Análise de Cluster
1) Foram coletadas cinco amostras, três da área um e duas da área dois. Utilize a análise exploratória de Cluster para analisar as semelhanças entre as áreas.
As cinco amostra (A1=4, A2=5, A3=1, B1=2 e B2=3) apresentam o mesmo indice de similaridade. Os grupos são 1 (sp1, sp2, sp4, sp14, sp15 e sp16), 2 (sp3, sp6, sp17, sp18 e sp19), 3 (sp5,sp7, sp20, sp21 e sp22), 4 (sp8, sp9, sp10 e sp11) e 5 (sp12 e sp13).
C1<-read.table("C1.txt",header=T)
C1## A1 A2 A3 B1 B2
## sp1 13 12 2 3 11
## sp2 8 9 5 12 31
## sp3 0 0 2 21 2
## sp4 3 11 4 0 0
## sp5 0 0 0 1 31
## sp6 0 0 11 12 0
## sp7 0 0 3 0 21
## sp8 2 3 0 0 0
## sp9 1 0 0 0 0
## sp10 1 0 0 0 0
## sp11 1 1 0 0 0
## sp12 0 1 0 0 0
## sp13 0 1 0 0 0
## sp14 0 0 1 0 0
## sp15 0 0 1 0 0
## sp16 0 0 1 0 0
## sp17 0 0 0 1 0
## sp18 0 0 0 1 0
## sp19 0 0 0 1 0
## sp20 0 0 0 0 1
## sp21 0 0 0 0 1
## sp22 0 0 0 0 1nrow(C1);ncol(C1)## [1] 22## [1] 5names(C1); row.names(C1);str(C1)## [1] "A1" "A2" "A3" "B1" "B2"## [1] "sp1" "sp2" "sp3" "sp4" "sp5" "sp6" "sp7" "sp8" "sp9" "sp10"
## [11] "sp11" "sp12" "sp13" "sp14" "sp15" "sp16" "sp17" "sp18" "sp19" "sp20"
## [21] "sp21" "sp22"## 'data.frame': 22 obs. of 5 variables:
## $ A1: int 13 8 0 3 0 0 0 2 1 1 ...
## $ A2: int 12 9 0 11 0 0 0 3 0 0 ...
## $ A3: int 2 5 2 4 0 11 3 0 0 0 ...
## $ B1: int 3 12 21 0 1 12 0 0 0 0 ...
## $ B2: int 11 31 2 0 31 0 21 0 0 0 ...library(vegan)## Carregando pacotes exigidos: permute## Carregando pacotes exigidos: lattice## This is vegan 2.6-4C1t<-log1p(C1)
C1t## A1 A2 A3 B1 B2
## sp1 2.6390573 2.5649494 1.0986123 1.3862944 2.4849066
## sp2 2.1972246 2.3025851 1.7917595 2.5649494 3.4657359
## sp3 0.0000000 0.0000000 1.0986123 3.0910425 1.0986123
## sp4 1.3862944 2.4849066 1.6094379 0.0000000 0.0000000
## sp5 0.0000000 0.0000000 0.0000000 0.6931472 3.4657359
## sp6 0.0000000 0.0000000 2.4849066 2.5649494 0.0000000
## sp7 0.0000000 0.0000000 1.3862944 0.0000000 3.0910425
## sp8 1.0986123 1.3862944 0.0000000 0.0000000 0.0000000
## sp9 0.6931472 0.0000000 0.0000000 0.0000000 0.0000000
## sp10 0.6931472 0.0000000 0.0000000 0.0000000 0.0000000
## sp11 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## sp12 0.0000000 0.6931472 0.0000000 0.0000000 0.0000000
## sp13 0.0000000 0.6931472 0.0000000 0.0000000 0.0000000
## sp14 0.0000000 0.0000000 0.6931472 0.0000000 0.0000000
## sp15 0.0000000 0.0000000 0.6931472 0.0000000 0.0000000
## sp16 0.0000000 0.0000000 0.6931472 0.0000000 0.0000000
## sp17 0.0000000 0.0000000 0.0000000 0.6931472 0.0000000
## sp18 0.0000000 0.0000000 0.0000000 0.6931472 0.0000000
## sp19 0.0000000 0.0000000 0.0000000 0.6931472 0.0000000
## sp20 0.0000000 0.0000000 0.0000000 0.0000000 0.6931472
## sp21 0.0000000 0.0000000 0.0000000 0.0000000 0.6931472
## sp22 0.0000000 0.0000000 0.0000000 0.0000000 0.6931472mC1<-vegdist(C1t, "bray")
mC1## sp1 sp2 sp3 sp4 sp5 sp6 sp7
## sp2 0.1581088
## sp3 0.5364767 0.4591672
## sp4 0.3650610 0.4047802 0.7959658
## sp5 0.5565311 0.4953160 0.6206773 1.0000000
## sp6 0.6735471 0.4984249 0.2912521 0.6943282 0.8494588
## sp7 0.5108210 0.4669707 0.5500074 0.7215711 0.2841677 0.7089816
## sp8 0.6074002 0.6643642 1.0000000 0.3760863 1.0000000 1.0000000 1.0000000
## sp9 0.8724304 0.8934882 1.0000000 0.7754547 1.0000000 1.0000000 1.0000000
## sp10 0.8724304 0.8934882 1.0000000 0.7754547 1.0000000 1.0000000 1.0000000
## sp11 0.7601591 0.7977475 1.0000000 0.5962406 1.0000000 1.0000000 1.0000000
## sp12 0.8724304 0.8934882 1.0000000 0.7754547 1.0000000 1.0000000 1.0000000
## sp13 0.8724304 0.8934882 1.0000000 0.7754547 1.0000000 1.0000000 1.0000000
## sp14 0.8724304 0.8934882 0.7682330 0.7754547 1.0000000 0.7586116 0.7318831
## sp15 0.8724304 0.8934882 0.7682330 0.7754547 1.0000000 0.7586116 0.7318831
## sp16 0.8724304 0.8934882 0.7682330 0.7754547 1.0000000 0.7586116 0.7318831
## sp17 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 0.7586116 1.0000000
## sp18 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 0.7586116 1.0000000
## sp19 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 0.7586116 1.0000000
## sp20 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 1.0000000 0.7318831
## sp21 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 1.0000000 0.7318831
## sp22 0.8724304 0.8934882 0.7682330 1.0000000 0.7142857 1.0000000 0.7318831
## sp8 sp9 sp10 sp11 sp12 sp13 sp14
## sp2
## sp3
## sp4
## sp5
## sp6
## sp7
## sp8
## sp9 0.5637914
## sp10 0.5637914 0.0000000
## sp11 0.2837911 0.3333333 0.3333333
## sp12 0.5637914 1.0000000 1.0000000 0.3333333
## sp13 0.5637914 1.0000000 1.0000000 0.3333333 0.0000000
## sp14 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp15 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.0000000
## sp16 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.0000000
## sp17 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp18 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp19 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp20 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp21 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp22 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp15 sp16 sp17 sp18 sp19 sp20 sp21
## sp2
## sp3
## sp4
## sp5
## sp6
## sp7
## sp8
## sp9
## sp10
## sp11
## sp12
## sp13
## sp14
## sp15
## sp16 0.0000000
## sp17 1.0000000 1.0000000
## sp18 1.0000000 1.0000000 0.0000000
## sp19 1.0000000 1.0000000 0.0000000 0.0000000
## sp20 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## sp21 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.0000000
## sp22 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.0000000 0.0000000dC1<-hclust(mC1, method="complete")
dC1##
## Call:
## hclust(d = mC1, method = "complete")
##
## Cluster method : complete
## Distance : bray
## Number of objects: 22Gráfico
plot(dC1, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C1",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC1,5, border=2:6)
Grupos
gC1<- cutree(dC1,5)
gC1## sp1 sp2 sp3 sp4 sp5 sp6 sp7 sp8 sp9 sp10 sp11 sp12 sp13 sp14 sp15 sp16
## 1 1 2 1 3 2 3 4 4 4 4 5 5 1 1 1
## sp17 sp18 sp19 sp20 sp21 sp22
## 2 2 2 3 3 3cgC1<- cbind(C1, cluster=gC1)
cgC1## A1 A2 A3 B1 B2 cluster
## sp1 13 12 2 3 11 1
## sp2 8 9 5 12 31 1
## sp3 0 0 2 21 2 2
## sp4 3 11 4 0 0 1
## sp5 0 0 0 1 31 3
## sp6 0 0 11 12 0 2
## sp7 0 0 3 0 21 3
## sp8 2 3 0 0 0 4
## sp9 1 0 0 0 0 4
## sp10 1 0 0 0 0 4
## sp11 1 1 0 0 0 4
## sp12 0 1 0 0 0 5
## sp13 0 1 0 0 0 5
## sp14 0 0 1 0 0 1
## sp15 0 0 1 0 0 1
## sp16 0 0 1 0 0 1
## sp17 0 0 0 1 0 2
## sp18 0 0 0 1 0 2
## sp19 0 0 0 1 0 2
## sp20 0 0 0 0 1 3
## sp21 0 0 0 0 1 3
## sp22 0 0 0 0 1 32) Faça o cluster das capitais brasileiras e compare os resultados.
Foram encontrados 6 grupos: 1 (Maceio, Aracaju, Salvador, Palmas e Rio branco), 2 (Boa vista, Manaus, Sao luis e Belem), 3 (Brasilia, Goiania, Cuiaba, Curitiba, Florianopolis, Porto alegre, Rio de janeiro, Sao paulo, Belo horizonte, Vitoria e Campo grande), 4 (Recife, João pessoa, Natal, Fortaleza e Teresina), 5 (Macapa) e 6 (Porto velho). O grupo 1 e 4 são mais semelhantes entre si, igualmente os grupo 3 e 6 são semelhantes. Os dois grande grupos supracitados são mais similares entre si do que o grande grupo de 2 e 5, que por sua vez são mais semelhantes entre si. Analisando os grupos, as cidades foram agrupadas por proximidade.
C2<-read.table("C2.txt",header=T)
C2## LAT LONG
## Aracaju 10.91 37.07
## Belem 1.46 48.50
## BeloHorizonte 19.92 43.94
## BoaVista 2.82 60.67
## Brasilia 15.78 47.93
## CampoGrande 20.44 54.65
## Cuiaba 15.60 56.10
## Curitiba 25.43 49.27
## Florianopolis 27.60 48.55
## Fortaleza 3.68 38.54
## Goiania 16.68 49.25
## JoaoPessoa 7.11 34.86
## Macapa 0.04 51.07
## Maceio 9.67 35.74
## Manaus 3.10 60.02
## Natal 5.79 35.21
## Palmas 10.21 48.36
## PortoAlegre 30.03 51.23
## PortoVelho 51.23 63.90
## Recife 8.05 34.88
## RioBranco 9.74 67.81
## RioJaneiro 22.90 43.21
## Salvador 12.97 38.51
## SaoLuis 2.53 44.30
## SaoPaulo 23.53 46.64
## Teresina 5.09 42.80
## Vitoria 20.32 40.34nrow(C2);ncol(C2)## [1] 27## [1] 2names(C2); row.names(C2);str(C2)## [1] "LAT" "LONG"## [1] "Aracaju" "Belem" "BeloHorizonte" "BoaVista"
