ANOSIM, PERMANOVA e SIMPER
Leonardo Castelo Branco Carvalho
03/02/2022
ANOSIM e PERMANOVA
Embora tenhamos respostas quanto a diversidade beta, não testamos diferenças estatísticas. Fazemos isso com análise de variância permutacional (PERMANOVA) ou análise de similaridade (ANOSIM). Eles testam se os locais amostrados diferem de acordo com uma variável de interesse.
PERMANOVA
A PERMANOVA (Permutation Multivariate Analysis of Variance) é uma análise multivariada não paramétrica que testa a hipótese nula de que a dispersão das observações são equivalentes em todos os grupos formados. Para tal a analise compara a SQ entre os grupos e dentro dos grupos.
Usamos o pacote vegan para calcular distâncias e rodar a PERMANOVA. Dessa forma podemos incluir todas as variáveis de interesse em um modelo, bem como suas interações.
Carregando os dados:
data(dune)
data(dune.env)Relembrando os dados:
head(dune)## Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
## 1 1 0 0 0 0 0 0 0
## 2 3 0 0 2 0 3 4 0
## 3 0 4 0 7 0 2 0 0
## 4 0 8 0 2 0 2 3 0
## 5 2 0 0 0 4 2 2 0
## 6 2 0 0 0 3 0 0 0
## Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
## 1 0 0 0 4 0 0 0 0
## 2 0 0 0 4 0 0 0 0
## 3 0 0 0 4 0 0 0 0
## 4 2 0 0 4 0 0 0 0
## 5 0 0 0 4 0 0 0 0
## 6 0 0 0 0 0 0 0 0
## Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
## 1 7 0 4 2 0 0 0 0
## 2 5 0 4 7 0 0 0 0
## 3 6 0 5 6 0 0 0 0
## 4 5 0 4 5 0 0 5 0
## 5 2 5 2 6 0 5 0 0
## 6 6 5 3 4 0 6 0 0
## Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
## 1 0 0 0 0 0 0
## 2 5 0 5 0 0 0
## 3 2 0 2 0 2 0
## 4 2 0 1 0 2 0
## 5 3 2 2 0 2 0
## 6 3 5 5 0 6 0head(dune.env)## A1 Moisture Management Use Manure
## 1 2.8 1 SF Haypastu 4
## 2 3.5 1 BF Haypastu 2
## 3 4.3 2 SF Haypastu 4
## 4 4.2 2 SF Haypastu 4
## 5 6.3 1 HF Hayfield 2
## 6 4.3 1 HF Haypastu 2Obtendo as distâncias entre os locais:
distancia_dune = vegdist(dune)Lembrando que o índice padrão da função vegdist é o Bray-Curtis!
Obtendo um dendrograma:
cluster_dune = hclust(distancia_dune, method = "average")
plot(cluster_dune)
Rodando a PERMANOVA:
adonis2(distancia_dune ~ Management*A1, data = dune.env, permutations = 1000)## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 1000
##
## adonis2(formula = distancia_dune ~ Management * A1, data = dune.env, permutations = 1000)
## Df SumOfSqs R2 F Pr(>F)
## Management 3 1.4686 0.34161 3.2629 0.001998 **
## A1 1 0.4409 0.10256 2.9387 0.015984 *
## Management:A1 3 0.5892 0.13705 1.3090 0.211788
## Residual 12 1.8004 0.41878
## Total 19 4.2990 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1A interação Management x A1 não foi significativa, o que fazer?
adonis2(distancia_dune ~ Management+A1, data = dune.env, permutations = 1000)## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 1000
##
## adonis2(formula = distancia_dune ~ Management + A1, data = dune.env, permutations = 1000)
## Df SumOfSqs R2 F Pr(>F)
## Management 3 1.4686 0.34161 3.0730 0.007992 **
## A1 1 0.4409 0.10256 2.7676 0.022977 *
## Residual 15 2.3895 0.55583
## Total 19 4.2990 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOSIM
Se você tiver tamanhos de grupo muito diferentes, considere a análise de semelhanças/similaridades (ANOSIM) em vez de PERMANOVA. Este teste não assume igualdade de variâncias entre os grupos. No entanto, ele só permite modelos simples de 1 variável sem interações e só pode ser usado para variáveis categóricas. Portanto é uma analise confirmatória pois verifica se os grupos obtidos são de fato diferentes via teste estatístico.
