC59
## Standard deviation 0.0008193 0.0007794 0.0007639 0.0006452 0.0006328
## Proportion of Variance 0.0002400 0.0002200 0.0002100 0.0001500 0.0001400
## Cumulative Proportion 0.9988600 0.9990800 0.9992900 0.9994400 0.9995800
## PC60 PC61 PC62 PC63 PC64
## Standard deviation 0.0005829 0.000556 0.0004514 0.0004149 0.0003571
## Proportion of Variance 0.0001200 0.000110 0.0000700 0.0000600 0.0000500
## Cumulative Proportion 0.9997100 0.999820 0.9998900 0.9999500 1.0000000
## PC65 PC66 PC67 PC68
## Standard deviation 1.541e-16 4.346e-17 3.523e-17 2.068e-17
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+005.5.1 Barplot indicating the variation described by principal components
red line = mean variation 
5.5.2 Identification of number of meaningful principal components
## [1] 3.566905e+01 1.312443e+01 8.391252e+00 5.795419e+00 4.535574e+00
## [6] 4.375473e+00 3.420405e+00 2.413865e+00 2.300362e+00 1.955160e+00
## [11] 1.814771e+00 1.588133e+00 1.501820e+00 1.166470e+00 1.120225e+00
## [16] 1.054878e+00 9.600532e-01 8.978311e-01 7.319216e-01 6.660304e-01
## [21] 6.114580e-01 5.444360e-01 4.918185e-01 4.485957e-01 4.285894e-01
## [26] 3.560819e-01 3.377277e-01 3.255998e-01 2.761840e-01 2.628573e-01
## [31] 2.288025e-01 2.088432e-01 1.946256e-01 1.821565e-01 1.522110e-01
## [36] 1.448982e-01 1.252212e-01 1.125256e-01 9.912279e-02 9.701187e-02
## [41] 9.007761e-02 8.138107e-02 7.301551e-02 7.128279e-02 6.363287e-02
## [46] 5.597993e-02 5.264923e-02 5.177088e-02 4.737946e-02 3.823936e-02
## [51] 3.550263e-02 3.362794e-02 3.039344e-02 2.508575e-02 2.419260e-02
## [56] 2.189478e-02 2.103118e-02 1.500493e-02 1.443536e-02 1.224522e-02
## [61] 1.114299e-02 7.345632e-03 6.203921e-03 4.597095e-03 8.558347e-28
## [66] 6.809021e-29 4.473211e-29 1.541363e-29## $tol
## [1] 1.329425
##
## $good
## [1] 1 2 3number of meaningful principal components = 3
5.5.3 PCA of shape variables
Sculpture groups L, I, S 
DNA sequenced yes/no 
5.5.4 Lollipop plot of superimposed extreme shapes on PC1 and PC2
5.5.5 Contribution of landmarks on principal components (%)
## LM PC1_contrib
## 16 16 9.988980
## 15 15 8.599067
## 17 17 8.411992
## 14 14 6.903180
## 32 32 6.593102
## 18 18 5.490817
## 30 30 5.249099
## 28 28 4.449743
## 27 27 4.145614
## 29 29 4.075704
## 26 26 4.024430
## 2 2 3.975830
## 1 1 3.949948
## 31 31 3.321723
## 4 4 3.298029
## 3 3 3.000399## LM PC2_contrib
## 26 26 15.010466
## 21 21 14.128936
## 32 32 9.973466
## 23 23 7.547510
## 31 31 6.871779
## 22 22 6.816225
## 6 6 6.620812
## 11 11 5.522807
## 25 25 3.535296