Need help Fixing PCA Vectors

Terrible_Coder · November 30, 2021, 5:09am

Hi,

I've already performed a principal components analysis (PCA) on the length measurements. However, I am having trouble producing a biplot that shows the skulls as points and measurements as vectors. My codes have the skulls as vectors and the measurements as points. Is there an easy way to switch these data points? I've attached my codes and a dput below. Thank you for helping.

CODES

#Log transform
Data1[,5:28] <- log(Data [5:28], 2)
#Keep length values
Data2 <- Data1
Data2 <- subset(Data2, select = c(museum, accession, species, forage, bcl, cbl, pl, fl, tl, zl, jl))
#Run PCA
Data2.pca <- prcomp(Data2[,c(5:11)], center = TRUE, scale = TRUE)
summary(Data2.pca)
#Scores
px <- scores(Data2.pca, choices = 1:5, display = "species", scaling = 0)
plot
biplot(Data2.pca, xlab="PC1", ylab="PC2", main= "PCA Plot")

DPUT of "Data"

structure(list(museum = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 4L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 4L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("AMNH",
"Burke", "Smithsonian", "TAMU"), class = "factor"), accession = structure(c(1L,
4L, 8L, 15L, 2L, 5L, 9L, 13L, 16L, 3L, 7L, 10L, 14L, 19L, 6L,
11L, 12L, 17L, 18L, 104L, 126L, 34L, 127L, 22L, 29L, 30L, 31L,
88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L, 99L, 100L,
101L, 102L, 103L, 108L, 109L, 110L, 111L, 112L, 113L, 114L, 115L,
116L, 117L, 118L, 120L, 121L, 122L, 123L, 124L, 125L, 129L, 128L,
119L, 149L, 26L, 20L, 147L, 146L, 21L, 149L, 148L, 68L, 69L,
70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L,
83L, 84L, 85L, 86L, 87L, 23L, 24L, 27L, 35L, 36L, 37L, 38L, 39L,
40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L,
53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L,
66L, 67L, 105L, 106L, 130L, 28L, 107L, 25L, 33L, 136L, 142L,
32L, 135L, 145L, 137L, 141L, 144L, 134L, 140L, 143L, 131L, 138L,
139L, 132L, 133L), .Label = c("101458", "101459", "101460", "101461",
"101462", "101464", "101465", "101466", "101467", "101468", "101469",
"101470", "101471", "101634", "101635", "101636", "101637", "101638",
"101639", "188365", "188636", "19112", "20171", "20172", "20173",
"206458", "21177", "2142", "26459", "26773", "26801", "30190",
"30191", "314979", "32159", "32160", "32161", "32162", "32163",
"32164", "32166", "32167", "32168", "32170", "32172", "32173",
"32175", "32176", "32177", "32180", "32182", "32183", "32184",
"32186", "32188", "32190", "32197", "32198", "32203", "32204",
"32205", "32210", "32226", "32230", "32237", "32606", "34260",
"34531", "34532", "34534", "34537", "34540", "34541", "34543",
"34545", "34546", "34547", "34548", "34549", "34552", "34554",
"34555", "34556", "34557", "34558", "34559", "34562", "38671",
"38672", "38673", "38674", "38675", "38678", "38679", "38680",
"38681", "38683", "38684", "38685", "38686", "38687", "38688",
"38694", "396645", "41398", "41399", "4212", "50155", "50156",
"50157", "50158", "50159", "50160", "50162", "50163", "50164",
"50165", "50166", "50167", "50169", "50170", "50171", "50172",
"50173", "50174", "573965", "574897", "5936", "60983", "61294",
"71858", "71859", "73587", "74430", "74431", "777354", "78510",
"78513", "91712", "91771", "92834", "937320", "98592", "98593",
"98594", "A07383", "A21329", "A22067", "A49492"), class = "factor"),
species = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L), .Label = c("A. cinerea", "E. lutris",
"L. canadensis", "P. brasiliensis"), class = "factor"), forage = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("hand",
