Ecologia Numérica

Aula 5 - Análises de correspondência e canônica (CA & CCA)

.pull-left[ # O que precisamos saber?
###- Uma CA é um método similar aos PCA, mas… (distância de chi-quadrado)
###- Tem bom desempenho com matrizes com muitos zeros (presença e ausência de espécies)
###- É um método para reduzir a multi-dimensionalidade dos dados
###- Busca relações unimodais ]
.pull-right[
]

Análises de correspondência - CA

.left-column[ # São uma família de análises multivaridas que procuram por relações não lineares]

.rigth-column[]

# CAs são úteis para entender distribuição de espécies em gradientes
.panelset[ .panel[.panel-name[Tabela de contingência]
]
.panel[.panel-name[Chi-quadrado]
r chisq <- chisq.test(spe[-8,])
## Warning in chisq.test(spe[-8, ]): Chi-squared approximation may be incorrect
r chisq
## ## Pearson's Chi-squared test ## ## data: spe[-8, ] ## X-squared = 1171.6, df = 728, p-value < 2.2e-16
] .panel[.panel-name[Autovetores]
## eigenvalue variance.percent cumulative.variance.percent ## Dim.1 6.009926e-01 51.502740611 51.50274 ## Dim.2 1.443709e-01 12.372025791 63.87477 ## Dim.3 1.072938e-01 9.194666172 73.06943 ## Dim.4 8.337321e-02 7.144760737 80.21419 ## Dim.5 5.157826e-02 4.420056824 84.63425 ## Dim.6 4.184649e-02 3.586082405 88.22033 ## Dim.7 3.388638e-02 2.903931729 91.12426 ## Dim.8 2.882547e-02 2.470231250 93.59450 ## Dim.9 1.684112e-02 1.443218695 95.03771 ## Dim.10 1.082639e-02 0.927779708 95.96549 ## Dim.11 1.014213e-02 0.869141057 96.83463 ## Dim.12 7.885549e-03 0.675760978 97.51040 ## Dim.13 6.123133e-03 0.524728790 98.03512 ## Dim.14 4.867260e-03 0.417105325 98.45223 ## Dim.15 4.606481e-03 0.394757532 98.84699 ## Dim.16 3.843808e-03 0.329399420 99.17639 ## Dim.17 3.067492e-03 0.262872192 99.43926 ## Dim.18 1.823032e-03 0.156226746 99.59549 ## Dim.19 1.641868e-03 0.140701719 99.73619 ## Dim.20 1.295163e-03 0.110990456 99.84718 ## Dim.21 8.775034e-04 0.075198638 99.92238 ## Dim.22 4.217149e-04 0.036139335 99.95852 ## Dim.23 2.148505e-04 0.018411852 99.97693 ## Dim.24 1.527935e-04 0.013093815 99.99002 ## Dim.25 8.948679e-05 0.007668671 99.99769 ## Dim.26 2.695049e-05 0.002309553 100.00000 ] .panel[.panel-name[Plot para Variáveis]
## corrplot 0.90 loaded
] ]

class: middle, center

Quais as Diferenças entre CAs e PCAs?