Selecionando a variável de interesse do arquivo de dados dune.env:
dune.env## A1 Moisture Management Use Manure
## 1 2.8 1 SF Haypastu 4
## 2 3.5 1 BF Haypastu 2
## 3 4.3 2 SF Haypastu 4
## 4 4.2 2 SF Haypastu 4
## 5 6.3 1 HF Hayfield 2
## 6 4.3 1 HF Haypastu 2
## 7 2.8 1 HF Pasture 3
## 8 4.2 5 HF Pasture 3
## 9 3.7 4 HF Hayfield 1
## 10 3.3 2 BF Hayfield 1
## 11 3.5 1 BF Pasture 1
## 12 5.8 4 SF Haypastu 2
## 13 6.0 5 SF Haypastu 3
## 14 9.3 5 NM Pasture 0
## 15 11.5 5 NM Haypastu 0
## 16 5.7 5 SF Pasture 3
## 17 4.0 2 NM Hayfield 0
## 18 4.6 1 NM Hayfield 0
## 19 3.7 5 NM Hayfield 0
## 20 3.5 5 NM Hayfield 0Analisando a variável “Management”:
dune.env$Management## [1] SF BF SF SF HF HF HF HF HF BF BF SF SF NM NM SF NM NM NM NM
## Levels: BF HF NM SFAssim, utiliza-se a função anosim no R:
anosim_dune = anosim(distancia_dune, grouping = dune.env$Management, permutations = 1000)
summary(anosim_dune)##
## Call:
## anosim(x = distancia_dune, grouping = dune.env$Management, permutations = 1000)
## Dissimilarity: bray
##
## ANOSIM statistic R: 0.2579
## Significance: 0.010989
##
## Permutation: free
## Number of permutations: 1000
##
## Upper quantiles of permutations (null model):
## 90% 95% 97.5% 99%
## 0.125 0.166 0.215 0.254
##
## Dissimilarity ranks between and within classes:
## 0% 25% 50% 75% 100% N
## Between 4 58.50 104.00 145.500 188.0 147
## BF 5 15.25 25.50 41.250 57.0 3
## HF 1 7.25 46.25 68.125 89.5 10
## NM 6 64.75 124.50 156.250 181.0 15
## SF 3 32.75 53.50 99.250 184.0 15Grafico:
plot(anosim_dune)## Warning in bxp(list(stats = structure(c(4, 58.5, 104, 145.5, 188, 5, 15.25, :
## some notches went outside hinges ('box'): maybe set notch=FALSE
SIMPER
Analise de porcentagem de similaridades. Mostra o quanto cada especie contribuiu para a formação dos grupos formados entre os locais.