"mouth"), class = "factor"), tl = c(94.1, 91.7, 89.2, 92.7,
90.5, 93.7, 90.6, 87.7, 90.4, 91.7, 96.3, 86.6, 91.9, 89.9,
91.7, 90.3, 89.1, 92.6, 95.6, 81.9, 91.4, 84.3, 85.3, 140.4,
126.1, 149.6, 119.2, 137.1, 127.2, 121.2, 129.9, 121.1, 127.9,
128.6, 111.6, 129, 124.2, 130.2, 129, 128.2, 118.4, 125,
129.2, 123.6, 123.8, 125.8, 133.2, 120.4, 128.5, 137.2, 133.4,
128.1, 129, 139, 125.1, 128.4, 120.8, 129.7, 123.1, 116.6,
140.5, 121.4, 124.5, 153, 135.5, 146.3, 139.6, 128.9, 135.8,
148.3, 147.8, 127.5, 137.3, 135.5, 116.1, 123.8, 127, 129.8,
124.9, 133.1, 129.4, 123.3, 114.9, 126.1, 119.5, 124, 135.6,
110.3, 114.4, 138.2, 121.6, 115.7, 113.9, 106.1, 113, 119.8,
111.7, 109.9, 119.7, 111.1, 115.4, 114.5, 111.6, 119.4, 113,
117.8, 114.1, 113.7, 110.6, 118.7, 115.7, 112.7, 109.5, 110.2,
114.2, 116, 120.1, 111.6, 112.6, 119.5, 111.1, 114.2, 109.7,
115.8, 109.4, 118.8, 114.7, 103.6, 108.9, 108.9, 107.8, 100.9,
105.5, 149.8, 155.2, 166.2, 149.5, 148.3, 149.9, 139.6, 158.5,
116.8, 147.2, 157.3, 117.2, 146.4, 145, 153.6, 134.5, 159.9
), bcw = c(48.4, 46.9, 46.3, 47.9, 46.4, 50.5, 45.9, 46.2,
46.9, 44.7, 47.7, 49.3, 46.6, 45, 44.8, 45.9, 46.3, 46.4,
47.8, 45, 44.3, 44.6, 50.2, 76.5, 74.6, 78.3, 75, 80.3, 72.9,
75.7, 77.5, 74.4, 74, 75.2, 73.6, 77, 75.5, 75.3, 76.8, 76,
78.1, 74.7, 76, 77.7, 79.4, 76.9, 78.1, 75.7, 77.6, 78, 83.5,
81.7, 82, 79.9, 77.4, 81.1, 75.6, 83.7, 79.7, 78.3, 80.1,
74.2, 78.2, 79.5, 77.2, 80.7, 81.5, 72.6, 76.7, 74.1, 82.1,
76.9, 76.3, 75.3, 70.7, 73.8, 77.8, 81.6, 77.2, 75.8, 83,
76.3, 68.3, 75.5, 74.1, 73.9, 78.2, 73.4, 75.5, 82.8, 73.4,
55.8, 57, 54.3, 54.6, 58.2, 55.2, 54.7, 57, 57.8, 59.8, 56.2,
54.7, 57, 57, 58.2, 57.9, 54.2, 57.1, 60.4, 57, 53.6, 56.3,
53.8, 57.1, 57.8, 59.7, 57.9, 54.8, 57.7, 56.8, 57.5, 54,
56.6, 56.7, 54.3, 54.6, 57.6, 56.1, 53.1, 52.7, 51.1, 54.1,
71.4, 71.9, 75.8, 67.8, 72.3, 72.9, 72.5, 77.5, 62.2, 69.4,
70.3, 65.6, 69.2, 74.7, 70.5, 66.8, 72.9), bcl = c(46.5,
44.3, 52.7, 49.3, 45.3, 44.9, 46.5, 46.3, 46.4, 45.6, 47.3,
49.7, 49.2, 48.3, 48.2, 48.2, 49.4, 44.8, 50.7, 40.9, 46.7,
43.7, 48.4, 70.3, 65.4, 77.4, 68, 69.7, 56.6, 59.1, 64.8,
62.3, 63.8, 63.1, 58.3, 61.6, 72, 70.6, 66, 58.9, 65.1, 67.5,
67.4, 58.6, 67.5, 71.1, 65.9, 64.2, 69.6, 65.4, 80.2, 75.9,
69.1, 62.9, 71.4, 76.5, 65.3, 66.7, 66.8, 64.9, 64.5, 58,
67.7, 70.3, 64.3, 69.7, 70.2, 58.9, 62.4, 67.2, 76, 66.6,
61.2, 71.8, 66.3, 59.5, 70.5, 66.8, 64.6, 69.5, 66.9, 68.8,
62.5, 69.1, 57.6, 61.5, 63.2, 62, 54.9, 73.3, 64.1, 63.6,
57.1, 52.3, 55.8, 56.6, 57.1, 56.7, 54.6, 55.2, 54.9, 54.7,
55.6, 57.9, 54.4, 52.9, 58.9, 52.5, 52.9, 52.1, 56, 57.7,
53, 53.4, 53.7, 57, 54.1, 50.8, 52.8, 54.5, 55.7, 55.8, 57.7,
57.5, 61.1, 63.3, 53.1, 56.5, 49.2, 52.3, 48.8, 48.9, 54.3,
64.2, 67.2, 71.4, 66.5, 58.7, 60, 73, 70.8, 61.6, 63.7, 65.9,
65.2, 59.5, 65.2, 66.1, 57.9, 66.3), cbl = c(91.2, 87.8,
85, 87.9, 87.5, 90.7, 88.5, 84.3, 85.6, 87.9, 93.1, 83.9,
87.7, 86.3, 89.5, 87, 84.9, 90, 92, 81.2, 91.4, 81.9, 87.8,
132.3, 121.4, 133, 115.1, 127.3, 125, 121.9, 124.9, 123.6,
118.6, 123.7, 110.8, 126.7, 118.6, 125.8, 120.9, 122.2, 118.8,
122.4, 126.1, 123.9, 121.5, 124.4, 128.7, 122.2, 121.9, 128,
133.7, 126, 119, 119.4, 123.6, 127.9, 113.2, 124.9, 116.9,
116.6, 130.4, 116.1, 126.4, 138.7, 128.8, 137.2, 133, 123.7,
129.6, 138.7, 139.2, 119.2, 126.3, 127.9, 109.8, 122, 116.5,
127.4, 117.6, 125, 127, 117.8, 106.6, 126, 115.4, 120.2,
133.1, 102, 102.8, 128.3, 119.1, 118.2, 117.6, 106.3, 112.8,
120.1, 113.5, 113.7, 120.5, 108.2, 118.3, 115.2, 111.7, 118.6,