## [5] "Brasilia" "CampoGrande" "Cuiaba" "Curitiba"
## [9] "Florianopolis" "Fortaleza" "Goiania" "JoaoPessoa"
## [13] "Macapa" "Maceio" "Manaus" "Natal"
## [17] "Palmas" "PortoAlegre" "PortoVelho" "Recife"
## [21] "RioBranco" "RioJaneiro" "Salvador" "SaoLuis"
## [25] "SaoPaulo" "Teresina" "Vitoria"## 'data.frame': 27 obs. of 2 variables:
## $ LAT : num 10.91 1.46 19.92 2.82 15.78 ...
## $ LONG: num 37.1 48.5 43.9 60.7 47.9 ...C2t<-log1p(C2)
C2t## LAT LONG
## Aracaju 2.47737838 3.639427
## Belem 0.90016135 3.901973
## BeloHorizonte 3.04070564 3.805328
## BoaVista 1.34025042 4.121798
## Brasilia 2.82018770 3.890391
## CampoGrande 3.06525834 4.019082
## Cuiaba 2.80940270 4.044804
## Curitiba 3.27449973 3.917408
## Florianopolis 3.35340672 3.902982
## Fortaleza 1.54329811 3.677313
## Goiania 2.87243406 3.917011
## JoaoPessoa 2.09309787 3.579622
## Macapa 0.03922071 3.952589
## Maceio 2.36743607 3.603866
## Manaus 1.41098697 4.111202
## Natal 1.91545094 3.589335
## Palmas 2.41680624 3.899140
## PortoAlegre 3.43495448 3.955657
## PortoVelho 3.95565704 4.172848
## Recife 2.20276476 3.580180
## RioBranco 2.37397509 4.231349
## RioJaneiro 3.17387846 3.788951
## Salvador 2.63691217 3.676554
## SaoLuis 1.26129787 3.813307
## SaoPaulo 3.19989686 3.863673
## Teresina 1.80664808 3.779634
## Vitoria 3.05964560 3.721831mC2<-vegdist(C2t, "bray")
mC2## Aracaju Belem BeloHorizonte BoaVista Brasilia
## Belem 0.168492849
## BeloHorizonte 0.056255343 0.192063568
## BoaVista 0.139866961 0.064292896 0.163869931
## Brasilia 0.046289523 0.167780471 0.022541057 0.140589558
## CampoGrande 0.073291781 0.192000278 0.017106971 0.145677255 0.027094180
## Cuiaba 0.056849988 0.176047769 0.034362812 0.125537005 0.012178476
## Curitiba 0.080781909 0.199246771 0.024638533 0.169009469 0.034621850
## Florianopolis 0.085214051 0.203528654 0.029098197 0.175491031 0.039078675
## Fortaleza 0.085730869 0.086582729 0.134703805 0.060615289 0.124880046
## Goiania 0.052117360 0.171444343 0.020531283 0.141776250 0.005841931
## JoaoPessoa 0.037667727 0.144659455 0.093724467 0.116304401 0.083811115
## Macapa 0.272175779 0.103657354 0.290532485 0.155517290 0.265657088
## Maceio 0.012036856 0.163864275 0.068245988 0.135141243 0.058293899
## Manaus 0.132156316 0.069743523 0.156497190 0.007404471 0.133249631
## Natal 0.052662211 0.128838382 0.108595836 0.101001142 0.098711105
## Palmas 0.025761470 0.136667220 0.054529143 0.110308509 0.031637842
## PortoAlegre 0.094304234 0.212296524 0.038251821 0.175904808 0.048225229
## PortoVelho 0.141218392 0.257247204 0.085643424 0.196199280 0.095553496
## Recife 0.028056066 0.153460930 0.084178550 0.124867300 0.074249161
## RioBranco 0.054654830 0.158071160 0.081237252 0.094741104 0.059115106
## RioJaneiro 0.064682581 0.202868353 0.010830006 0.174365874 0.033285810
## Salvador 0.015821137 0.176523956 0.040470226 0.147926072 0.030490715
## SaoLuis 0.124198916 0.045541566 0.149940499 0.036770985 0.138816127
## SaoPaulo 0.071831392 0.197041449 0.015639245 0.169075198 0.029506516
## Teresina 0.069292620 0.099035848 0.101328829 0.073184041 0.091429558
## Vitoria 0.051531766 0.201977305 0.007516976 0.173100668 0.030241358
## CampoGrande Cuiaba Curitiba Florianopolis Fortaleza
## Belem
## BeloHorizonte
## BoaVista
## Brasilia
## CampoGrande
## Cuiaba 0.020201365
## Curitiba 0.021778480 0.042181961
## Florianopolis 0.028188817 0.048603609 0.006459807
## Fortaleza 0.151461752 0.135289486 0.158815246 0.163162464
## Goiania 0.021255613 0.013986353 0.028785741 0.035241835 0.130626680
## JoaoPessoa 0.110654022 0.094315746 0.118090302 0.122488611 0.059439128
## Macapa 0.279206286 0.263912298 0.292430437 0.299051680 0.193147233
## Maceio 0.085253427 0.068839737 0.092728600 0.097151258 0.080199398
## Manaus 0.138530674 0.118355404 0.161812984 0.168300356 0.052705069
## Natal 0.125469716 0.109185315 0.132878833 0.137260298 0.042901006
## Palmas 0.057341592 0.040869698 0.064848312 0.069291122 0.094944760
## PortoAlegre 0.029922115 0.050172550 0.013626130 0.009163825 0.172069013
## PortoVelho 0.068637013 0.085051218 0.061133892 0.056686494 0.217834187
## Recife 0.101139875 0.084770845 0.108591859 0.112999959 0.068759540
## RioBranco 0.066002366 0.046210568 0.088022381 0.094346091 0.117091226
## RioJaneiro 0.024115263 0.044895943 0.016183892 0.020645264 0.142998897
## Salvador 0.057537362 0.041065786 0.065043902 0.069486594 0.094881722
## SaoLuis 0.165288638 0.149185179 0.172608408 0.176934973 0.040600844
## SaoPaulo 0.020501110 0.041071614 0.009002757 0.013465079 0.150026994
## Teresina 0.118230855 0.101919221 0.125653656 0.130043594 0.033836828
## Vitoria 0.021842512 0.042037973 0.029372416 0.033830844 0.130049484
## Goiania JoaoPessoa Macapa Maceio Manaus
## Belem
## BeloHorizonte
## BoaVista
## Brasilia
## CampoGrande
## Cuiaba
## Curitiba
## Florianopolis
## Fortaleza
## Goiania
## JoaoPessoa 0.089609171
## Macapa 0.266090725 0.251108295
## Maceio 0.064113995 0.025642497 0.268684954
## Manaus 0.134477545 0.108414468 0.160855501 0.127357712
## Natal 0.104492778 0.016762216 0.235819644 0.040651123 0.093074513
## Palmas 0.036130015 0.053652861 0.235845129 0.028048954 0.102877737
## PortoAlegre 0.042395242 0.131504826 0.298600955 0.106220517 0.168786949
## PortoVelho 0.089761672 0.177939591 0.341302615 0.152995183 0.190929204
## Recife 0.080056366 0.009621830 0.259439046 0.016024621 0.117008741
## RioBranco 0.060680219 0.075957033 0.246624656 0.050412727 0.089312255
## RioJaneiro 0.031231485 0.102101543 0.301086659 0.076659752 0.167011544
## Salvador 0.036326175 0.053457007 0.278859753 0.027852690 0.140302596
## SaoLuis 0.144540842 0.099139510 0.150154075 0.119101052 0.042237659
## SaoPaulo 0.027488646 0.109203644 0.293937665 0.083795796 0.161805016
## Teresina 0.097219562 0.043206416 0.202585505 0.063729212 0.065466165
## Vitoria 0.028177273 0.089026684 0.301781959 0.063529216 0.165644122
## Natal Palmas PortoAlegre PortoVelho Recife
## Belem
## BeloHorizonte
## BoaVista
## Brasilia
## CampoGrande
## Cuiaba
## Curitiba
## Florianopolis
## Fortaleza
## Goiania
## JoaoPessoa
## Macapa
## Maceio
## Manaus
## Natal
## Palmas 0.068621832
## PortoAlegre 0.146240177 0.078405161
## PortoVelho 0.192449381 0.125484729 0.047547369
## Recife 0.026264721 0.044053773 0.122037412 0.168606433
## RioBranco 0.090877611 0.029024997 0.095504256 0.111320922 0.066383720
## RioJaneiro 0.116946434 0.065311862 0.029803450 0.077241362 0.092570655
## Salvador 0.068426337 0.035052502 0.078600369 0.125678049 0.043857735
## SaoLuis 0.083003338 0.108979948 0.185797546 0.231301554 0.108182225
## SaoPaulo 0.124024443 0.061179959 0.022626112 0.070098069 0.099686558
## Teresina 0.026967768 0.061304882 0.139041723 0.185363641 0.052384430
## Vitoria 0.103911983 0.062619128 0.042981343 0.090344081 0.079472931
## RioBranco RioJaneiro Salvador SaoLuis SaoPaulo
## Belem
## BeloHorizonte
## BoaVista
## Brasilia
## CampoGrande
## Cuiaba
## Curitiba
## Florianopolis
## Fortaleza
## Goiania
## JoaoPessoa
## Macapa
## Maceio
## Manaus
## Natal
## Palmas
## PortoAlegre
## PortoVelho
## Recife
## RioBranco
## RioJaneiro 0.091560096
## Salvador 0.063297906 0.048911497
## SaoLuis 0.131055528 0.160909422 0.132802785
## SaoPaulo 0.087322217 0.007182181 0.056073980 0.163860282
## Teresina 0.083585564 0.109692832 0.078433939 0.054312876 0.116783008
## Vitoria 0.089281158 0.013194796 0.035739767 0.159397038 0.020375046
## Teresina
## Belem
## BeloHorizonte
## BoaVista
## Brasilia
## CampoGrande
## Cuiaba
## Curitiba
## Florianopolis
## Fortaleza
## Goiania
## JoaoPessoa
## Macapa
## Maceio
## Manaus
## Natal
## Palmas
## PortoAlegre
## PortoVelho
## Recife
## RioBranco
## RioJaneiro
## Salvador
## SaoLuis
## SaoPaulo
## Teresina
## Vitoria 0.105985319dC2<-hclust(mC2, method="complete")
dC2##
## Call:
## hclust(d = mC2, method = "complete")
##
## Cluster method : complete
## Distance : bray
## Number of objects: 27Gráfico
plot(dC2, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C2",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC2,6, border=2:6)
Grupos
gC2<- cutree(dC2,6)
gC2## Aracaju Belem BeloHorizonte BoaVista Brasilia
## 1 2 3 2 3
## CampoGrande Cuiaba Curitiba Florianopolis Fortaleza
## 3 3 3 3 4
## Goiania JoaoPessoa Macapa Maceio Manaus
## 3 4 5 1 2
## Natal Palmas PortoAlegre PortoVelho Recife
## 4 1 3 6 4
## RioBranco RioJaneiro Salvador SaoLuis SaoPaulo
## 1 3 1 2 3
## Teresina Vitoria
## 4 3cgC2<- cbind(C2, cluster=gC2)
cgC2## LAT LONG cluster
## Aracaju 10.91 37.07 1
## Belem 1.46 48.50 2
## BeloHorizonte 19.92 43.94 3
## BoaVista 2.82 60.67 2
## Brasilia 15.78 47.93 3
## CampoGrande 20.44 54.65 3
## Cuiaba 15.60 56.10 3
## Curitiba 25.43 49.27 3
## Florianopolis 27.60 48.55 3
## Fortaleza 3.68 38.54 4
## Goiania 16.68 49.25 3
## JoaoPessoa 7.11 34.86 4
## Macapa 0.04 51.07 5
## Maceio 9.67 35.74 1
## Manaus 3.10 60.02 2
## Natal 5.79 35.21 4
## Palmas 10.21 48.36 1
## PortoAlegre 30.03 51.23 3
## PortoVelho 51.23 63.90 6
## Recife 8.05 34.88 4
## RioBranco 9.74 67.81 1
## RioJaneiro 22.90 43.21 3
## Salvador 12.97 38.51 1
## SaoLuis 2.53 44.30 2
## SaoPaulo 23.53 46.64 3
## Teresina 5.09 42.80 4
## Vitoria 20.32 40.34 33) Faça o cluster da fauna de três áreas (‘aulapi.txt’)*. Utilize os coeficientes de associação ‘distancia euclidiana’ e Bray-Curtis’ e compare os resultados.
Utilizando o coeficiente de Bray-Curtis foi encontrado 5 grupos, em ordem decrescente de semelhança: 1 (A1,A2 e A3), 4 (B3), 2 (B1), 5 (C1 e C2) e 3 (B2 e C3). Enquanto o coeficiente de Distância Euclidiana gerou 4 grupos: 1 (A1, B2 e C3), 2 (A2, A3 e B3), 3 (B1) e 4 (C1 e C2). Os grupos 1 e 4 são mais próximos entre si, do mesmo modo os grupos 2 e 3 são mais semelhantes.
*Renomeado para C3.
C3<-read.table("C3.txt",header=T)
C3## sp1 sp2 sp3 sp4 sp5 sp6 sp7 sp8 sp9 sp10 sp11 sp12 sp13 sp14 sp15
## A1 3 3 1 2 3 3 2 5 5 1 85 2 5 5 4
## A2 44 3 4 90 4 18 5 3 3 5 3 3 5 3 4
## A3 5 1 70 3 50 1 67 1 2 2 1 3 3 1 5
## B1 0 14 0 4 0 13 120 0 0 0 0 5 0 0 15
## B2 0 0 9 3 0 0 0 0 0 1 70 50 8 10 0
## B3 14 12 0 6 32 0 9 8 0 85 0 0 0 0 1
## C1 21 30 25 0 0 0 0 13 8 0 0 0 16 22 10
## C2 24 25 0 0 0 0 0 11 14 0 0 20 0 0 19
## C3 0 0 0 7 22 12 0 0 0 0 0 12 17 20 9nrow(C3);ncol(C3)## [1] 9## [1] 15names(C3); row.names(C3);str(C3)## [1] "sp1" "sp2" "sp3" "sp4" "sp5" "sp6" "sp7" "sp8" "sp9" "sp10"
## [11] "sp11" "sp12" "sp13" "sp14" "sp15"## [1] "A1" "A2" "A3" "B1" "B2" "B3" "C1" "C2" "C3"## 'data.frame': 9 obs. of 15 variables:
## $ sp1 : int 3 44 5 0 0 14 21 24 0
## $ sp2 : int 3 3 1 14 0 12 30 25 0
## $ sp3 : int 1 4 70 0 9 0 25 0 0
## $ sp4 : int 2 90 3 4 3 6 0 0 7
## $ sp5 : int 3 4 50 0 0 32 0 0 22
## $ sp6 : int 3 18 1 13 0 0 0 0 12
## $ sp7 : int 2 5 67 120 0 9 0 0 0
## $ sp8 : int 5 3 1 0 0 8 13 11 0
## $ sp9 : int 5 3 2 0 0 0 8 14 0
## $ sp10: int 1 5 2 0 1 85 0 0 0
## $ sp11: int 85 3 1 0 70 0 0 0 0
## $ sp12: int 2 3 3 5 50 0 0 20 12
## $ sp13: int 5 5 3 0 8 0 16 0 17
## $ sp14: int 5 3 1 0 10 0 22 0 20
## $ sp15: int 4 4 5 15 0 1 10 19 9C3t<-log1p(C3)
C3t## sp1 sp2 sp3 sp4 sp5 sp6 sp7 sp8
## A1 1.386294 1.3862944 0.6931472 1.098612 1.386294 1.3862944 1.098612 1.7917595
## A2 3.806662 1.3862944 1.6094379 4.510860 1.609438 2.9444390 1.791759 1.3862944
## A3 1.791759 0.6931472 4.2626799 1.386294 3.931826 0.6931472 4.219508 0.6931472
## B1 0.000000 2.7080502 0.0000000 1.609438 0.000000 2.6390573 4.795791 0.0000000
## B2 0.000000 0.0000000 2.3025851 1.386294 0.000000 0.0000000 0.000000 0.0000000
## B3 2.708050 2.5649494 0.0000000 1.945910 3.496508 0.0000000 2.302585 2.1972246
## C1 3.091042 3.4339872 3.2580965 0.000000 0.000000 0.0000000 0.000000 2.6390573
## C2 3.218876 3.2580965 0.0000000 0.000000 0.000000 0.0000000 0.000000 2.4849066
## C3 0.000000 0.0000000 0.0000000 2.079442 3.135494 2.5649494 0.000000 0.0000000
## sp9 sp10 sp11 sp12 sp13 sp14 sp15
## A1 1.791759 0.6931472 4.4543473 1.098612 1.791759 1.7917595 1.6094379
## A2 1.386294 1.7917595 1.3862944 1.386294 1.791759 1.3862944 1.6094379
## A3 1.098612 1.0986123 0.6931472 1.386294 1.386294 0.6931472 1.7917595
## B1 0.000000 0.0000000 0.0000000 1.791759 0.000000 0.0000000 2.7725887
## B2 0.000000 0.6931472 4.2626799 3.931826 2.197225 2.3978953 0.0000000
## B3 0.000000 4.4543473 0.0000000 0.000000 0.000000 0.0000000 0.6931472
## C1 2.197225 0.0000000 0.0000000 0.000000 2.833213 3.1354942 2.3978953
## C2 2.708050 0.0000000 0.0000000 3.044522 0.000000 0.0000000 2.9957323
## C3 0.000000 0.0000000 0.0000000 2.564949 2.890372 3.0445224 2.3025851Bray-Curtis
mC3<-vegdist(C3t, "bray")
mC3## A1 A2 A3 B1 B2 B3 C1
## A2 0.2797460
## A3 0.3906023 0.3441442
## B1 0.6139334 0.5478403 0.5172709
## B2 0.4373725 0.5894142 0.6026655 0.8101994
## B3 0.5648573 0.4690447 0.4735969 0.6090384 0.8891980
## C1 0.4728200 0.4827732 0.5325941 0.7401733 0.6564688 0.6233629
## C2 0.5596537 0.5631617 0.6574870 0.5725496 0.8254379 0.5711716 0.3400284
## C3 0.5165241 0.4860973 0.5282868 0.5261336 0.5219348 0.7034512 0.6064157
## C2
## A2
## A3
## B1
## B2
## B3
## C1
## C2
## C3 0.7317608dC3<-hclust(mC3, method="complete")
dC3##
## Call:
## hclust(d = mC3, method = "complete")
##
## Cluster method : complete
## Distance : bray
## Number of objects: 9Gráfico
plot(dC3, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C3",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC3,5, border=2:6)
Grupos
gC3<- cutree(dC3,5)
gC3## A1 A2 A3 B1 B2 B3 C1 C2 C3
## 1 1 1 2 3 4 5 5 3cgC3<- cbind(C3, cluster=gC3)
cgC3## sp1 sp2 sp3 sp4 sp5 sp6 sp7 sp8 sp9 sp10 sp11 sp12 sp13 sp14 sp15 cluster
## A1 3 3 1 2 3 3 2 5 5 1 85 2 5 5 4 1
## A2 44 3 4 90 4 18 5 3 3 5 3 3 5 3 4 1
## A3 5 1 70 3 50 1 67 1 2 2 1 3 3 1 5 1
## B1 0 14 0 4 0 13 120 0 0 0 0 5 0 0 15 2
## B2 0 0 9 3 0 0 0 0 0 1 70 50 8 10 0 3
## B3 14 12 0 6 32 0 9 8 0 85 0 0 0 0 1 4
## C1 21 30 25 0 0 0 0 13 8 0 0 0 16 22 10 5
## C2 24 25 0 0 0 0 0 11 14 0 0 20 0 0 19 5
## C3 0 0 0 7 22 12 0 0 0 0 0 12 17 20 9 3Distância Euclidiana
mC3e<-vegdist(C3t, "euclidean")
mC3e## A1 A2 A3 B1 B2 B3 C1
## A2 5.700450
## A3 6.903270 6.316713
## B1 7.521120 7.387786 7.209153
## B2 5.401294 8.044140 8.314087 9.173068
## B3 7.615049 6.613724 6.921923 8.067030 10.035801
## C1 6.771893 7.502569 7.931208 9.287243 8.762570 8.857762
## C2 6.882649 7.690750 8.748798 7.638438 8.983244 7.992743 6.199365
## C3 6.564405 6.737954 7.556452 7.670264 6.993737 8.797906 8.431393
## C2
## A2
## A3
## B1
## B2
## B3
## C1
## C2
## C3 8.576294dC3e<-hclust(mC3e, method="complete")
dC3e##
## Call:
## hclust(d = mC3e, method = "complete")
##
## Cluster method : complete
## Distance : euclidean
## Number of objects: 9Gráfico
plot(dC3e, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C3",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC3e,4, border=2:6)
Grupos
gC3e<- cutree(dC3e,4)
gC3e## A1 A2 A3 B1 B2 B3 C1 C2 C3
## 1 2 2 3 1 2 4 4 1cgC3e<- cbind(C3, cluster=gC3e)
cgC3e## sp1 sp2 sp3 sp4 sp5 sp6 sp7 sp8 sp9 sp10 sp11 sp12 sp13 sp14 sp15 cluster
## A1 3 3 1 2 3 3 2 5 5 1 85 2 5 5 4 1
## A2 44 3 4 90 4 18 5 3 3 5 3 3 5 3 4 2
## A3 5 1 70 3 50 1 67 1 2 2 1 3 3 1 5 2
## B1 0 14 0 4 0 13 120 0 0 0 0 5 0 0 15 3
## B2 0 0 9 3 0 0 0 0 0 1 70 50 8 10 0 1
## B3 14 12 0 6 32 0 9 8 0 85 0 0 0 0 1 2
## C1 21 30 25 0 0 0 0 13 8 0 0 0 16 22 10 4
## C2 24 25 0 0 0 0 0 11 14 0 0 20 0 0 19 4
## C3 0 0 0 7 22 12 0 0 0 0 0 12 17 20 9 14) Os dados abióticos de três prados de ervas marinhas foram coletados. Descreva os três ambientes utilizando a analise de Cluster. discuta o uso do tipo de cluster escolhido e do coeficiente de associação.(HaloduleAbiotico.txt)*
Foram obtidos três grupos: 1 (SA, SB e SC), 2 (CA, CB e CC) e 3 (TA, TB e TC). Os grupos 2 e 3 apresentam maior índice de similaridade. Foi utilizado o índice de Bray-Curtis por se tratar de um índice simétrico (mais adequado para dados abióticos) e o cluster médio (para não tendenciar o resultado).