sim <- with(dune.env, simper(dune, Management))
summary(sim)##
## Contrast: SF_BF
##
## average sd ratio ava avb cumsum
## Agrostol 0.061374 0.034193 1.7949 4.6667 0.0000 0.09824
## Alopgeni 0.052667 0.036476 1.4439 4.3333 0.6667 0.18255
## Lolipere 0.048116 0.039445 1.2198 3.0000 6.0000 0.25957
## Trifrepe 0.046297 0.025525 1.8138 1.3333 4.6667 0.33368
## Poatriv 0.046020 0.033801 1.3615 4.6667 3.6667 0.40734
## Scorautu 0.043697 0.024922 1.7534 1.3333 4.3333 0.47729
## Bromhord 0.033677 0.025860 1.3023 0.5000 2.6667 0.53120
## Achimill 0.030152 0.020821 1.4482 0.1667 2.3333 0.57947
## Planlanc 0.028585 0.021549 1.3265 0.0000 2.0000 0.62522
## Elymrepe 0.028074 0.029778 0.9428 2.0000 1.3333 0.67016
## Bracruta 0.025501 0.023902 1.0669 2.0000 2.0000 0.71098
## Poaprat 0.025129 0.023967 1.0485 2.5000 4.0000 0.75121
## Sagiproc 0.024326 0.022149 1.0983 1.8333 0.6667 0.79014
## Bellpere 0.019859 0.017088 1.1622 0.6667 1.6667 0.82193
## Eleopalu 0.018611 0.042958 0.4333 1.3333 0.0000 0.85172
## Anthodor 0.017543 0.025804 0.6798 0.0000 1.3333 0.87981
## Juncbufo 0.016031 0.023708 0.6762 1.1667 0.0000 0.90547
## Vicilath 0.014671 0.013306 1.1026 0.0000 1.0000 0.92895
## Hyporadi 0.010286 0.015198 0.6768 0.0000 0.6667 0.94542
## Ranuflam 0.009306 0.013595 0.6845 0.6667 0.0000 0.96031
## Juncarti 0.006979 0.016109 0.4333 0.5000 0.0000 0.97148
## Callcusp 0.006979 0.016109 0.4333 0.5000 0.0000 0.98266
## Rumeacet 0.004526 0.010444 0.4333 0.3333 0.0000 0.98990
## Cirsarve 0.003983 0.009185 0.4336 0.3333 0.0000 0.99628
## Chenalbu 0.002326 0.005370 0.4333 0.1667 0.0000 1.00000
## Airaprae 0.000000 0.000000 NaN 0.0000 0.0000 1.00000
## Comapalu 0.000000 0.000000 NaN 0.0000 0.0000 1.00000
## Empenigr 0.000000 0.000000 NaN 0.0000 0.0000 1.00000
## Salirepe 0.000000 0.000000 NaN 0.0000 0.0000 1.00000
## Trifprat 0.000000 0.000000 NaN 0.0000 0.0000 1.00000
##
## Contrast: SF_HF
##
## average sd ratio ava avb cumsum
## Agrostol 0.047380 0.031273 1.5151 4.6667 1.4 0.08351
## Alopgeni 0.046433 0.032897 1.4115 4.3333 1.6 0.16535
## Lolipere 0.041986 0.027007 1.5546 3.0000 4.0 0.23935
## Planlanc 0.039198 0.033208 1.1804 0.0000 3.0 0.30844
## Rumeacet 0.038992 0.027369 1.4247 0.3333 3.2 0.37716
## Elymrepe 0.031877 0.029550 1.0787 2.0000 2.0 0.43334
## Poatriv 0.028466 0.021522 1.3227 4.6667 4.8 0.48352
## Bracruta 0.025261 0.021044 1.2004 2.0000 2.8 0.52804
## Eleopalu 0.024974 0.038877 0.6424 1.3333 0.8 0.57206
## Poaprat 0.023932 0.019180 1.2478 2.5000 3.4 0.61424
## Anthodor 0.023409 0.021430 1.0923 0.0000 1.8 0.65550
## Sagiproc 0.023144 0.020479 1.1301 1.8333 0.8 0.69629
## Trifprat 0.023080 0.023432 0.9850 0.0000 1.8 0.73697