114.3, 117.5, 114.7, 116.2, 107.8, 118.3, 116.7, 112.8, 111.8,
110.7, 113, 117.2, 119.7, 113.1, 112.2, 119.7, 111.1, 116.8,
107, 116.4, 108.5, 119.4, 114.2, 104, 111.4, 110.9, 107.5,
99.3, 106.8, 146.9, 157.6, 164.6, 151.9, 150, 149, 131.3,
158.9, 137.4, 149.5, 156, 106.9, 148.3, 135.5, 145.2, 135.3,
157.9), fl = c(18.9, 19.1, 15.8, 14, 13.3, 16.1, 13.7, 19.6,
15.2, 20, 19.7, 15.4, 15.6, 17.3, 16.6, 16.6, 16.4, 17.5,
16.4, 16.4, 17.8, 17, 19.5, 31.7, 31.6, 36.9, 23.5, 28.2,
30, 28.6, 27.7, 25.5, 27.6, 25, 28.1, 30.3, 25.9, 29.3, 28.1,
26, 25.9, 28.5, 31.3, 31.1, 28.3, 31.8, 30.9, 22.8, 29.7,
25.2, 33.4, 29.2, 29.6, 28.7, 24.4, 22.6, 25.3, 26.9, 24.8,
22.9, 38, 27.7, 24.2, 25.4, 31.8, 35.5, 29.4, 26.8, 31.1,
30.9, 32.2, 24, 29.5, 29.7, 20.1, 24.9, 25.7, 26.6, 24.1,
28.6, 23.5, 24.1, 21, 25.5, 21.4, 26, 28.4, 18.4, 19.4, 39.1,
26.1, 25.8, 31.9, 30.5, 33.6, 26.2, 25.8, 26.4, 35.1, 24.6,
34.5, 32, 26.9, 31.2, 26.8, 34.1, 27.8, 27.8, 26, 31.7, 29,
30.3, 27.6, 31.4, 26.2, 28.5, 30.6, 29.9, 24.6, 26.1, 25.1,
27.7, 26.2, 29.1, 23.3, 33.7, 27.5, 27.6, 25.9, 26.9, 30.5,
21, 27.1, 26.3, 31.7, 30.6, 25.9, 26.8, 22.8, 23.7, 34.9,
26.7, 39.2, 28.2, 29.5, 29.3, 30.3, 32.1, 28.8, 33.9), rwc = c(21.1,
21, 20, 21.4, 21.8, 21.5, 23, 20.6, 20.6, 21, 21.2, 22.2,
22.8, 20.6, 20.6, 20.7, 20, 21.6, 22.1, 19.2, 22.7, 20.4,
21.8, 37.7, 38.6, 41.7, 37.4, 37.6, 37.1, 36.6, 42.4, 37.7,
36.9, 38.3, 34.9, 38.3, 39, 39.5, 36.8, 36.1, 36.1, 38.8,
37.8, 35, 38.4, 37.7, 38.9, 37.8, 37.6, 42.1, 43.1, 38.1,
40.1, 38.1, 38.7, 39.7, 37.8, 39.6, 38.8, 37, 36.5, 31.5,
38.8, 44.4, 38.9, 42.5, 41, 38.1, 40.5, 44.5, 43, 38.1, 38.6,
42.5, 31.8, 37, 33.5, 41.9, 33.1, 40.1, 39.8, 37.4, 34.2,
37.6, 36.3, 37.6, 40.4, 35.8, 30.3, 38.4, 34.9, 27.2, 28.7,
25.5, 25.8, 30.1, 26.3, 26.2, 30.6, 24.8, 28.5, 28.5, 28.4,
28.2, 28.1, 28.2, 27.9, 26.4, 27.4, 29.7, 27.7, 25.3, 25.9,
26.6, 27.5, 28.2, 28.5, 27, 27, 30, 27.3, 27.4, 25.5, 28,
27.2, 28.8, 27.9, 26, 24.9, 25.2, 26.3, 24.6, 26.5, 33, 33.1,
36.6, 35.1, 34, 34.7, 30.6, 37.6, 26.8, 34.3, 36.6, 28.9,
32.5, 32.4, 35.1, 28.9, 35.8), rwm = c(33.8, 33.6, 32, 31.9,
35.2, 33.5, 34.6, 32.4, 33.1, 33.2, 33, 33.8, 33.4, 33.7,
33.7, 33, 32.7, 33.3, 32.2, 32.1, 36.4, 30.8, 33.3, 60.4,
56, 60.5, 55.6, 56.5, 54.2, 55.7, 58, 57.7, 55.3, 57.9, 55.1,
55.1, 54.4, 57.6, 54.8, 55.6, 57.7, 55.3, 57.2, 57, 56.4,
55.4, 58.1, 55.4, 54, 56.6, 60.1, 55.1, 57, 56.6, 58.2, 57.2,
57.9, 58.4, 56.2, 57.2, 57.2, 53.5, 55.5, 61, 57.5, 61.5,
62.6, 58.3, 58.1, 59.3, 59.2, 55.7, 57.4, 58.4, 53.7, 55.7,
54.5, 58.6, 51.3, 56.1, 56.2, 56, 52.8, 56.8, 52.4, 56.4,
57.9, 54.3, 55.7, 58, 53.3, 38.6, 38.4, 35.7, 35.7, 39, 36.4,
34.5, 37.8, 37.2, 37.8, 36.7, 37.6, 39.4, 36.5, 38.5, 37.2,
35.2, 38.1, 39.4, 38.2, 36.2, 37, 36.5, 36.6, 38, 37.6, 36.9,
37.8, 39.4, 38.6, 36.9, 34.7, 38.7, 36.2, 39.8, 37.6, 37.1,
36.2, 34.2, 39.6, 34.7, 36.4, 50.2, 51.6, 53.4, 50, 49.5,
48.1, 51.1, 54.2, 46.9, 49.4, 52.4, 47.5, 50.9, 49.7, 50.5,
48.2, 48.6), gsw = c(62.6, 58.4, 59.2, 60.1, 63.1, 64.4,
64.1, 58.4, 60.3, 59.8, 62.6, 56.1, 62.5, 59.3, 62.4, 57.9,
58, 59.7, 60.7, 59.9, 62.4, 57.6, 64.3, 103.7, 82.4, 103,
86.9, 102.7, 96, 91, 102.1, 98.8, 96.5, 93.9, 84.7, 94.1,
94.5, 100.3, 95.9, 94.5, 88.8, 96.6, 96.5, 97.6, 95.2, 96.3,
99.7, 99.3, 95, 98.5, 93.1, 98.7, 91.7, 97.7, 84.3, 99.2,
85.6, 100.1, 89.6, 91.3, 99.6, 83.9, 96, 106.7, 97.7, 104.2,
103, 90.2, 101.1, 99, 106, 93.7, 99.2, 101.3, 81.2, 93.9,
97, 104.2, 94.1, 98.5, 98.8, 91, 91.7, 97.9, 92.1, 98.2,
102.8, 79.8, 80.4, 96.9, 94.2, 76.5, 75.5, 67.8, 72.2, 76.3,