*Renomeado para C4.
C4<-read.table("C4.txt",header=T)
C4## Meanmm Gravel Sand mo CaCO3 MediaNumTalos
## SA 0.1977082 0.006820706 90.74722 0.7793154 2.026049 15.8
## SB 0.1567520 0.029504556 93.53834 0.7671558 1.683111 27.6
## SC 0.1291095 1.248660748 84.63238 1.1246418 1.725585 25.4
## CA 0.1877505 10.549661500 50.00886 14.8964874 55.111331 15.8
## CB 0.2312549 12.271879160 61.60721 9.2596896 48.454016 17.6
## CC 0.1424418 4.379080900 63.82608 7.5375690 36.201956 2.8
## TA 0.1488571 0.602777746 84.24157 5.0433597 45.048717 24.2
## TB 0.1562217 0.381141022 83.32625 7.6325583 48.014157 25.6
## TC 0.1019311 0.830105288 76.12643 7.7981446 44.563297 25.8
## NfolhasMdia compmedio TempC mmHg O2 Salinidade pH
## SA 1.2768436 10.395455 26.5 765.2 7.63 26.32565 7.78
## SB 1.1068510 10.200502 27.1 764.8 7.12 27.37123 8.07
## SC 1.1030042 8.912925 28.2 765.5 6.45 26.71685 8.06
## CA 1.5822222 20.793562 27.9 762.8 8.08 29.77950 8.32
## CB 1.2344612 17.311197 27.5 763.1 10.25 29.49495 8.03
## CC 0.9833333 10.471429 28.5 763.0 9.62 30.25719 8.31
## TA 1.6772310 7.040551 26.9 762.5 7.55 25.28981 7.68
## TB 1.2680418 6.413243 27.7 762.2 8.30 26.32682 7.99
## TC 1.2573583 7.390939 29.1 761.6 6.51 29.05001 8.17nrow(C4);ncol(C4)## [1] 9## [1] 13names(C4); row.names(C4);str(C4)## [1] "Meanmm" "Gravel" "Sand" "mo"
## [5] "CaCO3" "MediaNumTalos" "NfolhasMdia" "compmedio"
## [9] "TempC" "mmHg" "O2" "Salinidade"
## [13] "pH"## [1] "SA" "SB" "SC" "CA" "CB" "CC" "TA" "TB" "TC"## 'data.frame': 9 obs. of 13 variables:
## $ Meanmm : num 0.198 0.157 0.129 0.188 0.231 ...
## $ Gravel : num 0.00682 0.0295 1.24866 10.54966 12.27188 ...
## $ Sand : num 90.7 93.5 84.6 50 61.6 ...
## $ mo : num 0.779 0.767 1.125 14.896 9.26 ...
## $ CaCO3 : num 2.03 1.68 1.73 55.11 48.45 ...
## $ MediaNumTalos: num 15.8 27.6 25.4 15.8 17.6 2.8 24.2 25.6 25.8
## $ NfolhasMdia : num 1.28 1.11 1.1 1.58 1.23 ...
## $ compmedio : num 10.4 10.2 8.91 20.79 17.31 ...
## $ TempC : num 26.5 27.1 28.2 27.9 27.5 28.5 26.9 27.7 29.1
## $ mmHg : num 765 765 766 763 763 ...
## $ O2 : num 7.63 7.12 6.45 8.08 10.25 ...
## $ Salinidade : num 26.3 27.4 26.7 29.8 29.5 ...
## $ pH : num 7.78 8.07 8.06 8.32 8.03 8.31 7.68 7.99 8.17C4t<-log1p(C4)
C4t## Meanmm Gravel Sand mo CaCO3 MediaNumTalos NfolhasMdia
## SA 0.18040988 0.00679755 4.519037 0.5762287 1.1072579 2.821379 0.8227901
## SB 0.14561606 0.02907767 4.549005 0.5693714 0.9869769 3.353407 0.7451944
## SC 0.12142924 0.81033482 4.450063 0.7536032 1.0026832 3.273364 0.7433669
## CA 0.17206121 2.44665613 3.931999 2.7660982 4.0273378 2.821379 0.9486504
## CB 0.20803386 2.58564745 4.136880 2.3282226 3.9010433 2.923162 0.8040001
## CC 0.13316790 1.68251752 4.171708 2.1444763 3.6163613 1.335001 0.6847789
## TA 0.13876763 0.47173822 4.445489 1.7989601 3.8296999 3.226844 0.9847830
## TB 0.14515752 0.32290999 4.434693 2.1555409 3.8921092 3.280911 0.8189168
## TC 0.09706422 0.60437350 4.345446 2.1745409 3.8191025 3.288402 0.8141952
## compmedio TempC mmHg O2 Salinidade pH
## SA 2.433215 3.314186 6.641443 2.155245 3.307826 2.172476
## SB 2.415959 3.335770 6.640921 2.094330 3.345376 2.204972
## SC 2.293839 3.374169 6.641835 2.008214 3.322040 2.203869
## CA 3.081615 3.363842 6.638306 2.206074 3.426849 2.232163
## CB 2.907513 3.349904 6.638699 2.420368 3.417561 2.200552
## CC 2.439859 3.384390 6.638568 2.362739 3.442249 2.231089
## TA 2.084498 3.328627 6.637913 2.145931 3.269182 2.161022
## TB 2.003268 3.356897 6.637520 2.230014 3.307869 2.196113
## TC 2.127152 3.404525 6.636734 2.016235 3.402863 2.215937mC4<-vegdist(C4t, "bray")
mC4## SA SB SC CA CB CC TA
## SB 0.01643882
## SC 0.03500389 0.02374315
## CA 0.13507939 0.14530515 0.13078175
## CB 0.12626243 0.13341091 0.11931028 0.02153364
## CC 0.12829011 0.13593659 0.11989819 0.06444486 0.05276512
## TA 0.08545546 0.08476893 0.07650908 0.07507942 0.06751369 0.07432125
## TB 0.09004147 0.08689533 0.08295545 0.07211815 0.06052891 0.06906210 0.01547776
## TC 0.09720666 0.09037292 0.07523232 0.06791936 0.05748433 0.06269482 0.01915548
## TB
## SB
## SC
## CA
## CB
## CC
## TA
## TB
## TC 0.01468438dC4<-hclust(mC4, method="average")
dC4##
## Call:
## hclust(d = mC4, method = "average")
##
## Cluster method : average
## Distance : bray
## Number of objects: 9Gráfico
plot(dC4, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C4",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC4,3, border=2:6)
Grupos
gC4<- cutree(dC4,3)
gC4## SA SB SC CA CB CC TA TB TC
## 1 1 1 2 2 2 3 3 3cgC4<- cbind(C4, cluster=gC4)
cgC4## Meanmm Gravel Sand mo CaCO3 MediaNumTalos
## SA 0.1977082 0.006820706 90.74722 0.7793154 2.026049 15.8
## SB 0.1567520 0.029504556 93.53834 0.7671558 1.683111 27.6
## SC 0.1291095 1.248660748 84.63238 1.1246418 1.725585 25.4
## CA 0.1877505 10.549661500 50.00886 14.8964874 55.111331 15.8
## CB 0.2312549 12.271879160 61.60721 9.2596896 48.454016 17.6
## CC 0.1424418 4.379080900 63.82608 7.5375690 36.201956 2.8
## TA 0.1488571 0.602777746 84.24157 5.0433597 45.048717 24.2
## TB 0.1562217 0.381141022 83.32625 7.6325583 48.014157 25.6
## TC 0.1019311 0.830105288 76.12643 7.7981446 44.563297 25.8
## NfolhasMdia compmedio TempC mmHg O2 Salinidade pH cluster
## SA 1.2768436 10.395455 26.5 765.2 7.63 26.32565 7.78 1
## SB 1.1068510 10.200502 27.1 764.8 7.12 27.37123 8.07 1
## SC 1.1030042 8.912925 28.2 765.5 6.45 26.71685 8.06 1
## CA 1.5822222 20.793562 27.9 762.8 8.08 29.77950 8.32 2
## CB 1.2344612 17.311197 27.5 763.1 10.25 29.49495 8.03 2
## CC 0.9833333 10.471429 28.5 763.0 9.62 30.25719 8.31 2
## TA 1.6772310 7.040551 26.9 762.5 7.55 25.28981 7.68 3
## TB 1.2680418 6.413243 27.7 762.2 8.30 26.32682 7.99 3
## TC 1.2573583 7.390939 29.1 761.6 6.51 29.05001 8.17 35) Estas amostras representam apenas uma associação de espécies? Faça o dendrograma, justificando o uso de transformação dos dados, coeficiente de associação e técnica utilizada.
Não. Elas tem três associações: similaridade entre as amostras, distância das semelhanças e correlação entre as espécies. O uso de transformação dos dados auxilia a diminuir a influência excessiva das espécies dominantes, além de evitar uma grande diferença (a grau de magnitude) entre as réplicas. O índice de Bray-Curtis foi utilizado para diminuir a influência excessiva das espécies dominantes (por utilizar a soma da mínima abundâncias das espécies comuns as amostras). Enquanto a técnica de cluster médio visou evitar algum tipo de tendência nos resultados.
C5<-read.table("C5.txt",header=T)
C5## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
## Especie1 24 27 24 8 10 14 14 36 36 41
## Especie2 32 30 29 20 18 20 22 14 8 12
## Especie3 3 1 2 11 14 13 12 8 8 6nrow(C5);ncol(C5)## [1] 3## [1] 10names(C5); row.names(C5);str(C5)## [1] "X1" "X2" "X3" "X4" "X5" "X6" "X7" "X8" "X9" "X10"## [1] "Especie1" "Especie2" "Especie3"## 'data.frame': 3 obs. of 10 variables:
## $ X1 : int 24 32 3
## $ X2 : int 27 30 1
## $ X3 : int 24 29 2
## $ X4 : int 8 20 11
## $ X5 : int 10 18 14
## $ X6 : int 14 20 13
## $ X7 : int 14 22 12
## $ X8 : int 36 14 8
## $ X9 : int 36 8 8
## $ X10: int 41 12 6C5t<-log1p(C5)
C5t## X1 X2 X3 X4 X5 X6 X7
## Especie1 3.218876 3.3322045 3.218876 2.197225 2.397895 2.708050 2.708050
## Especie2 3.496508 3.4339872 3.401197 3.044522 2.944439 3.044522 3.135494
## Especie3 1.386294 0.6931472 1.098612 2.484907 2.708050 2.639057 2.564949
## X8 X9 X10
## Especie1 3.610918 3.610918 3.737670
## Especie2 2.708050 2.197225 2.564949
## Especie3 2.197225 2.197225 1.945910mC5<-vegdist(C5t, "bray")
mC5## Especie1 Especie2
## Especie2 0.1022667
## Especie3 0.2373059 0.2015688dC5<-hclust(mC5, method="average")
dC5##
## Call:
## hclust(d = mC5, method = "average")
##
## Cluster method : average
## Distance : bray
## Number of objects: 3Gráfico
plot(dC5, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C5",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC5,2, border=2:6)
Grupos
gC5<- cutree(dC5,2)
gC5## Especie1 Especie2 Especie3
## 1 1 2cgC5<- cbind(C5, cluster=gC5)
cgC5## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 cluster
## Especie1 24 27 24 8 10 14 14 36 36 41 1
## Especie2 32 30 29 20 18 20 22 14 8 12 1
## Especie3 3 1 2 11 14 13 12 8 8 6 26) Faça uma pergunta multivariada e descreva passo a passo a realização do dendrograma, explicando suas escolhas, faça uma conclusão.