## Juncarti 0.022850 0.025677 0.8899 0.5000 1.6 0.77724
## Trifrepe 0.022383 0.019487 1.1486 1.3333 2.8 0.81669
## Juncbufo 0.021643 0.022237 0.9733 1.1667 1.2 0.85484
## Scorautu 0.020509 0.016422 1.2489 1.3333 2.8 0.89099
## Achimill 0.015183 0.011393 1.3326 0.1667 1.2 0.91775
## Bromhord 0.013375 0.014504 0.9222 0.5000 0.8 0.94132
## Ranuflam 0.010661 0.013387 0.7964 0.6667 0.4 0.96011
## Bellpere 0.009991 0.012571 0.7948 0.6667 0.4 0.97772
## Callcusp 0.006623 0.015076 0.4393 0.5000 0.0 0.98939
## Cirsarve 0.003809 0.008669 0.4394 0.3333 0.0 0.99611
## Chenalbu 0.002208 0.005025 0.4393 0.1667 0.0 1.00000
## Airaprae 0.000000 0.000000 NaN 0.0000 0.0 1.00000
## Comapalu 0.000000 0.000000 NaN 0.0000 0.0 1.00000
## Empenigr 0.000000 0.000000 NaN 0.0000 0.0 1.00000
## Hyporadi 0.000000 0.000000 NaN 0.0000 0.0 1.00000
## Salirepe 0.000000 0.000000 NaN 0.0000 0.0 1.00000
## Vicilath 0.000000 0.000000 NaN 0.0000 0.0 1.00000
##
## Contrast: SF_NM
##
## average sd ratio ava avb cumsum
## Poatriv 0.078284 0.040947 1.9118 4.6667 0.0000 0.1014
## Alopgeni 0.071219 0.046958 1.5167 4.3333 0.0000 0.1936
## Agrostol 0.056508 0.044176 1.2792 4.6667 2.1667 0.2667
## Lolipere 0.054851 0.059914 0.9155 3.0000 0.3333 0.3378
## Eleopalu 0.048027 0.047168 1.0182 1.3333 2.1667 0.3999
## Poaprat 0.040724 0.031790 1.2810 2.5000 0.6667 0.4527
## Bracruta 0.040008 0.034398 1.1631 2.0000 2.8333 0.5045
## Elymrepe 0.035598 0.038515 0.9243 2.0000 0.0000 0.5506
## Scorautu 0.032475 0.034813 0.9328 1.3333 3.1667 0.5926
## Trifrepe 0.030430 0.031634 0.9619 1.3333 1.8333 0.6320
## Sagiproc 0.030304 0.030477 0.9943 1.8333 0.5000 0.6712
## Salirepe 0.029275 0.032014 0.9144 0.0000 1.8333 0.7092
## Anthodor 0.024541 0.036694 0.6688 0.0000 1.3333 0.7409
## Callcusp 0.022763 0.029443 0.7731 0.5000 1.1667 0.7704
## Ranuflam 0.022566 0.022819 0.9889 0.6667 1.3333 0.7996
## Juncarti 0.022543 0.028598 0.7883 0.5000 1.1667 0.8288
## Hyporadi 0.020108 0.031291 0.6426 0.0000 1.1667 0.8548
## Juncbufo 0.019860 0.029034 0.6840 1.1667 0.0000 0.8806
## Planlanc 0.015420 0.022769 0.6772 0.0000 0.8333 0.9005
## Airaprae 0.014883 0.021881 0.6802 0.0000 0.8333 0.9198
## Bellpere 0.012317 0.015921 0.7737 0.6667 0.3333 0.9357
## Comapalu 0.011883 0.017407 0.6826 0.0000 0.6667 0.9511
## Achimill 0.009294 0.014931 0.6224 0.1667 0.3333 0.9632
## Bromhord 0.007172 0.016333 0.4391 0.5000 0.0000 0.9724
## Rumeacet 0.005590 0.012751 0.4384 0.3333 0.0000 0.9797
## Empenigr 0.005225 0.012001 0.4354 0.0000 0.3333 0.9864
## Cirsarve 0.004782 0.010889 0.4391 0.3333 0.0000 0.9926
## Chenalbu 0.002893 0.006602 0.4382 0.1667 0.0000 0.9964
## Vicilath 0.002792 0.006425 0.4345 0.0000 0.1667 