70.3, 72.8, 77.3, 71.7, 75.8, 74.7, 74.3, 77.1, 72.6, 77.3,
74.7, 71.1, 72.2, 78.2, 77.7, 67.7, 71.2, 73.2, 75.1, 74.5,
75.7, 75.8, 73.1, 80.9, 74.9, 78.9, 68.8, 77.3, 72.7, 74.7,
72.2, 70, 68.7, 68.6, 88.5, 68.3, 69.3, 91.3, 101.2, 102.1,
95.1, 96.3, 96.5, 82.5, 101.9, 67.9, 92.2, 99, 69.7, 93,
87.8, 92, 82.2, 94), zw = c(1.4, 1.4, 1.8, 1.4, 1.9, 1, 1.5,
1.4, 1.3, 1.3, 1.7, 2.1, 1.4, 1.2, 1.5, 1.8, 1.6, 1.2, 1.2,
1.3, 1.3, 1.6, 1.5, 2.8, 2.5, 2.9, 2.7, 2.9, 2.3, 2.8, 2.2,
2.3, 2.4, 2.7, 2.6, 2.7, 2, 2.3, 2.3, 2.5, 2.6, 2.1, 2.6,
2.3, 2.7, 2.5, 2.7, 3.1, 2.3, 2.6, 2.6, 2.3, 2.9, 2.3, 2.2,
3.2, 3.3, 2.4, 2.8, 3.1, 2.7, 2.5, 2.1, 4.5, 2.9, 3.5, 2.8,
3.4, 3.1, 3.8, 2.2, 3.2, 2.6, 2.7, 2.5, 2.2, 2.4, 3.3, 2.3,
2.6, 3.9, 2.8, 2.5, 2.1, 3.4, 2.1, 2.5, 3, 3.6, 2.9, 2.5,
1.7, 1.2, 1.8, 2, 2.2, 2.6, 1.7, 1.4, 2.8, 1.8, 2.4, 2.1,
1.9, 1.6, 1.7, 1.7, 1.8, 1.5, 1.9, 1.7, 1.7, 1.9, 1.6, 1.7,
1.6, 1.6, 1.4, 1.4, 1.5, 2.4, 2, 1.8, 1.9, 2.3, 2.1, 2.4,
1.8, 3.1, 1.5, 1.4, 1.6, 1.4, 2.2, 2.7, 3.4, 2.9, 2.4, 2.3,
3.5, 3.1, 3, 2.5, 2.3, 2.5, 2.5, 3.1, 2.5, 3.5, 3.6), zh = c(4.2,
4.6, 4.6, 4.8, 5.6, 4.8, 5, 3.7, 4.4, 4.6, 4.1, 3.6, 6.5,
4.1, 4, 4.7, 4.5, 5.5, 4.3, 5.5, 5.3, 3.9, 6.2, 7.3, 6.2,
8.9, 7.9, 7.5, 7.2, 7.6, 7.6, 7.8, 8.5, 7.4, 6.3, 7.3, 6.7,
8.8, 8.4, 7.2, 6.8, 6.8, 7.6, 7.3, 8.7, 7.3, 7.7, 6.7, 6.7,
8.2, 7.7, 7, 6.7, 6.5, 6.7, 8.3, 6.9, 8, 6.5, 7.7, 8.3, 7.2,
7.7, 9, 8, 8.5, 9.3, 7.7, 8.1, 10.8, 8.7, 8.3, 8, 9.3, 6.2,
6.6, 6.4, 8.7, 8.3, 8.9, 8.2, 8.4, 6.8, 7, 8.6, 7.6, 7.6,
6.6, 7.1, 9.4, 8, 6.1, 5.1, 5.2, 4.8, 6.1, 5.3, 6.6, 5.7,
6, 5.8, 6, 6.4, 6.3, 6.2, 6, 5.1, 5.3, 5.5, 8, 5.5, 5.6,
5.9, 5.9, 5.7, 5.9, 6.4, 5.7, 5.6, 8.2, 5.5, 5.8, 5.8, 6,
5.2, 5.8, 5.9, 5.1, 5.5, 6, 4.6, 5.9, 5.5, 10.9, 10.7, 10.8,
8.8, 11.1, 12.1, 8.7, 10.3, 5.6, 10.3, 11.6, 7.6, 9.1, 8.9,
11.8, 7.6, 11.6), zl = c(35.8, 31, 30.2, 30.3, 30.2, 30.2,
29.3, 28.9, 29.9, 29.1, 32.7, 28.8, 31.6, 30, 31.4, 30.5,
30.8, 30.2, 31.2, 28.9, 33.1, 27.5, 30.3, 60.3, 41.5, 58.6,
52.2, 52.2, 53.6, 56.4, 53.3, 54.1, 54.1, 54.4, 53.4, 51.1,
50.9, 52.5, 55.3, 39.1, 55.5, 51.5, 54.6, 47.4, 40.2, 54.5,
37.2, 51.9, 37.7, 41.5, 44.4, 41.8, 42.3, 52.9, 39.6, 42,
37.5, 40.9, 42.1, 52.4, 53.5, 48.9, 56.4, 48.3, 44.2, 50.3,
42.1, 43.2, 44.4, 49.4, 52.4, 53.5, 51.5, 56.7, 49.4, 48.2,
51.6, 53.8, 50.2, 53.9, 56.9, 52.6, 46.6, 51.5, 48.2, 52.2,
55.6, 46.4, 40.9, 56.8, 48.8, 48.6, 37.7, 36.9, 37.3, 39.3,
36.8, 45.5, 37.3, 37.3, 36.8, 39.9, 44.2, 40.3, 36.3, 39.8,
37.1, 45.1, 35.8, 38.2, 37.4, 37.7, 35.3, 37, 38.7, 47.7,
41.7, 47.2, 38.8, 42.7, 39.2, 40.4, 33.8, 39.6, 35.3, 49.3,
37.6, 44.3, 37.5, 43.6, 40.5, 41.4, 42.6, 54.6, 59.6, 64.4,
59, 58.5, 55.3, 54.3, 62.4, 35.8, 58.5, 62.1, 42.7, 59.1,
57.2, 56.8, 51.8, 61.5), zfw = c(23.9, 21.7, 21.5, 22.5,
24, 24.8, 24.2, 21.4, 22.7, 22, 23, 19.5, 23.4, 22.5, 23.3,
21, 20.8, 22.7, 22.8, 21.6, 24.7, 22.6, 25, 37.7, 26.5, 37.5,
29.4, 33.7, 33.9, 31.3, 34.8, 34.6, 34.5, 31.2, 27.9, 34.1,
34.5, 34.5, 35.4, 32, 31.4, 33.6, 34.3, 33.5, 31.3, 33.3,
34.9, 34.3, 32, 33.8, 33.3, 32, 30.8, 33.4, 27.1, 32.4, 27.8,
34.8, 29.3, 30.1, 36.4, 27.2, 32.6, 36.9, 34.5, 34.2, 35.6,
29.4, 34.8, 34.6, 35, 29.9, 31.4, 33.1, 26.2, 32, 32.4, 32.8,
33, 32, 29.8, 29, 31.6, 32.1, 30.5, 32.8, 32.9, 24, 24.2,
31.8, 31, 30.3, 28.5, 24.8, 26.9, 29.1, 24.2, 28.3, 30.2,
25.8, 26.7, 26.3, 29.1, 27.6, 26.3, 27.7, 27.8, 27.4, 26.6,
28.9, 28.6, 23.6, 26.9, 25.9, 27.5, 26.7, 27.7, 27.7, 27.9,
29.5, 27.2, 28.6, 24.5, 28.3, 24.9, 28.1, 27, 25.3, 24.3,
25.2, 26.2, 24.6, 27.1, 33.7, 37.6, 39.3, 35.9, 37.7, 36.9,
29.6, 37.8, 23, 36.3, 37.1, 22.7, 34.7, 30.8, 33.3, 30.5,