Utilizando o coeficiente de Jaccard foi encontrado 5 grupos, em ordem decrescente de semelhança: 1 (spA, spB, spC e spE), 5 (spJ), 2 (spD e spI), 4 (spH) e 3 (spG). Este índice foi utilizado por ser um índice assimétrico, que não considera o duplo zero, ou seja considera que o zero pode ser falta de informação. Enquanto a técnica de cluster médio visou evitar algum tipo de tendência nos resultados.
C6<-read.table("C6.txt",header=T)
C6## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
## spA 15 0 6 0 2 0 5 0 15 0
## spB 4 1 1 1 0 0 2 6 8 1
## spC 0 4 1 0 8 19 6 0 0 7
## spD 0 8 0 16 0 3 0 2 0 5
## spE 1 0 0 0 10 0 0 0 0 11
## spG 0 0 1 0 0 0 0 0 0 0
## spH 1 0 0 0 0 0 0 0 0 0
## spI 0 0 0 8 0 0 0 0 0 0
## spJ 0 0 0 0 0 0 3 0 0 0nrow(C6);ncol(C6)## [1] 9## [1] 10names(C6); row.names(C6);str(C6)## [1] "A1" "A2" "A3" "A4" "A5" "A6" "A7" "A8" "A9" "A10"## [1] "spA" "spB" "spC" "spD" "spE" "spG" "spH" "spI" "spJ"## 'data.frame': 9 obs. of 10 variables:
## $ A1 : int 15 4 0 0 1 0 1 0 0
## $ A2 : int 0 1 4 8 0 0 0 0 0
## $ A3 : int 6 1 1 0 0 1 0 0 0
## $ A4 : int 0 1 0 16 0 0 0 8 0
## $ A5 : int 2 0 8 0 10 0 0 0 0
## $ A6 : int 0 0 19 3 0 0 0 0 0
## $ A7 : int 5 2 6 0 0 0 0 0 3
## $ A8 : int 0 6 0 2 0 0 0 0 0
## $ A9 : int 15 8 0 0 0 0 0 0 0
## $ A10: int 0 1 7 5 11 0 0 0 0C6t<-log1p(C6)
C6t## A1 A2 A3 A4 A5 A6 A7 A8
## spA 2.7725887 0.0000000 1.9459101 0.0000000 1.098612 0.000000 1.791759 0.000000
## spB 1.6094379 0.6931472 0.6931472 0.6931472 0.000000 0.000000 1.098612 1.945910
## spC 0.0000000 1.6094379 0.6931472 0.0000000 2.197225 2.995732 1.945910 0.000000
## spD 0.0000000 2.1972246 0.0000000 2.8332133 0.000000 1.386294 0.000000 1.098612
## spE 0.6931472 0.0000000 0.0000000 0.0000000 2.397895 0.000000 0.000000 0.000000
## spG 0.0000000 0.0000000 0.6931472 0.0000000 0.000000 0.000000 0.000000 0.000000
## spH 0.6931472 0.0000000 0.0000000 0.0000000 0.000000 0.000000 0.000000 0.000000
## spI 0.0000000 0.0000000 0.0000000 2.1972246 0.000000 0.000000 0.000000 0.000000
## spJ 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.000000 1.386294 0.000000
## A9 A10
## spA 2.772589 0.0000000
## spB 2.197225 0.6931472
## spC 0.000000 2.0794415
## spD 0.000000 1.7917595
## spE 0.000000 2.4849066
## spG 0.000000 0.0000000
## spH 0.000000 0.0000000
## spI 0.000000 0.0000000
## spJ 0.000000 0.0000000mC6<-vegdist(C6t, "jaccard")
mC6## spA spB spC spD spE spG spH
## spB 0.6114045
## spC 0.8043806 0.8231134
## spD 1.0000000 0.7982550 0.7015374
## spE 0.8735138 0.8996415 0.6664113 0.8631335
## spG 0.9332322 0.9279755 0.9398356 1.0000000 1.0000000
## spH 0.9332322 0.9279755 1.0000000 1.0000000 0.8756898 1.0000000
## spI 1.0000000 0.9377106 1.0000000 0.7639196 1.0000000 1.0000000 1.0000000
## spJ 0.8664644 0.8891573 0.8796713 1.0000000 1.0000000 1.0000000 1.0000000
## spI
## spB
## spC
## spD
## spE
## spG
## spH
## spI
## spJ 1.0000000dC6<-hclust(mC6, method="average")
dC6##
## Call:
## hclust(d = mC6, method = "average")
##
## Cluster method : average
## Distance : jaccard
## Number of objects: 9Gráfico
plot(dC6, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C6",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC6,5, border=2:6)
Grupos
gC6<- cutree(dC6,5)
gC6## spA spB spC spD spE spG spH spI spJ
## 1 1 1 2 1 3 4 2 5cgC6<- cbind(C6, cluster=gC6)
cgC6## A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 cluster
## spA 15 0 6 0 2 0 5 0 15 0 1
## spB 4 1 1 1 0 0 2 6 8 1 1
## spC 0 4 1 0 8 19 6 0 0 7 1
## spD 0 8 0 16 0 3 0 2 0 5 2
## spE 1 0 0 0 10 0 0 0 0 11 1
## spG 0 0 1 0 0 0 0 0 0 0 3
## spH 1 0 0 0 0 0 0 0 0 0 4
## spI 0 0 0 8 0 0 0 0 0 0 2
## spJ 0 0 0 0 0 0 3 0 0 0 57) Faça uma análise de Cluster utilizando os diferentes tipos de ligação média (os quatro) com a matriz de dados abaixo. Não é necessário transformar os dados. Utilize a distância euclidiana como índice similaridade.
Só foi possível encontrar um cluster de média. Foram formados 4 grupos: 1 (1 e 2), 2 (3, 4 e 5), 3 (7, 8, 6 e 9) e 4 (10). Os grupos 1 e 2 são mais semelhantes entre si, o mesmo ocorre entre os grupos 3 e 4.
C7<-read.table("C7.txt",header=T)
C7## sp1 sp2
## 1 15 75
## 2 21 72
## 3 33 58
## 4 32 46
## 5 34 32
## 6 51 27
## 7 54 45
## 8 64 42
## 9 66 20
## 10 82 15nrow(C7);ncol(C7)## [1] 10## [1] 2names(C7); row.names(C7);str(C7)## [1] "sp1" "sp2"## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10"## 'data.frame': 10 obs. of 2 variables:
## $ sp1: int 15 21 33 32 34 51 54 64 66 82
## $ sp2: int 75 72 58 46 32 27 45 42 20 15mC7<-vegdist(C7, "euclidean")
mC7## 1 2 3 4 5 6 7
## 2 6.708204
## 3 24.758837 18.439089
## 4 33.615473 28.231188 12.041595
## 5 47.010637 42.059482 26.019224 14.142136
## 6 60.000000 54.083269 35.846897 26.870058 17.720045
## 7 49.203658 42.638011 24.698178 22.022716 23.853721 18.248288
## 8 59.076222 52.430907 34.885527 32.249031 31.622777 19.849433 10.440307
## 9 75.006666 68.767725 50.328918 42.801869 34.176015 16.552945 27.730849
## 10 89.938868 83.486526 65.192024 58.830264 50.921508 33.241540 41.036569
## 8 9
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 22.090722
## 10 32.449961 16.763055dC7<-hclust(mC7, method="average")
dC7##
## Call:
## hclust(d = mC7, method = "average")
##
## Cluster method : average
## Distance : euclidean
## Number of objects: 10Gráfico
plot(dC7, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C7",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC7,4, border=2:6)
Grupos
gC7<- cutree(dC7,4)
gC7## 1 2 3 4 5 6 7 8 9 10
## 1 1 2 2 2 3 3 3 3 4cgC7<- cbind(C7, cluster=gC7)
cgC7## sp1 sp2 cluster
## 1 15 75 1
## 2 21 72 1
## 3 33 58 2
## 4 32 46 2
## 5 34 32 2
## 6 51 27 3
## 7 54 45 3
## 8 64 42 3
## 9 66 20 3
## 10 82 15 48) Faça uma análise de Cluster utilizando o método de médias não ponderadas (UPGMA) com a matriz de dados abaixo. Transforme os dados se achar necessário. Utilize o índice similaridade que você achar mais adequado. Justifique suas escolhas.
Foi utilizado o índice de Jaccard por se tratar de um índice assimétrico (não considera o duplo zero; considera que o zero pode ser falta de informação). Foram obtidos três grupos: 1 (sp1, sp2, sp3, sp7, sp8 e sp9), 2 (sp4, sp5 e sp6) e 3 (sp10). Os grupos 1 e 2 apresentam maior índice de similaridade.
C8<-read.table("C8.txt",header=T)
C8## X1 X2 X3 X4 X5 X6 X7 X8
## Sp1 0 1 1 1 0 0 0 1
## Sp2 0 1 1 0 1 0 0 1
## Sp3 0 1 1 1 0 0 0 1
## Sp4 1 0 0 0 1 1 1 0
## Sp5 1 1 1 1 1 1 1 0
## Sp6 1 1 1 1 0 1 1 0
## Sp7 1 1 1 0 1 0 0 1
## Sp8 0 1 1 1 0 0 0 1
## Sp9 0 1 1 1 0 0 0 1
## Sp10 0 0 0 0 0 0 0 1nrow(C8);ncol(C8)## [1] 10## [1] 8names(C8); row.names(C8);str(C8)## [1] "X1" "X2" "X3" "X4" "X5" "X6" "X7" "X8"## [1] "Sp1" "Sp2" "Sp3" "Sp4" "Sp5" "Sp6" "Sp7" "Sp8" "Sp9" "Sp10"## 'data.frame': 10 obs. of 8 variables:
## $ X1: int 0 0 0 1 1 1 1 0 0 0
## $ X2: int 1 1 1 0 1 1 1 1 1 0
## $ X3: int 1 1 1 0 1 1 1 1 1 0
## $ X4: int 1 0 1 0 1 1 0 1 1 0
## $ X5: int 0 1 0 1 1 0 1 0 0 0
## $ X6: int 0 0 0 1 1 1 0 0 0 0
## $ X7: int 0 0 0 1 1 1 0 0 0 0
## $ X8: int 1 1 1 0 0 0 1 1 1 1C8t<-log1p(C8)
C8t## X1 X2 X3 X4 X5 X6 X7
## Sp1 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Sp2 0.0000000 0.6931472 0.6931472 0.0000000 0.6931472 0.0000000 0.0000000
## Sp3 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Sp4 0.6931472 0.0000000 0.0000000 0.0000000 0.6931472 0.6931472 0.6931472
## Sp5 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472
## Sp6 0.6931472 0.6931472 0.6931472 0.6931472 0.0000000 0.6931472 0.6931472
## Sp7 0.6931472 0.6931472 0.6931472 0.0000000 0.6931472 0.0000000 0.0000000
## Sp8 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Sp9 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Sp10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## X8
## Sp1 0.6931472
## Sp2 0.6931472
## Sp3 0.6931472
## Sp4 0.0000000
## Sp5 0.0000000
## Sp6 0.0000000
## Sp7 0.6931472
## Sp8 0.6931472
## Sp9 0.6931472
## Sp10 0.6931472mC8<-vegdist(C8t, "jaccard")
mC8## Sp1 Sp2 Sp3 Sp4 Sp5 Sp6 Sp7
## Sp2 0.4000000
## Sp3 0.0000000 0.4000000
## Sp4 1.0000000 0.8571429 1.0000000
## Sp5 0.6250000 0.6250000 0.6250000 0.4285714
## Sp6 0.5714286 0.7500000 0.5714286 0.5714286 0.1428571
## Sp7 0.5000000 0.2000000 0.5000000 0.7142857 0.5000000 0.6250000
## Sp8 0.0000000 0.4000000 0.0000000 1.0000000 0.6250000 0.5714286 0.5000000
## Sp9 0.0000000 0.4000000 0.0000000 1.0000000 0.6250000 0.5714286 0.5000000
## Sp10 0.7500000 0.7500000 0.7500000 1.0000000 1.0000000 1.0000000 0.8000000
## Sp8 Sp9
## Sp2
## Sp3
## Sp4
## Sp5
## Sp6
## Sp7
## Sp8
## Sp9 0.0000000
## Sp10 0.7500000 0.7500000dC8<-hclust(mC8, method="average")
dC8##
## Call:
## hclust(d = mC8, method = "average")
##
## Cluster method : average
## Distance : jaccard
## Number of objects: 10Gráfico
plot(dC8, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma C8",xlab="Amostras",cex.lab=1.2)
rect.hclust(dC8,3, border=2:6)
Grupos
gC8<- cutree(dC8,3)
gC8## Sp1 Sp2 Sp3 Sp4 Sp5 Sp6 Sp7 Sp8 Sp9 Sp10
## 1 1 1 2 2 2 1 1 1 3cgC8<- cbind(C8, cluster=gC8)
cgC8## X1 X2 X3 X4 X5 X6 X7 X8 cluster
## Sp1 0 1 1 1 0 0 0 1 1
## Sp2 0 1 1 0 1 0 0 1 1
## Sp3 0 1 1 1 0 0 0 1 1
## Sp4 1 0 0 0 1 1 1 0 2
## Sp5 1 1 1 1 1 1 1 0 2
## Sp6 1 1 1 1 0 1 1 0 2
## Sp7 1 1 1 0 1 0 0 1 1
## Sp8 0 1 1 1 0 0 0 1 1
## Sp9 0 1 1 1 0 0 0 1 1
## Sp10 0 0 0 0 0 0 0 1 3Análises Multivariadas
1) Estime os seguintes coeficientes de associação: distância euclidiana, Bray curtis. Qual o índice mais adequado? Qual a justificativa.
O índice de Bray-Curtis é o mais adequado para análise de dados bióticos.