1.0000
## Trifprat 0.000000 0.000000 NaN 0.0000 0.0000 1.0000
##
## Contrast: BF_HF
##
## average sd ratio ava avb cumsum
## Rumeacet 0.038666 0.02606 1.4838 0.0000 3.2 0.08163
## Poatriv 0.033301 0.02579 1.2911 3.6667 4.8 0.15194
## Planlanc 0.031852 0.01830 1.7401 2.0000 3.0 0.21918
## Bromhord 0.028651 0.01799 1.5926 2.6667 0.8 0.27967
## Lolipere 0.028431 0.02215 1.2834 6.0000 4.0 0.33970
## Elymrepe 0.027822 0.02959 0.9404 1.3333 2.0 0.39843
## Trifrepe 0.025838 0.01656 1.5603 4.6667 2.8 0.45298
## Anthodor 0.023582 0.02042 1.1547 1.3333 1.8 0.50277
## Achimill 0.023426 0.01474 1.5893 2.3333 1.2 0.55223
## Bracruta 0.022733 0.01802 1.2617 2.0000 2.8 0.60022
## Alopgeni 0.021610 0.02308 0.9363 0.6667 1.6 0.64584
## Trifprat 0.021514 0.02207 0.9747 0.0000 1.8 0.69126
## Juncarti 0.020084 0.02555 0.7860 0.0000 1.6 0.73367
## Scorautu 0.019318 0.01356 1.4241 4.3333 2.8 0.77445
## Bellpere 0.018290 0.01486 1.2305 1.6667 0.4 0.81306
## Agrostol 0.017605 0.02284 0.7708 0.0000 1.4 0.85023
## Juncbufo 0.015000 0.02066 0.7260 0.0000 1.2 0.88190
## Vicilath 0.012848 0.01140 1.1274 1.0000 0.0 0.90903
## Sagiproc 0.011685 0.01297 0.9008 0.6667 0.8 0.93369
## Eleopalu 0.010169 0.02111 0.4817 0.0000 0.8 0.95516
## Hyporadi 0.008950 0.01312 0.6824 0.6667 0.0 0.97406
## Poaprat 0.007203 0.01010 0.7133 4.0000 3.4 0.98927
## Ranuflam 0.005084 0.01055 0.4817 0.0000 0.4 1.00000
## Airaprae 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Chenalbu 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Cirsarve 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Comapalu 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Empenigr 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Salirepe 0.000000 0.00000 NaN 0.0000 0.0 1.00000
## Callcusp 0.000000 0.00000 NaN 0.0000 0.0 1.00000
##
## Contrast: BF_NM
##
## average sd ratio ava avb cumsum
## Lolipere 0.090681 0.02644 3.4292 6.0000 0.3333 0.1243
## Poatriv 0.054684 0.04465 1.2248 3.6667 0.0000 0.1992
## Poaprat 0.052511 0.01813 2.8966 4.0000 0.6667 0.2712
## Trifrepe 0.051287 0.02756 1.8611 4.6667 1.8333 0.3415
## Bromhord 0.039689 0.02920 1.3590 2.6667 0.0000 0.3959
## Bracruta 0.035723 0.02869 1.2452 2.0000 2.8333 0.4448
## Eleopalu 0.033759 0.03573 0.9449 0.0000 2.1667 0.4911
## Agrostol 0.033446 0.03473 0.9630 0.0000 2.1667 0.5369
## Achimill 0.033190 0.02338 1.4198 2.3333 0.3333 0.5824
## Scorautu 0.031356 0.02026 1.5480 4.3333 3.1667 0.6254
## Anthodor 0.028060 0.03295 0.8517 1.3333 1.3333 0.6638
## Planlanc 0.027319 0.02193 1.2458 2.0000 0.8333 0.7013
## Salirepe 0.026770 0.02927 0.9145 0.0000 1.8333 0.7379
## Bellpere 0.023529 0.01909 1.2322 1.6667 0.3333 0.7702
## Hyporadi 