35.5), zfl = c(28.5, 24.9, 29.7, 24.3, 24.6, 25.2, 23.7,
22.8, 23.6, 23.4, 27, 22.5, 23.5, 23.7, 24.9, 24.1, 23.5,
25.1, 25.8, 23.9, 24.9, 22.2, 24, 38.8, 29.6, 37.8, 30.6,
37, 34, 32.3, 34.2, 33.8, 33.6, 33.4, 28.2, 32.8, 35.9, 34.5,
35.2, 31.1, 30.8, 33.4, 37.7, 33.8, 31.4, 33.5, 33.1, 33,
33.1, 35.5, 36.7, 33.6, 31.3, 34, 29.1, 34.8, 29, 34.4, 31.1,
30.2, 33.8, 30, 36.1, 40.3, 35.2, 39.5, 37.1, 33.5, 36.1,
38.1, 40.6, 31.2, 36.8, 36.5, 26.6, 33.4, 33.9, 36.6, 35,
34.9, 35.9, 32.6, 28.9, 32.9, 32, 34.4, 38.9, 28.5, 24, 33.4,
31.4, 31.2, 29.3, 28.4, 30.2, 31.6, 28.5, 29.4, 30.9, 29,
29.9, 30.1, 29.3, 31.6, 30.5, 31.2, 29.2, 30.1, 28, 31.5,
30.2, 30.8, 27.7, 30, 30.9, 30.9, 31.6, 31, 29.5, 31.1, 27.8,
31.8, 26.9, 31.1, 27.7, 33.3, 29.9, 26.3, 28.8, 27.1, 29,
26.4, 27, 38.5, 44.5, 45.1, 39.9, 42.1, 38.2, 34.7, 42.8,
26.4, 39.6, 42.9, 27.8, 40.6, 38, 38.6, 35.8, 42.4), pl = c(40.9,
40.7, 36.6, 39.4, 38.3, 40.7, 40.4, 38.5, 37.8, 39.1, 43.3,
38.4, 40.6, 38.6, 40.1, 37.5, 36.4, 41.1, 41.9, 37, 39.8,
37.3, 40.1, 60.4, 56.3, 55.8, 51.4, 56.8, 53.9, 55.2, 54,
55.5, 54.2, 55.6, 54, 53.1, 50.2, 55, 54.8, 52.7, 50.3, 54.2,
54.2, 55.3, 55, 52.5, 57.3, 53.5, 51.4, 55.4, 57.3, 56, 53,
56.3, 50.1, 55.3, 50.2, 57.2, 52, 53.2, 55.5, 54.5, 54.9,
62.6, 57.8, 63, 59.1, 52.2, 59.1, 58.4, 60.9, 52.1, 56.7,
54.6, 47.9, 53.6, 55.7, 57.4, 52, 55.2, 54, 50.6, 48, 53.9,
53.1, 54.9, 58, 43.4, 44.5, 56.8, 51.9, 54.6, 52.3, 46.7,
50.8, 54.1, 49, 52.3, 51.9, 45.8, 55.4, 49.3, 52.1, 53.3,
50.2, 54.4, 50.3, 52, 46.9, 53.2, 50.3, 49.6, 47.3, 53.7,
51.9, 55.7, 52, 51.4, 48.9, 54.6, 49.6, 50.2, 48.3, 51.6,
47.9, 55, 50.4, 48.8, 48.8, 52, 53.7, 49.4, 49.8, 70.2, 72.7,
78.3, 72.8, 71.9, 74, 65.2, 74.9, 52.7, 68.4, 75.5, 56.5,
70.3, 65.9, 72.3, 65.2, 77.9), pw = c(11, 11, 9.8, 10.8,
10.5, 11.4, 10.8, 10.4, 10.4, 10.3, 10.9, 11.3, 11.2, 9.9,
10.9, 10.6, 10.4, 9.8, 10, 10, 10.3, 9.6, 10.7, 25.8, 22.5,
25.5, 22.5, 25.5, 24.3, 22.9, 26.4, 23.8, 23.9, 23.2, 21.7,
24.2, 23.3, 24.3, 22.7, 24.8, 22.1, 24.1, 25.3, 24.6, 24.8,
25.3, 24.5, 26, 24.5, 26, 26.4, 24.5, 24.1, 26.2, 21.6, 24.3,
22.5, 24.6, 23, 23.6, 24.9, 21.9, 25.4, 27, 23.5, 28, 27,
23.1, 25.3, 25.6, 27.6, 19.3, 24.4, 26.9, 21.4, 24.7, 23.8,
28.9, 22.3, 25.4, 25.3, 24.3, 24.5, 24.7, 22.7, 26.2, 25.8,
21.3, 20.8, 24.7, 24.7, 13.1, 14.7, 14.6, 14.1, 15.1, 16.2,
14.2, 15.8, 14.1, 15.1, 14.4, 14.2, 15.7, 14.7, 15, 15.2,
13.1, 14.6, 15.2, 14.6, 13.9, 14.4, 14.3, 14.3, 14.8, 15.2,
14.1, 15, 16.1, 14.2, 15.1, 13.3, 14.9, 15.1, 14.8, 14.5,
14.3, 15, 14.7, 13.3, 13.9, 13.9, 15.6, 15.9, 17.8, 15.2,
16.1, 15.5, 16.8, 17.7, 17.4, 16.1, 17.7, 17.1, 16.8, 16.8,
17.1, 15.6, 16.7), mw = c(53.6, 53.8, 49.7, 53, 52.3, 56.6,
55.7, 48.1, 52.1, 52.8, 54.8, 50.7, 55, 51.5, 54.9, 50, 51.7,
51.6, 55.7, 52.1, 54.3, 51.1, 58.6, 96.2, 79.4, 97.1, 80.7,
93.7, 91, 85.5, 94.5, 90.1, 91.5, 90.3, 81.4, 96.6, 90.1,
91.6, 91.6, 87.8, 86.5, 89.9, 90.3, 88.4, 93.2, 93.3, 92.1,
92.3, 90, 91.8, 89.2, 91.7, 87.8, 91.3, 81.4, 92.6, 82.8,
96.4, 85.7, 88.9, 94, 81.2, 94.3, 107.1, 92.3, 100.6, 100.3,
90.5, 94.9, 99.1, 100.8, 87.4, 98.1, 97.4, 71.1, 86.9, 91.7,
96.7, 88.1, 92.6, 97.6, 88.8, 82.1, 91.5, 88.1, 91.5, 97,
77.4, 77.2, 99, 91.1, 68.6, 66.9, 58.8, 64, 69.6, 63.7, 66.5,
69.8, 65.4, 70.4, 67.8, 67, 68.1, 69.4, 65.7, 68, 63.3, 62.6,
72.8, 70.2, 61.9, 63.6, 63.6, 65.8, 65.7, 69.9, 68.5, 66.2,
62.7, 66.9, 68, 63.1, 68.4, 65.6, 68.7, 66.4, 61.5, 61.3,
63.9, 64.4, 63.5, 63.4, 79.2, 85, 82, 80.3, 78.4, 80, 71.6,
85, 57, 75.9, 84.8, 58.6, 81.1, 72.9, 81.7, 70.4, 83), iod = c(17.8,