AM1<-read.table("AM1.txt",header=T)## Warning in read.table("AM1.txt", header = T): incomplete final line found by
## readTableHeader on 'AM1.txt'AM1## Estacao1 Estacao2 Estacao3 Estacao4 Estacao5
## Especie1 2 5 4 8 0
## Especie2 0 1 4 8 1
## Especie3 2 5 1 4 0
## Especie4 0 3 2 4 1nrow(AM1);ncol(AM1)## [1] 4## [1] 5names(AM1); row.names(AM1);str(AM1)## [1] "Estacao1" "Estacao2" "Estacao3" "Estacao4" "Estacao5"## [1] "Especie1" "Especie2" "Especie3" "Especie4"## 'data.frame': 4 obs. of 5 variables:
## $ Estacao1: int 2 0 2 0
## $ Estacao2: int 5 1 5 3
## $ Estacao3: int 4 4 1 2
## $ Estacao4: int 8 8 4 4
## $ Estacao5: int 0 1 0 1library(vegan)
AM1t<-log1p(AM1)
AM1t## Estacao1 Estacao2 Estacao3 Estacao4 Estacao5
## Especie1 1.098612 1.7917595 1.6094379 2.197225 0.0000000
## Especie2 0.000000 0.6931472 1.6094379 2.197225 0.6931472
## Especie3 1.098612 1.7917595 0.6931472 1.609438 0.0000000
## Especie4 0.000000 1.3862944 1.0986123 1.609438 0.6931472Bray-Curtis
mAM1<-vegdist(AM1t, "bray")
mAM1## Especie1 Especie2 Especie3
## Especie2 0.2430928
## Especie3 0.1264995 0.4231163
## Especie4 0.2869807 0.1795269 0.2607788dAM1<-hclust(mAM1, method="average")
dAM1##
## Call:
## hclust(d = mAM1, method = "average")
##
## Cluster method : average
## Distance : bray
## Number of objects: 4Gráfico
plot(dAM1, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM1",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM1,2, border=2:6)
Grupos
gAM1<- cutree(dAM1,2)
gAM1## Especie1 Especie2 Especie3 Especie4
## 1 2 1 2cgAM1<- cbind(AM1, cluster=gAM1)
cgAM1## Estacao1 Estacao2 Estacao3 Estacao4 Estacao5 cluster
## Especie1 2 5 4 8 0 1
## Especie2 0 1 4 8 1 2
## Especie3 2 5 1 4 0 1
## Especie4 0 3 2 4 1 2Distância Euclidiana
mAM1e<-vegdist(AM1t, "euclidean")
mAM1e## Especie1 Especie2 Especie3
## Especie2 1.701279
## Especie3 1.088615 2.019761
## Especie4 1.567878 1.042540 1.419932dAM1e<-hclust(mAM1e, method="complete")
dAM1e##
## Call:
## hclust(d = mAM1e, method = "complete")
##
## Cluster method : complete
## Distance : euclidean
## Number of objects: 4Gráfico
plot(dAM1e, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM1",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM1e,2, border=2:6)
Grupos
gAM1e<- cutree(dAM1e,2)
gAM1e## Especie1 Especie2 Especie3 Especie4
## 1 2 1 2cgAM1e<- cbind(AM1, cluster=gAM1e)
cgAM1e## Estacao1 Estacao2 Estacao3 Estacao4 Estacao5 cluster
## Especie1 2 5 4 8 0 1
## Especie2 0 1 4 8 1 2
## Especie3 2 5 1 4 0 1
## Especie4 0 3 2 4 1 22) Faça uma matriz com o índice de Jaccard e com o índice de Sorensen com os dados abaixo.
Ambos os índices tiveram resultados semelhantes.
AM2<-read.table("AM2.txt",header=T)## Warning in read.table("AM2.txt", header = T): incomplete final line found by
## readTableHeader on 'AM2.txt'AM2## Estacao1 Estacao2 Estacao3 Estacao4
## Especie1 1 0 0 1
## Especie2 1 1 1 0
## Especie3 1 0 1 1
## Especie4 0 1 1 1nrow(AM2);ncol(AM2)## [1] 4## [1] 4names(AM2); row.names(AM2);str(AM2)## [1] "Estacao1" "Estacao2" "Estacao3" "Estacao4"## [1] "Especie1" "Especie2" "Especie3" "Especie4"## 'data.frame': 4 obs. of 4 variables:
## $ Estacao1: int 1 1 1 0
## $ Estacao2: int 0 1 0 1
## $ Estacao3: int 0 1 1 1
## $ Estacao4: int 1 0 1 1library(vegan)
AM2t<-log1p(AM2)
AM2t## Estacao1 Estacao2 Estacao3 Estacao4
## Especie1 0.6931472 0.0000000 0.0000000 0.6931472
## Especie2 0.6931472 0.6931472 0.6931472 0.0000000
## Especie3 0.6931472 0.0000000 0.6931472 0.6931472
## Especie4 0.0000000 0.6931472 0.6931472 0.6931472Índice de Soresen
The naming conventions vary. The one adopted here is traditional rather than truthful to priority. The function finds either quantitative or binary variants of the indices under the same name, which correctly may refer only to one of these alternatives For instance, the Bray index is known also as Steinhaus, Czekanowski and Sørensen index.
mAM2<-vegdist(AM2t, "bray")
mAM2## Especie1 Especie2 Especie3
## Especie2 0.6000000
## Especie3 0.2000000 0.3333333
## Especie4 0.6000000 0.3333333 0.3333333dAM2<-hclust(mAM2, method="average")
dAM2##
## Call:
## hclust(d = mAM2, method = "average")
##
## Cluster method : average
## Distance : bray
## Number of objects: 4Gráfico
plot(dAM2, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM2",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM2,2, border=2:6)
Grupos
gAM2<- cutree(dAM2,2)
gAM2## Especie1 Especie2 Especie3 Especie4
## 1 2 1 2cgAM2<- cbind(AM2, cluster=gAM2)
cgAM2## Estacao1 Estacao2 Estacao3 Estacao4 cluster
## Especie1 1 0 0 1 1
## Especie2 1 1 1 0 2
## Especie3 1 0 1 1 1
## Especie4 0 1 1 1 2Índice de Jaccard
mAM2j<-vegdist(AM2t, "jaccard")
mAM2j## Especie1 Especie2 Especie3
## Especie2 0.7500000
## Especie3 0.3333333 0.5000000
## Especie4 0.7500000 0.5000000 0.5000000dAM2j<-hclust(mAM2j, method="average")
dAM2j##
## Call:
## hclust(d = mAM2j, method = "average")
##
## Cluster method : average
## Distance : jaccard
## Number of objects: 4Gráfico
plot(dAM2j, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM2",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM2j,2, border=2:6)
Grupos
gAM2j<- cutree(dAM2j,2)
gAM2j## Especie1 Especie2 Especie3 Especie4
## 1 2 1 2cgAM2j<- cbind(AM2, cluster=gAM2j)
cgAM2j## Estacao1 Estacao2 Estacao3 Estacao4 cluster
## Especie1 1 0 0 1 1
## Especie2 1 1 1 0 2
## Especie3 1 0 1 1 1
## Especie4 0 1 1 1 23) Faça um estudo entre vários índices e indique o mais adequado para os dados abaixo.
Utilizando o coeficiente de Soresen e Jaccard resultaram em 5 grupos, em ordem decrescente de semelhança: 2 (Especie2 e Especie4), 4 (Especie5), 3 (Especie3), 1 (Especie1) e 5 (Especie5). Enquanto o coeficiente de Distância Euclidiana gerou 5 grupos, em ordem decrescente de semelhança: 2 (Especie2 e Especie6), 4 (Especie4), 5 (Especie5), o 1 (Especie1) e 3 (Especie3) são igualmente dissemelhante dos outros grupos. Os índices de Soresen e Jaccard são mais adequados por serem índices assimétricos, que não considera o duplo zero, ou seja considera que o zero pode ser falta de informação.
AM3<-read.table("AM3.txt",header=T)
AM3## X1986 X1987 X1988 X1989
## Especie1 0 1 15 2
## Especie2 4 4 2 2
## Especie3 0 12 1 10
## Especie4 25 2 1 4
## Especie5 2 0 1 5
## Especie6 7 2 0 0nrow(AM3);ncol(AM3)## [1] 6## [1] 4names(AM3); row.names(AM3);str(AM3)## [1] "X1986" "X1987" "X1988" "X1989"## [1] "Especie1" "Especie2" "Especie3" "Especie4" "Especie5" "Especie6"## 'data.frame': 6 obs. of 4 variables:
## $ X1986: int 0 4 0 25 2 7
## $ X1987: int 1 4 12 2 0 2
## $ X1988: int 15 2 1 1 1 0
## $ X1989: int 2 2 10 4 5 0library(vegan)
AM3t<-log1p(AM3)
AM3t## X1986 X1987 X1988 X1989
## Especie1 0.000000 0.6931472 2.7725887 1.098612
## Especie2 1.609438 1.6094379 1.0986123 1.098612
## Especie3 0.000000 2.5649494 0.6931472 2.397895
## Especie4 3.258097 1.0986123 0.6931472 1.609438
## Especie5 1.098612 0.0000000 0.6931472 1.791759
## Especie6 2.079442 1.0986123 0.0000000 0.000000Índice Soresen
The naming conventions vary. The one adopted here is traditional rather than truthful to priority. The function finds either quantitative or binary variants of the indices under the same name, which correctly may refer only to one of these alternatives For instance, the Bray index is known also as Steinhaus, Czekanowski and Sørensen index.
mAM3<-vegdist(AM3t, "bray")
mAM3## Especie1 Especie2 Especie3 Especie4 Especie5
## Especie2 0.4207932
## Especie3 0.5137331 0.3856270
## Especie4 0.5572014 0.2547142 0.4476462
## Especie5 0.5601893 0.3576680 0.4621129 0.3358861
## Especie6 0.8209478 0.3697925 0.7512777 0.3538799 0.6750424dAM3<-hclust(mAM3, method="average")
dAM3##
## Call:
## hclust(d = mAM3, method = "average")
##
## Cluster method : average
## Distance : bray
## Number of objects: 6Gráfico
plot(dAM3, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM3",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM3,5, border=2:6)
Grupos
gAM3<- cutree(dAM3,5)
gAM3## Especie1 Especie2 Especie3 Especie4 Especie5 Especie6
## 1 2 3 2 4 5cgAM3<- cbind(AM3, cluster=gAM3)
cgAM3## X1986 X1987 X1988 X1989 cluster
## Especie1 0 1 15 2 1
## Especie2 4 4 2 2 2
## Especie3 0 12 1 10 3
## Especie4 25 2 1 4 2
## Especie5 2 0 1 5 4
## Especie6 7 2 0 0 5Índice de Jaccard
mAM3j<-vegdist(AM3t, "jaccard")
mAM3j## Especie1 Especie2 Especie3 Especie4 Especie5
## Especie2 0.5923356
## Especie3 0.6787631 0.5566101
## Especie4 0.7156446 0.4060116 0.6184470
## Especie5 0.7181043 0.5268858 0.6321166 0.5028663
## Especie6 0.9016709 0.5399248 0.8579766 0.5227641 0.8060004dAM3j<-hclust(mAM3j, method="average")
dAM3j##
## Call:
## hclust(d = mAM3j, method = "average")
##
## Cluster method : average
## Distance : jaccard
## Number of objects: 6Gráfico
plot(dAM3j, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM3",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM3j,5, border=2:6)
Grupos
gAM3j<- cutree(dAM3j,5)
gAM3j## Especie1 Especie2 Especie3 Especie4 Especie5 Especie6
## 1 2 3 2 4 5cgAM3j<- cbind(AM3, cluster=gAM3j)
cgAM3j## X1986 X1987 X1988 X1989 cluster
## Especie1 0 1 15 2 1
## Especie2 4 4 2 2 2
## Especie3 0 12 1 10 3
## Especie4 25 2 1 4 2
## Especie5 2 0 1 5 4
## Especie6 7 2 0 0 5Distância Euclidiana
mAM3e<-vegdist(AM3t, "euclidean")
mAM3e## Especie1 Especie2 Especie3 Especie4 Especie5
## Especie2 2.496413
## Especie3 3.084778 2.314267
## Especie4 3.919772 1.845092 3.658825
## Especie5 2.547927 1.869783 2.855401 2.429725
## Especie6 3.658234 1.701689 3.564348 2.111864 2.420709dAM3e<-hclust(mAM3e, method="average")
dAM3e##
## Call:
## hclust(d = mAM3e, method = "average")
##
## Cluster method : average
## Distance : euclidean
## Number of objects: 6Gráfico
plot(dAM3e, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma AM3",xlab="Amostras",cex.lab=1.2)
rect.hclust(dAM3e,5, border=2:6)
Grupos
gAM3e<- cutree(dAM3e,5)
gAM3e## Especie1 Especie2 Especie3 Especie4 Especie5 Especie6
## 1 2 3 4 5 2cgAM3e<- cbind(AM3, cluster=gAM3e)
cgAM3e## X1986 X1987 X1988 X1989 cluster
## Especie1 0 1 15 2 1
## Especie2 4 4 2 2 2
## Especie3 0 12 1 10 3
## Especie4 25 2 1 4 4
## Especie5 2 0 1 5 5
## Especie6 7 2 0 0 24) Faça a matriz de distância dos dados do arquivo exerpast.txt*. Justifique qual a transformação dos dados realizada.
O arquivo exerpast.txt não estava anexado ao exercício, impossibilitando a realização dessa atividade.
5) Faça a matriz de similaridade dos dados do arquivo biot1.txt*. Justifique qual a transformação dos dados realizada.
O arquivo biot1.txt não estava anexado ao exercício, impossibilitando a realização dessa atividade.
Ordenação: Métodos Indiretos
library(vegan)
library(BBmisc)## Warning: package 'BBmisc' was built under R version 4.2.3##
## Attaching package: 'BBmisc'## The following object is masked from 'package:base':
##
## isFALSElibrary(factoextra)## Carregando pacotes exigidos: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(ggplot2)
library(FactoMineR)
library(ade4)##
## Attaching package: 'ade4'## The following object is masked from 'package:FactoMineR':
##
## reconstlibrary(gplots)## Warning: package 'gplots' was built under R version 4.2.3##
## Attaching package: 'gplots'## The following object is masked from 'package:stats':
##
## lowess1) Os dados abaixo mostram a contaminação por HPA (hidrocarbonetos) no estuário do Pina. Elabore uma hipótese. Faça as análises necessárias para responder à hipótese (descritivas e inferenciais).Apresente a sequencia de análises de modo didático, no programa escolhido. Destaque as conclusões do trabalho.
Quanto mais pireno, fluoreno e benzopireno maior a concentração de HPAs no estuário. O benzopireno atuou como indicador negativo da presença de HPAs, enquanto o pireno e fluoreno estavam mais presentes nas regiões com mais HPAs.
