Most analyses based on package ‘geomorph’ (Adams et al., 2020), in parts following routine outlined by Theska et al. (2020).
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 S
Sculpture 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 YES
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 99
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
## 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+00
red line = mean variation
## [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
##
## $good
## [1] 1 2 3 4
number of meaningful principal components = 4
Sculpture groups L, I, S
DNA sequenced yes/no
PC2_contrib <- fviz_contrib(lugu.pca, choice = "var", axes = 2)
LM_contrib_PC2 <- data.frame(LM = rep(NA, nrow(PC2_contrib$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$PC1_contrib),]
## LM PC1_contrib
## 9 9 18.171720
## 12 12 16.313943
## 10 10 12.163689
## 11 11 11.770819
## 5 5 7.845882
important_LMs_PC2 <- LM_contrib_PC2[LM_contrib_PC2$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 12.68280
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
## 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 14
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
## 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+00
red line = mean variation
## [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 4
number of meaningful principal components = 4
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.
## 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 10.76605
Performed on two-dimensional, fixed landmark coordinates using function gpagen {geomorph}
Procrustes superimposition: Shape independent of location, size and orientation.
## 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 40
Shape difference between the mean reference shape and the most extreme outliers and an example smooth form (OUT_CIP)
## 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+00
red line = mean variation
## [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 3
number of meaningful principal components = 3
Sculpture groups L, I, S
DNA sequenced yes/no
## 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