17.4, 16.7, 18.5, 16.3, 20.5, 18.1, 17.5, 17.1, 16.8, 18,
17.6, 18.9, 18.8, 16.6, 17.3, 16.6, 18.9, 18.6, 15.2, 18.1,
15.4, 18.5, 41.1, 36.1, 39.1, 35.9, 40.6, 39.3, 37.7, 40.4,
37, 38.4, 37.1, 33.1, 39.7, 38.6, 40.5, 38.6, 37.5, 35.7,
38.3, 36.9, 37.1, 39.5, 38.5, 40.7, 32, 39.1, 40.1, 41.1,
40.2, 39.2, 38.9, 36.1, 38.2, 36.4, 42.5, 38.8, 37.8, 39.4,
33.6, 39.5, 45.9, 40.6, 40.8, 43.2, 37.8, 37.4, 47.2, 41.4,
37, 39, 40.1, 33.7, 36.2, 36.7, 41.8, 36.7, 41.4, 38.8, 37.5,
35.4, 36.5, 37.6, 39.7, 41, 32.3, 33.3, 37.6, 34.7, 25.9,
24.7, 22.3, 24.5, 28, 25.3, 25, 26.8, 23.2, 23.8, 25.6, 25.8,
27.2, 27.7, 24.9, 25.1, 24.1, 21.9, 26, 24.9, 23.7, 23.9,
22.9, 24.3, 24.1, 26.6, 23, 25.1, 27.1, 23.7, 24.2, 24.1,
24.7, 34.4, 25.8, 25.7, 23.2, 23.2, 23.8, 23.5, 24.9, 24.5,
18.7, 18, 20.3, 17.8, 17.2, 16.8, 17.6, 19.3, 15.8, 18.1,
19.8, 15.9, 15.9, 19.3, 18, 15.6, 17.1), osa = c(14.8, 19.4,
20.4, 18.9, 20.2, 21.5, 19.1, 20.6, 19.6, 20.5, 19.6, 24,
21.6, 19.5, 19.2, 18.3, 20.1, 19.5, 20.8, 14.7, 14.2, 12.9,
16.2, 12.5, 12.7, 13.1, 14.8, 12.4, 13.8, 12.8, 13.5, 13.7,
13.3, 13.3, 12.2, 13.1, 13.1, 12.9, 13.1, 13, 12.7, 12.4,
15.3, 12.9, 13.4, 21.6, 21.4, 14.6, 20.7, 21.2, 20.7, 21.2,
21.6, 21.5, 21.4, 20.8, 15.9, 18.9, 20.8, 21.3, 20.5, 13.1,
20.6, 14.6, 15.1, 13.9, 14.4, 14.8, 14.4, 15, 13.7, 20, 21,
19.4, 22.4, 20.3, 20.2, 19.2, 19.5, 18.9, 21.1, 21.5, 21.5,
21.4, 20.8, 19.5, 20.9, 17.8, 19.8, 21.6, 20.9, 20.2, 30.4,
21.6, 21.4, 21.3, 20.6, 30.4, 21.8, 20.3, 20.7, 22.7, 22.1,
21.4, 22.1, 25.1, 21.2, 20.7, 20, 21.2, 21.7, 20.3, 22.4,
21.8, 21.2, 18.1, 21, 22.7, 19.8, 14.5, 15, 13, 22.6, 14.9,
13.5, 13.9, 15.9, 14.8, 19.3, 14.4, 13.1, 15.8, 20.8, 15.4,
15.9, 14, 13.1, 14.9, 15.1, 14.6, 14.7, 14.3, 14.1, 13.8,
15.2, 14.5, 14.8, 14.6, 14.5, 13.2), mrw = c(15.1, 12.7,
12.4, 13.4, 14.4, 14.5, 13.7, 13.2, 12.5, 13.2, 15.6, 11.1,
13.1, 12.1, 13.4, 13.5, 13.5, 13.4, 13.9, 12.2, 13.9, 12.5,
12.6, 23.5, 18.8, 24.9, 18.9, 20.9, 20.1, 19.8, 20.3, 20,
19.9, 21.7, 16.4, 20.7, 19, 21.5, 21.4, 20, 17.5, 20.1, 20.1,
21.4, 19.9, 20.9, 21.3, 20, 20, 22.5, 21.9, 20.7, 19.8, 20.5,
20.2, 19.8, 18, 20.3, 18.6, 17.8, 20.3, 18.8, 22.2, 24.8,
22.5, 20.9, 21.9, 21.2, 18.5, 25.3, 24.1, 20.1, 20.4, 22.4,
18.3, 21.5, 20.2, 23, 21, 21.4, 22.4, 20, 19, 21.6, 18.1,
20.5, 22.7, 18.5, 16.7, 21.2, 20.5, 17.2, 16.7, 16.4, 15.4,
18.5, 16.2, 16.6, 17.5, 16.1, 16.7, 17.1, 15.1, 18, 17.5,
16.6, 16.3, 15.6, 16.4, 16.9, 17.2, 15.5, 14.9, 15.8, 16.8,
16.5, 17.3, 16.2, 16.6, 18.4, 16.3, 17.7, 14, 17.5, 15, 18.4,
17.4, 14.2, 16.9, 15.2, 15.9, 15.4, 15.1, 20.4, 24.6, 24.3,
22.4, 22.4, 21.4, 17.8, 24.6, 12.7, 20.9, 24.1, 13.1, 23.4,
19.1, 22, 17.8, 24), mrh = c(27.8, 26.7, 25.9, 28, 26.2,
29, 28, 24.4, 27.1, 21.3, 28.5, 25.9, 27.9, 25.1, 27.8, 26.2,
26.7, 26.2, 27.7, 24.7, 27.5, 23.2, 26.4, 57.1, 37.2, 52.3,
42.8, 55, 48.8, 46.7, 51, 47.4, 50, 46.5, 41.5, 51.8, 49.8,
50.6, 50.7, 46, 43.4, 49.7, 49.4, 45.1, 46.6, 48.2, 50.3,
49.7, 43.9, 55.6, 53.9, 49.2, 40.5, 47.6, 48.3, 49, 40.8,
52.9, 41.6, 48.8, 49.8, 42.7, 51.9, 57.5, 53.3, 55.1, 54.2,
49.5, 49.7, 57.2, 54.4, 44.1, 50.7, 56.8, 37, 48.4, 45.1,
54.2, 46.9, 51, 49.2, 49.2, 37.7, 52.3, 51.5, 51.6, 54.3,
35.7, 33.2, 54.4, 46.8, 35.9, 30.5, 30.3, 30.1, 33.7, 33,
31.9, 33.2, 32.1, 32.9, 32.5, 31.8, 34, 30.5, 32.6, 32.1,
31.7, 32.2, 32.4, 33, 31.1, 31.1, 30.1, 32, 30.4, 33.3, 33.2,
30.6, 33.9, 31.7, 31.8, 29.1, 33, 29, 34.4, 33.8, 29.2, 30.5,
29.7, 33.3, 30.2, 30.7, 38.1, 43.6, 42.7, 39.9, 40.1, 38.5,
35.5, 43.2, 24.9, 38, 44, 27, 40.6, 40.9, 38.7, 36.8, 43.2
), mat = c(21.9, 20.3, 20.7, 22.1, 21.4, 22.3, 20.8, 18.5,