O1<-read.table("O1.txt",header=T)
O1## st1 st2 st3 st4 st5 st6 st7 st8 st9 st10
## OM 14.1 5.3 6.0 4.0 4.3 10.9 12.2 6.7 10.4 8.50
## Sand 26.6 20.9 78.9 42.4 51.9 20.8 3.6 21.7 51.3 19.70
## Silt 50.2 41.9 14.0 30.3 38.4 40.5 59.0 46.9 38.9 79.70
## Clay 23.2 37.0 7.0 27.3 9.8 38.7 37.4 31.3 9.7 0.58
## Acenaphtylene 2.1 3.5 0.7 1.6 1.1 3.0 2.7 2.7 1.7 1.60
## Fluorene 5.1 10.0 6.0 11.2 3.3 5.0 3.5 2.4 1.4 1.00
## Phenanthrene 21.9 31.4 23.8 37.4 13.7 31.2 14.4 14.6 11.4 11.10
## Anthracene 2.6 5.8 2.5 5.3 1.3 5.6 14.1 2.5 1.8 2.10
## Fluoranthene 38.9 61.5 54.4 45.3 26.4 59.2 34.1 23.3 0.2 35.70
## Pyrene 34.8 91.1 43.6 44.4 24.6 56.8 31.4 25.3 17.7 27.50
## Benzoanthracene 16.4 28.6 16.9 15.3 0.2 30.2 14.8 10.8 0.2 17.70
## Benzofluoranthene 19.8 24.6 13.7 20.0 11.8 22.7 18.6 12.9 7.8 11.10
## Benzopyrene 21.1 24.1 20.7 19.9 10.1 32.6 15.4 13.5 10.6 16.70
## Indenopyrene 20.1 37.9 24.0 25.1 0.2 38.0 23.1 0.2 13.2 17.40
## HPAsLMW 42.5 75.1 43.3 77.6 26.5 58.1 46.4 32.4 24.1 21.70
## HPAsHMW 233.0 422.5 268.0 256.0 119.4 359.3 204.9 136.3 83.9 178.90O1n<-normalize(O1, method =
"standardize", range = c(0, 1), margin = 1L,
on.constant = "quiet")
O1acp = prcomp(O1n, scale. = TRUE)
O1acp## Standard deviations (1, .., p=10):
## [1] 3.05811609 0.60336726 0.40242820 0.23971859 0.20080994 0.10752238
## [7] 0.07986192 0.06614982 0.03844117 0.01852973
##
## Rotation (n x k) = (10 x 10):
## PC1 PC2 PC3 PC4 PC5 PC6
## st1 0.3255490 0.133607212 -0.04627801 0.05254377 -0.075024713 0.08571836
## st2 0.3201026 0.292489307 0.17077340 -0.02671411 -0.168585195 0.17269581
## st3 0.3169114 -0.035534320 0.56078821 0.36397030 0.037913806 0.23682462
## st4 0.3213449 0.127440230 0.31904322 -0.27402295 0.004820482 -0.79293709
## st5 0.3136997 -0.406310308 0.10391046 0.14263428 0.625657058 -0.07998598
## st6 0.3208127 0.295084080 0.12919637 0.02734769 -0.184141420 0.31261695
## st7 0.3183827 0.262194970 -0.34069064 -0.28014395 -0.133766497 -0.07756532
## st8 0.3206857 0.006432586 -0.31730501 -0.43243187 0.476611408 0.31393942
## st9 0.2890960 -0.747002982 -0.03294080 -0.24417920 -0.534937161 0.08272292
## st10 0.3142375 -0.011476165 -0.55416247 0.66540866 -0.089023247 -0.24989767
## PC7 PC8 PC9 PC10
## st1 -0.254297941 0.22669466 -0.75048143 -0.42309316
## st2 0.804235042 -0.21235559 -0.02147516 -0.17751691
## st3 -0.337320181 -0.05909603 0.42009364 -0.31633438
## st4 -0.001650828 0.25597456 0.08911392 0.03714588
## st5 0.110234801 -0.36088277 -0.30323103 0.27051958
## st6 -0.145309695 0.20650307 -0.08183185 0.76842220
## st7 -0.355815523 -0.68388042 0.12553995 -0.03699020
## st8 0.037498332 0.40385678 0.31127508 -0.14941395
## st9 0.041588275 0.04256593 0.02887051 0.01804688
## st10 0.108369326 0.17033742 0.19941165 0.01899081O1acp$sdev## [1] 3.05811609 0.60336726 0.40242820 0.23971859 0.20080994 0.10752238
## [7] 0.07986192 0.06614982 0.03844117 0.01852973head(O1acp$rotation)## PC1 PC2 PC3 PC4 PC5 PC6
## st1 0.3255490 0.13360721 -0.04627801 0.05254377 -0.075024713 0.08571836
## st2 0.3201026 0.29248931 0.17077340 -0.02671411 -0.168585195 0.17269581
## st3 0.3169114 -0.03553432 0.56078821 0.36397030 0.037913806 0.23682462
## st4 0.3213449 0.12744023 0.31904322 -0.27402295 0.004820482 -0.79293709
## st5 0.3136997 -0.40631031 0.10391046 0.14263428 0.625657058 -0.07998598
## st6 0.3208127 0.29508408 0.12919637 0.02734769 -0.184141420 0.31261695
## PC7 PC8 PC9 PC10
## st1 -0.254297941 0.22669466 -0.75048143 -0.42309316
## st2 0.804235042 -0.21235559 -0.02147516 -0.17751691
## st3 -0.337320181 -0.05909603 0.42009364 -0.31633438
## st4 -0.001650828 0.25597456 0.08911392 0.03714588
## st5 0.110234801 -0.36088277 -0.30323103 0.27051958
## st6 -0.145309695 0.20650307 -0.08183185 0.76842220head(O1acp$x)## PC1 PC2 PC3 PC4 PC5
## OM -1.5292234 -0.04581607 -0.10082961 0.02023706 -0.1531494795
## Sand 0.3804630 -1.92932175 0.64461439 0.07054242 0.0708335147
## Silt 1.0180441 -0.85118193 -1.34530864 0.09601473 0.0279692617
## Clay -0.7395254 0.30703570 -0.17815076 -0.62657631 0.1585318253
## Acenaphtylene -1.9702098 0.16889039 0.02878939 0.07100249 0.0008884248
## Fluorene -1.8297802 0.20418364 0.14971024 0.06311325 0.0326863297
## PC6 PC7 PC8 PC9 PC10
## OM 0.09585991 -0.06310650 -0.0029821872 -0.064896522 -0.037234538
## Sand 0.05998324 -0.03794383 -0.0068024746 0.023369178 -0.002066773
## Silt -0.06499342 0.02001271 0.0002074494 0.007324113 0.003447663
## Clay 0.18906844 -0.06304991 -0.0155008528 0.024613354 0.012429697
## Acenaphtylene 0.04889775 0.04069852 0.0064420961 -0.001648160 -0.001279597
## Fluorene -0.04206926 0.04718992 0.0017283611 -0.023822808 -0.017875470biplot(O1acp)
autovalores <- get_eigenvalue(O1acp)
fviz_eig(O1acp)
O1s = as.data.frame(O1acp$x)
ggplot(data = O1s, aes(x = PC1, y = PC2, label =
rownames(O1s))) +
geom_hline(yintercept = 0, colour = "gray65") + geom_vline(xintercept = 0, colour = "gray65") +
geom_text(colour = "blue", alpha = 0.8, size = 4) +
ggtitle("O1acp")
fviz_pca_ind(O1acp, col.ind = "cos2", gradient.cols =
c("#00AFBB", "#E7B800", "#FC4E07"),repel = TRUE)
fviz_pca_var(O1acp, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
fviz_pca_biplot(O1acp, repel = TRUE,col.var = "#2E9FDF",
col.ind = "#696969")
O1acp$eig## NULLO1acp$var$coord## NULLhead(O1acp$ind$coord)## NULLO1acp = dudi.pca(O1, nf = 5, scannf = FALSE)
O1acp$eig## [1] 9.3520740010 0.3640520494 0.1619484583 0.0574650004 0.0403246302
## [6] 0.0115610613 0.0063779260 0.0043757992 0.0014777233 0.0003433508O1acp$c1## CS1 CS2 CS3 CS4 CS5
## st1 -0.3255490 0.133607212 0.04627801 0.05254377 -0.075024713
## st2 -0.3201026 0.292489307 -0.17077340 -0.02671411 -0.168585195
## st3 -0.3169114 -0.035534320 -0.56078821 0.36397030 0.037913806
## st4 -0.3213449 0.127440230 -0.31904322 -0.27402295 0.004820482
## st5 -0.3136997 -0.406310308 -0.10391046 0.14263428 0.625657058
## st6 -0.3208127 0.295084080 -0.12919637 0.02734769 -0.184141420
## st7 -0.3183827 0.262194970 0.34069064 -0.28014395 -0.133766497
## st8 -0.3206857 0.006432586 0.31730501 -0.43243187 0.476611408
## st9 -0.2890960 -0.747002982 0.03294080 -0.24417920 -0.534937161
## st10 -0.3142375 -0.011476165 0.55416247 0.66540866 -0.089023247O1acp$co## Comp1 Comp2 Comp3 Comp4 Comp5
## st1 -0.9955666 0.080614217 0.01862358 0.01259572 -0.0150657077
## st2 -0.9789109 0.176478472 -0.06872403 -0.00640387 -0.0338535821
## st3 -0.9691517 -0.021440245 -0.22567699 0.08725045 0.0076134690
## st4 -0.9827101 0.076893262 -0.12839199 -0.06568839 0.0009680007
## st5 -0.9593301 -0.245154337 -0.04181650 0.03419209 0.1256381536
## st6 -0.9810826 0.178044072 -0.05199226 0.00655575 -0.0369774267
## st7 -0.9736512 0.158199860 0.13710352 -0.06715571 -0.0268616416
## st8 -0.9806940 0.003881212 0.12769249 -0.10366196 0.0957083061
## st9 -0.8840890 -0.450717142 0.01325631 -0.05853429 -0.1074206968
## st10 -0.9609747 -0.006924342 0.22301061 0.15951082 -0.0178767524O1rAC=CA(O1, ncp = 5, graph = TRUE)## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
fviz_ca_row(O1rAC)
fviz_ca_col(O1rAC)
fviz_ca_biplot(O1rAC)
2) Imagine um problema de comunidades para responder com os dados abaixo. mostre a sequência da análise multivariada. Explique a escolha de transformação, coeficiente de associação e método multivariado.
O uso de transformação dos dados auxilia a diminuir a influência excessiva das espécies dominantes, além de evitar uma grande diferença (a grau de magnitude) entre as réplicas. O índice de Jaccard foi utilizado por se tratar de um índice assimétrico (não considera o duplo zero; considera que o zero pode ser falta de informação). Enquanto a técnica de cluster médio visou evitar algum tipo de tendência nos resultados.
O2<-read.table("O2.txt",header=T)
O2## Area1x1 Area1x2 Area1x3 Area1x4 Area2x1 Area2x2 Area2x3 Area2x4
## Especie1 0 1 1 1 0 0 0 1
## Especie2 0 1 1 0 1 0 0 1
## Especie3 0 1 1 1 0 0 0 1
## Especie4 1 0 0 0 1 1 1 0
## Especie5 1 1 1 1 1 1 1 0
## Especie6 1 1 1 1 0 1 1 0
## Especie7 1 1 1 0 1 0 0 1
## Especie8 0 1 1 1 0 0 0 1
## Especie9 0 1 1 1 0 0 0 1
## Especie10 0 0 0 0 0 0 0 1nrow(O2);ncol(O2)## [1] 10## [1] 8names(O2); row.names(O2);str(O2)## [1] "Area1x1" "Area1x2" "Area1x3" "Area1x4" "Area2x1" "Area2x2" "Area2x3"
## [8] "Area2x4"## [1] "Especie1" "Especie2" "Especie3" "Especie4" "Especie5" "Especie6"
## [7] "Especie7" "Especie8" "Especie9" "Especie10"## 'data.frame': 10 obs. of 8 variables:
## $ Area1x1: int 0 0 0 1 1 1 1 0 0 0
## $ Area1x2: int 1 1 1 0 1 1 1 1 1 0
## $ Area1x3: int 1 1 1 0 1 1 1 1 1 0
## $ Area1x4: int 1 0 1 0 1 1 0 1 1 0
## $ Area2x1: int 0 1 0 1 1 0 1 0 0 0
## $ Area2x2: int 0 0 0 1 1 1 0 0 0 0
## $ Area2x3: int 0 0 0 1 1 1 0 0 0 0
## $ Area2x4: int 1 1 1 0 0 0 1 1 1 1O2t<-log1p(O2)
O2t## Area1x1 Area1x2 Area1x3 Area1x4 Area2x1 Area2x2 Area2x3
## Especie1 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Especie2 0.0000000 0.6931472 0.6931472 0.0000000 0.6931472 0.0000000 0.0000000
## Especie3 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Especie4 0.6931472 0.0000000 0.0000000 0.0000000 0.6931472 0.6931472 0.6931472
## Especie5 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472 0.6931472
## Especie6 0.6931472 0.6931472 0.6931472 0.6931472 0.0000000 0.6931472 0.6931472
## Especie7 0.6931472 0.6931472 0.6931472 0.0000000 0.6931472 0.0000000 0.0000000
## Especie8 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Especie9 0.0000000 0.6931472 0.6931472 0.6931472 0.0000000 0.0000000 0.0000000
## Especie10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Area2x4
## Especie1 0.6931472
## Especie2 0.6931472
## Especie3 0.6931472
## Especie4 0.0000000
## Especie5 0.0000000
## Especie6 0.0000000
## Especie7 0.6931472
## Especie8 0.6931472
## Especie9 0.6931472
## Especie10 0.6931472mO2<-vegdist(O2t, "jaccard")
mO2## Especie1 Especie2 Especie3 Especie4 Especie5 Especie6 Especie7
## Especie2 0.4000000
## Especie3 0.0000000 0.4000000
## Especie4 1.0000000 0.8571429 1.0000000
## Especie5 0.6250000 0.6250000 0.6250000 0.4285714
## Especie6 0.5714286 0.7500000 0.5714286 0.5714286 0.1428571
## Especie7 0.5000000 0.2000000 0.5000000 0.7142857 0.5000000 0.6250000
## Especie8 0.0000000 0.4000000 0.0000000 1.0000000 0.6250000 0.5714286 0.5000000
## Especie9 0.0000000 0.4000000 0.0000000 1.0000000 0.6250000 0.5714286 0.5000000
## Especie10 0.7500000 0.7500000 0.7500000 1.0000000 1.0000000 1.0000000 0.8000000
## Especie8 Especie9
## Especie2
## Especie3
## Especie4
## Especie5
## Especie6
## Especie7
## Especie8
## Especie9 0.0000000
## Especie10 0.7500000 0.7500000dO2<-hclust(mO2, method="average")
dO2##
## Call:
## hclust(d = mO2, method = "average")
##
## Cluster method : average
## Distance : jaccard
## Number of objects: 10Gráfico
plot(dO2, hang=-1,ann=FALSE, cex.axis=1.1,col=1)
title(ylab="Dissimilaridade",
main="Dendrograma O2",xlab="Amostras",cex.lab=1.2)
rect.hclust(dO2,5, border=2:6)
Grupos
gO2<- cutree(dO2,5)
gO2## Especie1 Especie2 Especie3 Especie4 Especie5 Especie6 Especie7 Especie8
## 1 2 1 3 4 4 2 1
## Especie9 Especie10
## 1 5cgO2<- cbind(O2, cluster=gO2)
cgO2## Area1x1 Area1x2 Area1x3 Area1x4 Area2x1 Area2x2 Area2x3 Area2x4
## Especie1 0 1 1 1 0 0 0 1
## Especie2 0 1 1 0 1 0 0 1
## Especie3 0 1 1 1 0 0 0 1
## Especie4 1 0 0 0 1 1 1 0
## Especie5 1 1 1 1 1 1 1 0
## Especie6 1 1 1 1 0 1 1 0
## Especie7 1 1 1 0 1 0 0 1
## Especie8 0 1 1 1 0 0 0 1
## Especie9 0 1 1 1 0 0 0 1
## Especie10 0 0 0 0 0 0 0 1
## cluster
## Especie1 1
## Especie2 2
## Especie3 1
## Especie4 3
## Especie5 4
## Especie6 4
## Especie7 2
## Especie8 1
## Especie9 1
## Especie10 53) Os dados da pesca de fundo da plataforma continental de um país foram disponibilizados (gfa.txt). Analise os dados da comunidade, apresentando e discutindo os resultados.