0.021721 0.02450 0.8864 0.6667 1.1667 0.8000
## Ranuflam 0.020314 0.02275 0.8928 0.0000 1.3333 0.8278
## Elymrepe 0.019993 0.02926 0.6833 1.3333 0.0000 0.8552
## Callcusp 0.017833 0.02681 0.6653 0.0000 1.1667 0.8796
## Juncarti 0.017694 0.02600 0.6806 0.0000 1.1667 0.9039
## Vicilath 0.015773 0.01447 1.0902 1.0000 0.1667 0.9255
## Sagiproc 0.015432 0.01857 0.8310 0.6667 0.5000 0.9466
## Airaprae 0.013410 0.01969 0.6809 0.0000 0.8333 0.9650
## Comapalu 0.010739 0.01571 0.6835 0.0000 0.6667 0.9797
## Alopgeni 0.009997 0.01463 0.6833 0.6667 0.0000 0.9934
## Empenigr 0.004787 0.01105 0.4332 0.0000 0.3333 1.0000
## Chenalbu 0.000000 0.00000 NaN 0.0000 0.0000 1.0000
## Cirsarve 0.000000 0.00000 NaN 0.0000 0.0000 1.0000
## Juncbufo 0.000000 0.00000 NaN 0.0000 0.0000 1.0000
## Rumeacet 0.000000 0.00000 NaN 0.0000 0.0000 1.0000
## Trifprat 0.000000 0.00000 NaN 0.0000 0.0000 1.0000
##
## Contrast: HF_NM
##
## average sd ratio ava avb cumsum
## Poatriv 0.071553 0.013681 5.2302 4.8 0.0000 0.09913
## Lolipere 0.054533 0.029625 1.8408 4.0 0.3333 0.17468
## Rumeacet 0.046546 0.030806 1.5109 3.2 0.0000 0.23917
## Poaprat 0.041750 0.018852 2.2146 3.4 0.6667 0.29701
## Planlanc 0.041633 0.029560 1.4084 3.0 0.8333 0.35469
## Bracruta 0.035340 0.020104 1.7579 2.8 2.8333 0.40365
## Eleopalu 0.032043 0.032315 0.9916 0.8 2.1667 0.44805
## Agrostol 0.031915 0.028887 1.1048 1.4 2.1667 0.49227
## Trifrepe 0.030372 0.022871 1.3280 2.8 1.8333 0.53434
## Elymrepe 0.029811 0.038676 0.7708 2.0 0.0000 0.57565
## Anthodor 0.028717 0.024799 1.1580 1.8 1.3333 0.61543
## Juncarti 0.027414 0.028537 0.9607 1.6 1.1667 0.65341
## Trifprat 0.025843 0.025972 0.9951 1.8 0.0000 0.68922
## Salirepe 0.025340 0.027291 0.9285 0.0 1.8333 0.72432
## Alopgeni 0.024459 0.032399 0.7549 1.6 0.0000 0.75821
## Scorautu 0.020703 0.014125 1.4658 2.8 3.1667 0.78689
## Ranuflam 0.019285 0.019939 0.9672 0.4 1.3333 0.81361
## Juncbufo 0.018181 0.024648 0.7376 1.2 0.0000 0.83880
## Hyporadi 0.017141 0.026548 0.6457 0.0 1.1667 0.86255
## Callcusp 0.016833 0.024901 0.6760 0.0 1.1667 0.88587
## Achimill 0.016555 0.014900 1.1111 1.2 0.3333 0.90881
## Sagiproc 0.015282 0.016535 0.9243 0.8 0.5000 0.92998
## Airaprae 0.012605 0.018243 0.6910 0.0 0.8333 0.94744
## Bromhord 0.012094 0.015169 0.7973 0.8 0.0000 0.96420
## Comapalu 0.010105 0.014556 0.6942 0.0 0.6667 0.97820
## Bellpere 0.008801 0.013732 0.6409 0.4 0.3333 0.99039
## Empenigr 0.004536 0.010325 0.4393 0.0 0.3333 0.99668
## Vicilath 0.002399 0.005461 0.4393 0.0 0.1667 1.00000
## Chenalbu 0.000000 0.000000 NaN 0.0 0.0000 1.00000
## Cirsarve 0.000000 0.000000 NaN 0.0 0.0000 1.00000
## Permutation: free
## Number of permutations: 0