20.6, 20.7, 25, 21.3, 21.2, 19.8, 21.3, 20.8, 21, 20.7, 21.3,
18.4, 21.5, 16.9, 18.3, 34.6, 21.5, 33.6, 25.1, 30.9, 29.3,
26.3, 28.7, 27.5, 28.3, 28.7, 23.2, 30.5, 27.2, 31.6, 31.2,
28.3, 25.5, 30.7, 31.5, 26.1, 29.9, 30.6, 29.5, 30.5, 27.9,
32.5, 32.1, 29.6, 26.4, 28.2, 28.5, 28.3, 22.7, 30.3, 22,
28.1, 29.9, 22.9, 29.7, 35.1, 31.4, 32.3, 31.1, 28, 29.3,
31.3, 35.8, 28.2, 30.9, 34, 25.3, 30.2, 26.8, 34, 26.8, 30.2,
32, 28.9, 24, 33, 28.6, 30.3, 33.6, 21.4, 22.6, 29.8, 30.7,
27.9, 24.8, 25, 24, 27.4, 26.3, 26.7, 26.8, 25.8, 26.5, 24.5,
25.2, 28.7, 26.3, 25.8, 25.9, 25.5, 26, 26.9, 26.8, 24.2,
25.4, 23.6, 26.2, 26, 26.6, 26.3, 23.9, 25.5, 24.8, 24.4,
24.3, 25.5, 21.5, 28.7, 27.7, 23.1, 26.2, 22.3, 22.4, 21.8,
25.1, 30.8, 38.7, 37.6, 31.4, 33.9, 32.1, 27, 35.6, 17.2,
33, 34.8, 20.4, 32.1, 29, 33.1, 28.1, 35.8), olc = c(13,
13.3, 12.3, 10.6, 12.1, 11.9, 11.4, 11.3, 12.1, 12.5, 13.4,
12.3, 12.1, 13, 11.8, 12.3, 11.6, 12.8, 12.1, 12.2, 13.1,
10.9, 13, 21.5, 16.8, 19.9, 18.1, 19.6, 20.5, 19, 19.7, 19.8,
20.1, 19.2, 16.8, 18.6, 20.3, 20.6, 21.2, 16.6, 18.9, 20.1,
20.9, 17.5, 15.9, 18.9, 19.1, 19.4, 16.3, 16.7, 15.2, 18.5,
17.8, 20.2, 14.4, 18.2, 16.3, 17.2, 15.8, 17.8, 21.6, 19,
17.8, 16.7, 14.9, 18.5, 17.5, 16.6, 19.7, 19, 17.1, 17.8,
19, 22.9, 18.6, 17.2, 19.1, 17.3, 18.6, 20.5, 20.5, 18.4,
19.7, 18.3, 18.2, 20.1, 19.8, 16.9, 16.8, 19.2, 19.9, 16.2,
13.8, 13.7, 12.8, 15, 14, 16.1, 16.1, 15.5, 14.5, 12.3, 15.5,
10.8, 14.1, 14.7, 14.2, 16.3, 13.9, 15.6, 13.8, 15.5, 14.9,
14.4, 15.8, 15.6, 13.6, 14.7, 16.1, 14.9, 14, 14.6, 13.6,
14.5, 14.5, 16.1, 13.2, 13.2, 15.3, 12.6, 15.4, 14.1, 14.3,
17.5, 18.9, 18.3, 19.6, 19.1, 20.4, 18.5, 23.4, 17.4, 20.2,
21.5, 18.5, 21.6, 19.3, 19.7, 18.8, 22.1), mam = c(10.5,
8.3, 9.4, 10.5, 9.6, 11.1, 11.5, 8.2, 11.4, 10.4, 10.5, 11.2,
11.6, 10, 11.7, 10.6, 10, 10.4, 10, 10.5, 11.4, 9.5, 10.8,
24.7, 19.1, 22.3, 20.3, 20.9, 18.8, 22.7, 19.7, 20, 20.8,
21.3, 18.5, 19.3, 19.4, 21.6, 21.4, 19.7, 21.3, 20.7, 20.7,
19.8, 21.8, 21.4, 20.3, 21.2, 20.5, 19.8, 21, 22, 20.8, 20.6,
20.4, 22.2, 20.3, 22.5, 18, 20.9, 20.2, 17.3, 20.5, 22.6,
21.4, 21.1, 22.1, 18.3, 20.9, 21.4, 21.5, 21.5, 19.3, 20.7,
16.3, 18.7, 18, 19.1, 16.7, 19.6, 19.4, 18.7, 16.9, 18.8,
21, 19.6, 21, 15.7, 17.7, 21.9, 19.3, 16.6, 16, 14, 13.5,
14.7, 15.4, 14.9, 16.3, 14.7, 15.4, 16.5, 14.9, 15.3, 14.3,
16.2, 14.9, 13.6, 16.6, 15, 15.6, 15, 14.9, 15.4, 15.6, 15.3,
15.3, 15.7, 16.3, 15, 13.9, 16.5, 14.9, 16.2, 15.5, 14.7,
14.8, 14.6, 14.3, 13.4, 12.6, 13.3, 14.4, 17, 18, 18, 17.3,
17.8, 17.2, 16.3, 19.4, 14.4, 17.8, 19, 14.3, 16, 16.7, 17,
15.4, 18), jl = c(61.6, 59.4, 56.3, 58.1, 58.6, 60.7, 59.1,
57.1, 56.7, 59.2, 63.2, 55.8, 58.8, 57.4, 60.1, 58.4, 55.3,
59.7, 61, 55.8, 62.6, 55.9, 60.8, 94.6, 80.2, 93.8, 80.6,
87.2, 85.3, 83, 85.2, 85.4, 83.3, 84.7, 74.9, 85.5, 81.5,
85.7, 84.7, 81, 80.4, 82.8, 84.2, 83.9, 81.6, 83.9, 85.4,
82.9, 81.7, 87.2, 90.4, 85.2, 80.8, 84.4, 81.9, 86.7, 76.1,
84.9, 79.5, 79.7, 88.8, 74.9, 85.5, 95.2, 88.6, 97.7, 92.1,
83.9, 89.4, 94.4, 93, 83.5, 87.4, 90.2, 72.9, 82.1, 84, 90.4,
82.5, 87.6, 86.4, 82.3, 77.2, 84.7, 79.8, 85.6, 91.1, 71.8,
70.4, 85.2, 82, 76.6, 72.3, 66.5, 69.8, 76.9, 69.9, 71.4,
76.7, 69.5, 74.5, 70.8, 72.5, 76.2, 71.7, 74.8, 72.3, 72.5,
70.3, 73.7, 72.8, 72.1, 70.1, 71.2, 72.9, 74.1, 76.9, 73.3,
71.2, 74.5, 69.7, 73.3, 68.2, 75.3, 69, 78.5, 71.7, 65.6,
68.6, 68, 68.9, 63.6, 68.8, 96.9, 107.1, 110.5, 100.9, 101.4,
99.5, 91, 108.5, 78.2, 100.7, 105.7, 77.8, 100.2, 95.6, 97.8,
88.4, 106.3)), class = "data.frame", row.names = c(NA, -150L
))