A matriz não está abrindo.
4) Um emissário submarino foi monitorado durante 11 anos. O emissário localizado em Loch Linnhe (lnmb.txt), iniciou as emissões em 1966 com aumento em 1970 e redução drástica da poluição em 1972. Com a analise multivariada, mostre as diferenças na macrofauna neste monitoramento ambiental. Explique as escolhas metodológicas.
Houve grande diminuição na diversidade de espécies conforme o aumento da poluição, posteriormente, em 1973, após a drástica redução da poluição, em 1972, a diversidade voltou a crescer. O uso de transformação dos dados auxilia a diminuir a influência excessiva das espécies dominantes, além de evitar uma grande diferença (a grau de magnitude) entre as réplicas. O log1p é uma das transformações indicadas para dados bióticos.
O4<-read.table("O4.txt",header=T)
O4## A1963 A1964 A1965 A1966 A1967 A1968 A1969 A1970 A1971 A1972 A1973
## sp1 0 0 0 0 0 0 124 146 58 0 4
## sp2 2 0 0 1 1 2 0 4 4 30 0
## sp3 0 0 0 44 26 18 20 0 15 18 13
## sp4 0 0 1 12 36 47 25 0 5 58 0
## sp5 77 1 0 46 186 438 241 0 0 0 246
## sp6 0 0 0 0 213 0 997 0 0 0 0
## sp7 2 0 0 0 0 0 0 0 0 0 0
## sp8 0 0 0 0 0 101 2 0 1 0 13
## sp9 0 0 0 0 0 0 0 0 7 0 0
## sp10 2 5 9 2 13 0 58 45 27 136 15
## sp11 2 20 27 0 0 0 0 0 0 0 0
## sp12 2 125 0 0 4 5 112 2 117 55 0
## sp13 0 1 1 0 7 9 2 1 32 2 0
## sp14 0 0 4 7 36 3 32 73 34 0 1
## sp15 0 0 0 2 1 0 0 0 24 0 0
## sp16 0 0 0 0 7 0 0 0 0 0 0
## sp17 6 0 0 0 11 0 2 0 1 0 0
## sp18 0 0 0 9 2 0 0 2 1 3 0
## sp19 0 2 0 0 0 0 0 0 0 0 0
## sp20 0 0 0 1 40 7 2 31 1 0 5
## sp21 0 0 1 8 24 0 21 0 0 0 23
## sp24 0 0 0 2 0 0 0 0 0 0 0
## sp25 2 0 0 0 0 0 229 0 22 0 0
## sp26 2 426 0 0 0 0 235 45 0 0 0
## sp27 2 0 6 47 26 6 54 0 2 10 33
## sp28 0 1 0 0 0 0 0 0 0 0 0
## sp29 48 3 122 135 195 398 221 525 119 211 44
## sp30 10 18 9 5 67 48 77 198 38 4 37
## sp31 8 0 3 33 0 0 0 0 0 0 0
## sp32 0 0 0 0 0 0 4 0 0 0 0
## sp33 0 0 0 0 0 0 5 0 0 0 0
## sp34 2 0 0 17 4 569 98 17 101 192 30
## sp35 0 23 4 0 1 0 1 12 0 0 1
## sp36 0 0 0 0 2 2 1 0 0 0 1
## sp37 0 17 1 2 1 0 0 0 0 0 0
## sp38 0 0 2 0 0 0 0 0 0 0 0
## sp39 0 1 0 0 0 0 0 0 0 0 0
## sp40 8 0 0 93 87 4 0 0 0 0 0
## sp41 0 0 0 4 0 47 0 1 0 0 0
## sp42 4 18 48 9 59 14 8 490 0 0 43
## sp43 0 0 0 0 0 0 0 0 10 0 0
## sp44 74 2 0 0 0 0 0 0 24 0 0
## sp45 0 0 0 0 10 0 0 0 0 0 0
## sp46 4 9 17 9 31 3 37 7 0 0 0
## sp47 0 0 0 0 0 0 0 0 5 0 0
## sp48 0 2 0 0 0 0 0 0 0 0 0
## sp49 2 0 0 0 0 0 0 0 0 0 0
## sp50 2 0 0 0 0 0 0 0 0 0 0
## sp51 0 3 2 0 0 2 1 0 0 0 5
## sp52 0 1 0 53 233 448 8 0 0 0 0
## sp53 0 0 0 1 0 0 0 0 0 0 0
## sp54 0 0 0 35 0 0 0 0 0 776 0
## sp56 6 0 0 0 0 0 0 0 0 0 9
## sp57 2 0 0 0 0 0 0 0 0 0 0
## sp59 0 0 0 0 0 2 4 0 4 0 1
## sp60 0 0 0 262 0 0 0 0 0 0 0
## sp61 8 18 56 0 0 0 21 1 8 6 2
## sp62 0 0 0 0 0 61 194 0 1 0 73
## sp63 0 0 0 0 905 88 0 0 0 0 0
## sp64 44 0 0 205 0 32 94 0 6 0 0
## sp65 0 0 0 0 0 0 0 0 73 0 0
## sp66 176 0 0 2 0 156 0 4 103 21 0
## sp67 2 1 2 0 0 9 0 107 0 0 6
## sp68 2 0 0 116 28 1158 437 0 0 0 167
## sp70 0 0 0 44 126 0 15 0 0 0 0
## sp71 0 0 0 0 2 0 0 0 0 0 0
## sp72 6 0 43 23 459 26 4 0 0 0 0
## sp73 6 0 27 0 3 114 107 0 0 0 490
## sp74 0 0 69 0 0 0 0 0 0 0 0
## sp75 0 6 13 0 0 0 0 2 0 0 1
## sp76 0 10 44 0 0 0 4 7 2 0 135
## sp77 32 1 0 4 0 2 0 0 0 0 0
## sp78 80 0 20 0 37 0 17 2644 84 0 0
## sp79 18 0 9 0 7 1 0 0 0 0 0
## sp80 0 0 0 0 36 0 0 0 0 0 0
## sp81 0 46 0 0 0 0 37 0 0 0 0
## sp82 12 0 0 478 211 55 0 0 0 0 0
## sp83 0 0 42 0 0 70 49 305 437 0 126
## sp84 6 0 0 0 0 0 0 0 0 0 0
## sp85 0 0 0 0 4 0 0 0 0 0 0
## sp86 28 0 0 0 0 0 0 0 0 0 0
## sp87 280 217 17 4579 1482 817 1649 0 0 0 0
## sp88 0 11 0 23 172 0 0 0 0 0 0
## sp90 0 9 0 0 0 0 0 0 0 0 0
## sp91 0 0 0 4 0 15 7 4 1220 1585 7
## sp92 0 0 1 0 0 0 0 0 0 0 0
## sp93 0 21 0 57 0 64 46 0 0 0 0
## sp95 0 0 5 0 9 0 0 0 3 0 0
## sp96 1 7 10 4 0 5 0 2 4 0 0
## sp97 0 0 9 0 0 0 0 0 0 0 0
## sp98 0 0 0 0 0 0 0 0 24 436 8
## sp99 357 798 106 517 1664 1224 220 357 0 46 403
## sp100 2739 1741 26 3610 8602 3456 2022 0 0 51 4905
## sp101 39 172 0 73 383 647 79 0 0 0 0
## sp102 0 0 2 0 0 12 0 0 0 1 0
## sp103 0 0 0 0 0 0 0 0 0 0 51
## sp104 0 0 26 0 0 0 0 0 8 4 0
## sp105 13 54 27 13 148 174 0 13 0 0 0
## sp106 0 0 0 0 0 0 0 4 2 0 0
## sp107 221 1559 179 276 593 773 276 359 0 41 662
## sp108 62 130 0 25 56 50 0 0 0 0 0
## sp109 126 273 700 259 469 189 392 0 21 91 476
## sp110 0 0 0 0 0 0 0 0 0 256 0
## sp111 0 10000 2000 0 0 0 0 0 0 0 0
## sp113 0 430 31 122 91 21 31 510 0 0 0
## sp114 48 53 14 246 1166 58 181 0 0 0 56
## sp115 0 0 0 32 13 94 11 0 0 0 0O4n<-log1p(O4)
O4acp = prcomp(O4n, scale. = TRUE)
O4acp## Standard deviations (1, .., p=11):
## [1] 2.1544672 1.2899469 1.0873404 0.8586420 0.8100321 0.7130997 0.6918629
## [8] 0.6154049 0.5633819 0.5031998 0.4266883
##
## Rotation (n x k) = (11 x 11):
## PC1 PC2 PC3 PC4 PC5 PC6
## A1963 0.34008122 0.13115700 -0.03878690 0.18750757 -0.23006761 0.80778866
## A1964 0.29666172 0.16973381 0.45314204 0.34626192 -0.03327357 -0.19973524
## A1965 0.27430706 -0.06082100 0.59444459 0.19312464 0.16714160 0.05027496
## A1966 0.35349709 0.25820652 -0.27798258 0.12424493 -0.21688805 -0.18925053
## A1967 0.35335888 0.25776606 -0.12703365 -0.12140492 -0.27401616 -0.26270117
## A1968 0.37623869 0.08792743 -0.27942120 -0.15090807 0.01349773 0.05416077
## A1969 0.35940193 -0.07005184 -0.12722534 -0.34097826 0.17537885 -0.21186910
## A1970 0.22131084 -0.37427963 0.38761446 -0.41543599 -0.39580158 -0.13070812
## A1971 0.08041778 -0.66913941 -0.15152393 -0.02586959 -0.27208783 0.17957222
## A1972 0.19136399 -0.44298115 -0.27911062 0.64710220 0.09666545 -0.27662885
## A1973 0.32936081 -0.14307880 -0.03181099 -0.21548442 0.72451732 0.16294741
## PC7 PC8 PC9 PC10 PC11
## A1963 -0.07273490 -0.18227490 0.26366087 0.01507342 -0.1294863
## A1964 -0.50622227 -0.24590201 -0.20078662 -0.23399418 0.3242663
## A1965 0.27061390 0.57348887 -0.04815413 0.16544606 -0.2609952
## A1966 0.12549266 0.06696879 -0.11718004 0.69724749 0.3356835
## A1967 0.27309595 0.26616295 0.41582052 -0.53972006 0.1552164
## A1968 0.09572366 -0.01611703 -0.74605890 -0.27316354 -0.3257349
## A1969 -0.60187735 0.10907167 0.30119341 0.18996537 -0.3960644
## A1970 0.26604481 -0.47176844 0.01585690 0.12816828 -0.0658550
## A1971 -0.24550787 0.42416833 -0.14336853 -0.08993245 0.3834625
## A1972 0.17310062 -0.23959860 0.16238353 -0.06060175 -0.2592750
## A1973 0.20603353 -0.17332894 0.08194658 -0.03609195 0.4377404O4acp$sdev## [1] 2.1544672 1.2899469 1.0873404 0.8586420 0.8100321 0.7130997 0.6918629
## [8] 0.6154049 0.5633819 0.5031998 0.4266883head(O4acp$rotation)## PC1 PC2 PC3 PC4 PC5 PC6
## A1963 0.3400812 0.13115700 -0.0387869 0.1875076 -0.23006761 0.80778866
## A1964 0.2966617 0.16973381 0.4531420 0.3462619 -0.03327357 -0.19973524
## A1965 0.2743071 -0.06082100 0.5944446 0.1931246 0.16714160 0.05027496
## A1966 0.3534971 0.25820652 -0.2779826 0.1242449 -0.21688805 -0.18925053
## A1967 0.3533589 0.25776606 -0.1270336 -0.1214049 -0.27401616 -0.26270117
## A1968 0.3762387 0.08792743 -0.2794212 -0.1509081 0.01349773 0.05416077
## PC7 PC8 PC9 PC10 PC11
## A1963 -0.07273490 -0.18227490 0.26366087 0.01507342 -0.1294863
## A1964 -0.50622227 -0.24590201 -0.20078662 -0.23399418 0.3242663
## A1965 0.27061390 0.57348887 -0.04815413 0.16544606 -0.2609952
## A1966 0.12549266 0.06696879 -0.11718004 0.69724749 0.3356835
## A1967 0.27309595 0.26616295 0.41582052 -0.53972006 0.1552164
## A1968 0.09572366 -0.01611703 -0.74605890 -0.27316354 -0.3257349head(O4acp$x)## PC1 PC2 PC3 PC4 PC5 PC6
## sp1 -0.2136189 -2.6113174 0.3741798 -2.1243384 -0.5517976 -0.22261691
## sp2 -0.8045952 -1.2290256 -0.6286553 0.9161723 -0.5180671 -0.07171139
## sp3 0.9576974 -0.8995137 -1.9644752 0.1158088 0.3748682 -0.86478291
## sp4 0.7187939 -0.7007519 -1.7429832 0.7431894 -0.2133935 -1.27763445
## sp5 3.1660009 1.4204637 -1.8646414 -1.3415847 1.1485036 1.13939354
## sp6 -0.1386597 0.7055739 -0.6650418 -1.3663746 0.1185600 -1.25811968
## PC7 PC8 PC9 PC10 PC11
## sp1 -0.96062207 -0.3449460 0.42970131 0.5346917 0.21514770
## sp2 0.53404118 -0.7205104 0.10375764 -0.1158934 -0.33940573
## sp3 0.14618617 0.4647749 -0.01299089 0.1437996 0.60880460
## sp4 0.17722882 0.5299222 -0.10223825 -0.2993230 -0.84795020
## sp5 -0.08157891 -0.3393633 0.33113260 -0.2896390 0.07822426
## sp6 -1.17358092 0.7092278 1.90913837 -0.6045543 -0.95485736biplot(O4acp)
autovalores <- get_eigenvalue(O4acp)
fviz_eig(O4acp)
O4s = as.data.frame(O4acp$x)
ggplot(data = O4s, aes(x = PC1, y = PC2, label =
rownames(O4s))) +
geom_hline(yintercept = 0, colour = "gray65") + geom_vline(xintercept = 0, colour = "gray65") +
geom_text(colour = "blue", alpha = 0.8, size = 4) +
ggtitle("O4acp")
fviz_pca_ind(O4acp, col.ind = "cos2", gradient.cols =
c("#00AFBB", "#E7B800", "#FC4E07"),repel = TRUE)
fviz_pca_var(O4acp, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
fviz_pca_biplot(O4acp, repel = TRUE,col.var = "#2E9FDF",
col.ind = "#696969")
O4acp$eig## NULLO4acp$var$coord## NULLhead(O4acp$ind$coord)## NULLO4acp = dudi.pca(O4, nf = 5, scannf = FALSE)
O4acp$eig## [1] 5.120765384 1.914593418 1.796556263 1.004444419 0.620407320 0.192402169