Terrible_Coder · November 30, 2021, 8:47am

Try the following code:

Import data

Data1 <- Data
#Log transform
Data1[,5:28] <- log(Data [5:28], 2)
Data1

#Keep length values
Data2 <- Data1
Data2 <- subset(Data2, select = c(species, bcl, cbl, pl, fl, tl, zl, jl))
Data2

#Run PCA
p <- prcomp(Data2[,c(2:8)], center = TRUE, scale = TRUE)
s <- summary(p)

Screeplot

layout(matrix(1:2, ncol=2))
screeplot(p)
screeplot(p, type="lines")
par(mfrow = c(1,1))

Show PC1 and PC2 data

to plot different PCs, change the numbers

p$x[,1:2]

See importance

s$importance

Create groups

pch.group <- c(rep(21, times=23), rep(22, times=67), rep(23, times=41), rep(24, times=16))
col.group <- c(rep("blue", times=23), rep("purple", times=67),rep("red", times=41), rep("green", times=16))

Plot individuals

plot(p$x[,1], p$x[,2],
xlab=paste("PCA 1 (", round(s$importance[2]*100, 1), "%)", sep = ""),
ylab=paste("PCA 2 (", round(s$importance[5]*100, 1), "%)", sep = ""),
pch=pch.group, col="black", bg=col.group, cex=2, las=1, asp=1,
xlim= c(-4,4),ylim= c(-9,6), main= "PCA Plot")

pch = symbols

cex = symbol size

bg = background colors

las = orientation of axis labels

asp=1 esnusres axes are same scale

Add grid lines

abline(v=0, lty=2, col="grey50")
abline(h=0, lty=2, col="grey50")

Add labels

text(p$x[,1], p$x[,2], labels=row.names(p$x), pos=c(1,3,4,2), font=2)

Get co-ordinates of variables (loadings), and multiply by 10

l.x <- p$rotation[,1]*10
l.y <- p$rotation[,2]*10

Draw arrows

arrows(x0=0, x1=l.x, y0=0, y1=l.y, col="red", length=0.15, lwd=1.5)

Label position

l.pos <- l.y # Create a vector of y axis coordinates
lo <- which(l.y < 0) # Get the variables on the bottom half of the plot
hi <- which(l.y > 0) # Get variables on the top half

Replace values in the vector

l.pos <- replace(l.pos, lo, "1")
l.pos <- replace(l.pos, hi, "3")

Variable labels

text(l.x, l.y, labels=row.names(p$rotation), col="red", pos=l.pos)

Add legend

legend("bottomleft",
legend=c("A. cinerea ", "E. lutris ", "L. canadensis", "P. brasiliensis"), col="black",
pt.bg= c("blue","purple","red","green" ),
pch= c(21,22,23,24),
pt.cex=1.5)

system · December 7, 2021, 8:47am

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