## [7] 0.145363452 0.114966131 0.052272872 0.029129128 0.009099445O4acp$c1## CS1 CS2 CS3 CS4 CS5
## A1963 -0.425469649 -0.037266501 0.003054981 0.024817306 0.287160130
## A1964 -0.097914543 0.670194062 0.186255429 -0.013127192 0.015176398
## A1965 -0.034353082 0.683607735 0.197695513 -0.011038244 -0.053019144
## A1966 -0.362376903 -0.050047503 -0.023526865 -0.044457197 -0.664320538
## A1967 -0.429104756 -0.038141992 -0.006761807 0.001532921 0.203584402
## A1968 -0.412557988 -0.036150457 0.005185200 0.028317101 0.142310417
## A1969 -0.388956630 -0.044297696 -0.016937512 -0.031077426 -0.496533652
## A1970 -0.004549601 -0.002436295 0.064564527 0.992208951 -0.058942833
## A1971 0.016894552 -0.193754116 0.679875029 0.012809814 -0.025624380
## A1972 0.004378929 -0.191535992 0.677365546 -0.103306005 0.001490364
## A1973 -0.413453288 -0.025889328 0.008963738 0.005353020 0.400996647O4acp$co## Comp1 Comp2 Comp3 Comp4 Comp5
## A1963 -0.962799872 -0.051565223 0.004094765 0.024872394 0.226184374
## A1964 -0.221571878 0.927339708 0.249648724 -0.013156331 0.011953832
## A1965 -0.077737961 0.945900051 0.264982519 -0.011062746 -0.041761027
## A1966 -0.820026615 -0.069250146 -0.031534393 -0.044555880 -0.523258312
## A1967 -0.971025797 -0.052776630 -0.009063234 0.001536324 0.160355167
## A1968 -0.933581935 -0.050020966 0.006950018 0.028379958 0.112092137
## A1969 -0.880174167 -0.061294205 -0.022702308 -0.031146410 -0.391099395
## A1970 -0.010295341 -0.003371074 0.086539500 0.994411402 -0.046426876
## A1971 0.038230864 -0.268095311 0.911275097 0.012838249 -0.020183284
## A1972 0.009909125 -0.265026119 0.907911493 -0.103535318 0.001173899
## A1973 -0.935607919 -0.035822762 0.012014607 0.005364903 0.315848776O4rAC=CA(O4, ncp = 5, graph = TRUE)
fviz_ca_row(O4rAC)
fviz_ca_col(O4rAC)
fviz_ca_biplot(O4rAC)
5) Um estudo avaliou os metais existentes no sedimento ao longo do estuário do rio Clyde (clev.txt). O que você pode concluir, com uma análise de componentes principais
Os pontos S3, S4, S5 e S9 tem maior presença de Ni, N, C e Zn; enquanto S1 tem mais Mn. S2, S10 e S11 apresentam mais Co e Dep; enquanto S6, S7 e S8 apresentam mais Pb, Cr, Cu e CD.
O5<-read.table("O5.txt",header=T)
O5## Cu Mn Co Ni Zn Cd Pb Cr Dep C N
## S1 26 2470 14 34 160 0.0 70 53 144 3.0 0.53
## S2 30 1170 15 32 156 0.2 59 15 152 3.0 0.46
## S3 37 394 12 38 182 0.2 81 77 140 2.9 0.36
## S4 74 349 12 41 227 0.5 97 113 106 3.7 0.46
## S5 115 317 10 37 329 2.2 137 177 112 5.6 0.69
## S6 344 221 10 37 652 5.7 319 314 82 11.2 1.07
## S7 194 257 11 34 425 3.7 175 227 74 7.1 0.72
## S8 127 246 10 33 292 2.2 130 182 70 6.8 0.58
## S9 36 194 6 16 89 0.4 42 57 64 1.9 0.29
## S10 30 326 11 26 108 0.1 44 52 80 3.2 0.38
## S11 24 439 12 34 119 0.1 58 36 83 2.1 0.35
## S12 22 801 12 33 118 0.0 52 51 83 2.3 0.45O5n<-normalize(O5, method =
"standardize", range = c(0, 1), margin = 1L,
on.constant = "quiet")
O5acp = prcomp(O5n, scale. = TRUE)
O5acp## Standard deviations (1, .., p=11):
## [1] 2.685040798 1.601516582 0.827792521 0.529694285 0.408267741 0.201050376
## [7] 0.168560768 0.141360792 0.061981739 0.022245062 0.006933159
##
## Rotation (n x k) = (11 x 11):
## PC1 PC2 PC3 PC4 PC5 PC6
## Cu 0.3692918 -0.008798325 0.08566842 0.01319915 -0.14653949 0.34137072
## Mn -0.1528147 -0.416436390 0.69745348 -0.26243961 0.44503441 0.01719028
## Co -0.1124543 -0.551308864 -0.10715591 -0.43776570 -0.63305153 -0.08447970
## Ni 0.1285326 -0.458182119 -0.65416376 -0.16632035 0.49611365 0.08352748
## Zn 0.3667664 -0.098461821 0.02341109 0.08839758 -0.04278365 0.13077205
## Cd 0.3684938 0.016517835 0.10679085 0.01973303 -0.15612112 -0.05535524
## Pb 0.3657750 -0.083603444 0.04845997 0.07719823 -0.01557157 0.51285641
## Cr 0.3671100 0.017638024 -0.03596383 0.02606053 0.27694125 -0.50360462
## Dep -0.1298160 -0.515619037 0.04733760 0.82978930 -0.09554791 -0.09196917
## C 0.3655305 -0.052664115 0.07749255 -0.03757516 -0.14526031 -0.56585385
## N 0.3489606 -0.163481802 0.20728453 -0.08273782 0.01464340 0.06002599
## PC7 PC8 PC9 PC10 PC11
## Cu 0.285416033 0.068690664 -0.42925494 -0.46693686 0.47911850
## Mn 0.200007911 -0.027684229 0.06187098 -0.06958446 -0.01103393
## Co 0.069751498 -0.125684726 -0.13342497 0.18391746 0.01051390
## Ni -0.007126267 0.042166004 0.15748760 -0.18388268 0.06637994
## Zn 0.089031271 -0.259976564 -0.18937526 -0.23636668 -0.81317103
## Cd 0.012867943 -0.574004603 0.65295548 -0.11568192 0.23521849
## Pb 0.224820117 0.296544942 0.20689169 0.63649085 -0.03520325
## Cr 0.158147610 -0.311529305 -0.43483650 0.44291043 0.15911920
## Dep -0.021495071 -0.005711615 -0.01523298 -0.00540663 0.09027741
## C 0.159903599 0.619669543 0.24180424 -0.19493319 -0.09422364
## N -0.874036822 0.104206914 -0.12847366 0.03032419 0.07513800O5acp$sdev## [1] 2.685040798 1.601516582 0.827792521 0.529694285 0.408267741 0.201050376
## [7] 0.168560768 0.141360792 0.061981739 0.022245062 0.006933159head(O5acp$rotation)## PC1 PC2 PC3 PC4 PC5 PC6
## Cu 0.3692918 -0.008798325 0.08566842 0.01319915 -0.14653949 0.34137072
## Mn -0.1528147 -0.416436390 0.69745348 -0.26243961 0.44503441 0.01719028
## Co -0.1124543 -0.551308864 -0.10715591 -0.43776570 -0.63305153 -0.08447970
## Ni 0.1285326 -0.458182119 -0.65416376 -0.16632035 0.49611365 0.08352748
## Zn 0.3667664 -0.098461821 0.02341109 0.08839758 -0.04278365 0.13077205
## Cd 0.3684938 0.016517835 0.10679085 0.01973303 -0.15612112 -0.05535524
## PC7 PC8 PC9 PC10 PC11
## Cu 0.285416033 0.06869066 -0.42925494 -0.46693686 0.47911850
## Mn 0.200007911 -0.02768423 0.06187098 -0.06958446 -0.01103393
## Co 0.069751498 -0.12568473 -0.13342497 0.18391746 0.01051390
## Ni -0.007126267 0.04216600 0.15748760 -0.18388268 0.06637994
## Zn 0.089031271 -0.25997656 -0.18937526 -0.23636668 -0.81317103
## Cd 0.012867943 -0.57400460 0.65295548 -0.11568192 0.23521849head(O5acp$x)## PC1 PC2 PC3 PC4 PC5 PC6
## S1 -1.9901978 -2.5925991 1.6494046 -0.20917747 0.57236748 -0.03055485
## S2 -2.0777660 -1.9387861 0.3844035 0.39033965 -0.90910549 -0.02966809
## S3 -1.3198958 -0.8872213 -1.0243895 0.90130502 0.06142146 0.01614936
## S4 -0.3225322 -0.6335797 -1.2562513 -0.05805345 0.34181334 0.08260451
## S5 1.4657264 -0.2319292 -0.3600954 0.62667691 0.42293729 -0.15357301
## S6 6.6430329 -0.4131231 0.5225512 0.09893492 -0.16913210 0.28157725
## PC7 PC8 PC9 PC10 PC11
## S1 0.10070668 0.003412817 -0.003693618 0.004641114 -0.0043519185
## S2 -0.07177275 -0.011638953 0.012230141 -0.027392724 0.0050795869
## S3 0.20223711 -0.004545111 0.022233953 0.040195884 0.0034297114
## S4 0.09258297 0.049536083 -0.118587290 -0.035951416 -0.0012115907
## S5 -0.38897428 -0.060921891 0.035723781 -0.005389966 -0.0054462264
## S6 0.01123855 0.157291564 -0.002460709 0.006448158 0.0002251101biplot(O5acp)
autovalores <- get_eigenvalue(O5acp)
fviz_eig(O5acp)
O5s = as.data.frame(O5acp$x)
ggplot(data = O5s, aes(x = PC1, y = PC2, label =
rownames(O5s))) +
geom_hline(yintercept = 0, colour = "gray65") + geom_vline(xintercept = 0, colour = "gray65") +
geom_text(colour = "blue", alpha = 0.8, size = 4) +
ggtitle("O5acp")
fviz_pca_ind(O5acp, col.ind = "cos2", gradient.cols =
c("#00AFBB", "#E7B800", "#FC4E07"),repel = TRUE)
fviz_pca_var(O5acp, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
fviz_pca_biplot(O5acp, repel = TRUE,col.var = "#2E9FDF",
col.ind = "#696969")
O5acp$eig## NULLO5acp$var$coord## NULLhead(O5acp$ind$coord)## NULLO5acp = dudi.pca(O5, nf = 5, scannf = FALSE)
O5acp$eig## [1] 7.2094440894 2.5648553612 0.6852404581 0.2805760360 0.1666825482
## [6] 0.0404212536 0.0284127326 0.0199828736 0.0038417360 0.0004948428
## [11] 0.0000480687O5acp$c1## CS1 CS2 CS3 CS4 CS5
## Cu 0.3692918 -0.008798325 -0.08566842 -0.01319915 0.14653949
## Mn -0.1528147 -0.416436390 -0.69745348 0.26243961 -0.44503441
## Co -0.1124543 -0.551308864 0.10715591 0.43776570 0.63305153
## Ni 0.1285326 -0.458182119 0.65416376 0.16632035 -0.49611365
## Zn 0.3667664 -0.098461821 -0.02341109 -0.08839758 0.04278365
## Cd 0.3684938 0.016517835 -0.10679085 -0.01973303 0.15612112
## Pb 0.3657750 -0.083603444 -0.04845997 -0.07719823 0.01557157
## Cr 0.3671100 0.017638024 0.03596383 -0.02606053 -0.27694125
## Dep -0.1298160 -0.515619037 -0.04733760 -0.82978930 0.09554791
## C 0.3655305 -0.052664115 -0.07749255 0.03757516 0.14526031
## N 0.3489606 -0.163481802 -0.20728453 0.08273782 -0.01464340O5acp$co## Comp1 Comp2 Comp3 Comp4 Comp5
## Cu 0.9915635 -0.01409066 -0.07091568 -0.006991515 0.059827345
## Mn -0.4103138 -0.66692978 -0.57734678 0.139012763 -0.181693193
## Co -0.3019444 -0.88293029 0.08870286 0.231881988 0.258454517
## Ni 0.3451154 -0.73378626 0.54151187 0.088098937 -0.202547198
## Zn 0.9847827 -0.15768824 -0.01937952 -0.046823694 0.017467185
## Cd 0.9894210 0.02645359 -0.08840066 -0.010452473 0.063739219
## Pb 0.9821207 -0.13389230 -0.04011480 -0.040891463 0.006357368
## Cr 0.9857054 0.02824759 0.02977059 -0.013804112 -0.113066179
## Dep -0.3485613 -0.82577244 -0.03918571 -0.439534652 0.039009130
## C 0.9814643 -0.08434245 -0.06414775 0.019903348 0.059305100
## N 0.9369735 -0.26181882 -0.17158858 0.043825752 -0.005978428O5rAC=CA(O5, ncp = 5, graph = TRUE)
fviz_ca_row(O5rAC)
fviz_ca_col(O5rAC)
fviz_ca_biplot(O5rAC)