# O princípio das CCAs .center[ ]
## Examinando o CCA .panelset[ .panel[.panel-name[Resultado do CCA]
## ## Call: ## cca(X = spe[-8, ], Y = env2[-8, ]) ## ## Partitioning of scaled Chi-square: ## Inertia Proportion ## Total 1.1669 1.0000 ## Constrained 0.8119 0.6957 ## Unconstrained 0.3550 0.3043 ## ## Eigenvalues, and their contribution to the scaled Chi-square ## ## Importance of components: ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7 ## Eigenvalue 0.5238 0.1174 0.06467 0.04353 0.02766 0.01304 0.010291 ## Proportion Explained 0.4489 0.1006 0.05542 0.03730 0.02370 0.01118 0.008819 ## Cumulative Proportion 0.4489 0.5495 0.60489 0.64219 0.66590 0.67708 0.685894 ## CCA8 CCA9 CCA10 CA1 CA2 CA3 ## Eigenvalue 0.006444 0.003301 0.001739 0.11112 0.06492 0.05298 ## Proportion Explained 0.005523 0.002828 0.001491 0.09522 0.05563 0.04541 ## Cumulative Proportion 0.691417 0.694245 0.695736 0.79096 0.84659 0.89200 ## CA4 CA5 CA6 CA7 CA8 CA9 ## Eigenvalue 0.03283 0.02666 0.01846 0.009778 0.008924 0.007580 ## Proportion Explained 0.02813 0.02284 0.01582 0.008379 0.007648 0.006496 ## Cumulative Proportion 0.92013 0.94297 0.95880 0.967177 0.974824 0.981321 ## CA10 CA11 CA12 CA13 CA14 CA15 ## Eigenvalue 0.006050 0.004378 0.003488 0.003046 0.002280 0.001718 ## Proportion Explained 0.005184 0.003752 0.002989 0.002610 0.001954 0.001472 ## Cumulative Proportion 0.986505 0.990257 0.993246 0.995856 0.997810 0.999282 ## CA16 CA17 CA18 ## Eigenvalue 0.0004838 0.0003296 2.431e-05 ## Proportion Explained 0.0004146 0.0002824 2.084e-05 ## Cumulative Proportion 0.9996967 0.9999792 1.000e+00 ## ## Accumulated constrained eigenvalues ## Importance of components: ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7 ## Eigenvalue 0.5238 0.1174 0.06467 0.04353 0.02766 0.01304 0.01029 ## Proportion Explained 0.6452 0.1446 0.07966 0.05362 0.03407 0.01606 0.01268 ## Cumulative Proportion 0.6452 0.7898 0.86943 0.92304 0.95712 0.97318 0.98585 ## CCA8 CCA9 CCA10 ## Eigenvalue 0.006444 0.003301 0.001739 ## Proportion Explained 0.007938 0.004065 0.002143 ## Cumulative Proportion 0.993792 0.997857 1.000000 ## ## Scaling 2 for species and site scores ## * Species are scaled proportional to eigenvalues ## * Sites are unscaled: weighted dispersion equal on all dimensions ## ## ## Species scores ## ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 ## Cogo 1.22828 1.342555 -0.10906 -0.100159 0.18534 -0.074317 ## Satr 1.52022 -0.421716 0.32612 -0.478415 -0.13070 -0.152732 ## Phph 1.20045 -0.161518 -0.02017 0.142390 0.01173 0.175138 ## Babl 0.97743 -0.255475 -0.05499 0.221357 -0.02155 0.075746 ## Thth 1.29443 1.453249 -0.05728 -0.279764 0.33355 0.254947 ## Teso 0.85559 1.127382 -0.06573 0.084079 0.08054 -0.245575 ## Chna -0.46100 0.183183 -0.06858 0.060764 -0.35952 -0.046001 ## Pato -0.14056 0.342522 0.05341 0.360135 -0.47087 -0.060211 ## Lele 0.09107 -0.053870 -0.19916 0.110481 0.05680 -0.179387 ## Sqce 0.01177 -0.117150 -0.36500 0.059876 0.19580 -0.149331 ## Baba -0.31689 0.259956 0.14240 0.117877 -0.24005 -0.063566 ## Albi -0.32755 0.229336 0.23308 0.157160 -0.22305 0.179066 ## Gogo -0.26665 0.018880 -0.11623 -0.061712 -0.12414 0.002118 ## Eslu -0.18252 -0.277660 -0.03434 0.037586 0.14606 0.137742 ## Pefl -0.12659 -0.176025 0.03020 0.252790 0.12590 0.023888 ## Rham -0.57446 0.084305 0.32200 0.053609 -0.08985 0.057710 ## Legi -0.62007 0.065743 0.18508 0.005399 -0.02495 0.013164 ## Scer -0.52162 -0.148838 -0.01142 -0.153528 0.19238 0.076606 ## Cyca -0.58647 0.108430 0.36280 0.023499 0.08189 -0.068617 ## Titi -0.29270 -0.189259 0.04018 0.161322 0.04980 -0.067383 ## Abbr -0.70893 0.019004 0.36327 -0.067807 0.09745 -0.036085 ## Icme -0.79079 -0.011847 0.59621 -0.187170 0.44436 0.105730 ## Gyce -0.76105 -0.041287 -0.01602 -0.210332 0.04596 0.003539 ## Ruru -0.35856 -0.190255 -0.33418 0.087879 0.09814 -0.064540 ## Blbj -0.74241 0.004951 0.25289 -0.085053 0.07711 -0.086048 ## Alal -0.64710 0.040949 -0.51840 -0.445714 -0.18001 0.136457 ## Anan -0.65036 0.038946 0.37834 -0.017452 0.06610 0.067195 ## ## ## Site scores (weighted averages of species scores) ## ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 ## 1 2.90231 -3.59248 5.04291 -10.99019 -4.7248 -11.71188 ## 2 2.43975 -2.49959 1.78469 -2.21766 -2.0220 1.04881 ## 3 2.18453 -2.38056 1.17956 -0.76922 -1.2574 3.01218 ## 4 1.43681 -2.01477 0.35299 0.70591 0.1610 2.74653 ## 5 0.20167 -1.48734 -1.39453 1.51318 2.4144 -1.22925 ## 6 1.16771 -1.81747 -0.50115 1.21480 0.5871 0.39246 ## 7 2.07534 -2.23779 0.68700 -0.78303 -1.0432 -0.06277 ## 9 0.33610 -1.49928 -3.65227 2.65603 3.5337 -3.66883 ## 10 1.38696 -1.46817 -1.34646 2.06022 0.5451 1.07074 ## 11 2.23445 0.39648 0.43772 -2.01398 1.1436 2.43572 ## 12 2.26655 0.80356 0.54321 -2.08926 1.0862 1.92474 ## 13 2.37228 2.63296 0.73116 -2.54974 1.7019 1.56827 ## 14 1.92196 2.78951 0.10116 -1.48364 1.8443 1.10118 ## 15 1.40666 1.98480 -0.63527 0.01651 1.1403 -3.26118 ## 16 0.76550 1.33943 -0.34052 1.87765 -1.2416 -4.47936 ## 17 0.32806 0.88913 -0.09699 1.67765 -2.2357 0.21434 ## 18 0.07578 0.72095 -0.25536 1.48245 -1.6099 0.49089 ## 19 -0.18799 0.02658 -0.62065 1.35897 -2.0108 0.52679 ## 20 -0.59914 -0.07126 -0.46679 0.47383 -1.3946 0.31426 ## 21 -0.71162 -0.09092 0.07444 0.12993 -0.6527 0.21050 ## 22 -0.76850 -0.07165 0.21576 0.06105 -0.1062 -0.86912 ## 23 -0.78322 -0.48026 -6.71095 -4.27093 -0.5972 1.13190 ## 24 -0.95982 -0.12488 -3.88562 -3.72811 -1.5708 0.74052 ## 25 -0.72816 -0.51767 -3.86269 -3.19230 -0.1748 1.66079 ## 26 -0.83048 -0.23803 -0.30332 -0.92216 0.1731 0.51909 ## 27 -0.82212 -0.18147 0.29192 -0.40338 0.3721 -0.21440 ## 28 -0.85978 -0.14338 0.69694 -0.47506 0.9519 -0.23143 ## 29 -0.66734 0.15806 0.81062 -0.17811 0.4473 0.40004 ## 30 -0.87414 -0.08059 1.23436 -0.16784 1.0382 0.77144 ## ## ## Site constraints (linear combinations of constraining variables) ## ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 ## 1 3.58349 -4.69241 5.163034 -10.460392 -4.2174 -8.3382 ## 2 1.17112 -3.52071 0.990473 0.626423 -1.9289 1.7325 ## 3 1.79427 -2.22123 0.885357 -0.722446 -0.1247 1.2824 ## 4 1.68327 -1.52358 0.015228 1.484626 0.1233 0.1003 ## 5 0.82882 -1.73051 -1.628064 0.694959 2.0643 -0.4130 ## 6 1.84781 -1.63584 0.226144 -0.274405 -0.1881 2.1801 ## 7 2.05060 -0.73235 -0.279140 0.359418 1.3796 -1.2164 ## 9 0.02952 -1.80313 -1.786407 2.216371 2.1408 -1.5175 ## 10 1.06995 -1.04385 0.003823 -0.562023 -0.6249 -1.3263 ## 11 1.55367 1.02910 0.286770 0.003986 0.5823 -0.4513 ## 12 1.47097 1.04413 -0.163614 -0.053012 -0.6944 1.1969 ## 13 1.56138 1.74457 -0.476732 -0.116590 0.3382 -0.1656 ## 14 1.95600 2.32296 -0.102909 -0.851082 1.0895 0.5512 ## 15 1.30132 1.49028 0.291083 -0.643518 0.6949 -0.9058 ## 16 0.30360 0.47553 -0.284330 1.131299 -0.5654 -1.0797 ## 17 0.28929 0.70902 -0.267014 0.176291 -0.4042 0.8460 ## 18 0.13731 0.43204 -0.370799 0.877752 -0.9081 -0.3490 ## 19 0.44286 0.73917 0.096677 0.178506 -1.0103 0.2019 ## 20 -0.25350 0.16247 0.023660 0.602872 -1.7329 0.2290 ## 21 -0.66014 -0.09817 -0.086573 0.817861 -1.1078 -0.4347 ## 22 -0.44750 0.46080 -0.330861 -0.129368 -0.3505 -1.0452 ## 23 -0.04201 1.04957 -4.149278 -4.927474 -0.1723 1.9115 ## 24 -1.34040 -0.07807 -3.032487 -1.554081 0.8112 -0.4967 ## 25 -1.01887 -0.85119 -4.848035 -3.778175 -1.4930 2.3199 ## 26 -0.89500 -0.33984 -0.703386 -0.241858 0.3915 0.1520 ## 27 -1.27686 -0.57971 0.131121 -0.310433 -0.1965 -0.4644 ## 28 -0.85592 0.07735 0.636200 0.193984 0.4874 -0.4986 ## 29 -0.61651 0.03421 1.078781 -0.107326 0.3596 1.4882 ## 30 -0.83933 0.01874 1.139485 -0.643621 1.3816 0.1496 ## ## ## Biplot scores for constraining variables ## ## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 ## ele 0.8049 -0.53385 -0.1640 0.1433 0.09700 -0.031190 ## slo 0.4534 -0.40316 0.2016 -0.4500 -0.20564 -0.472915 ## dis -0.6962 0.23321 0.4344 -0.2407 0.26281 0.274195 ## pH 0.1538 0.28892 0.1238 -0.1355 0.37016 -0.300204 ## har -0.5533 0.49784 0.1044 -0.1189 0.46852 0.104247 ## pho -0.4297 -0.03666 -0.5085 -0.4939 0.06424 0.225592 ## nit -0.6912 0.18509 -0.2099 -0.1266 -0.28415 0.001309 ## amm -0.4139 -0.11510 -0.6225 -0.3978 -0.17178 0.209148 ## oxy 0.7861 0.38111 0.3241 0.2001 -0.24654 -0.013469 ## bod -0.4582 -0.18403 -0.6361 -0.4922 0.14534 0.167807 ]
.panel[.panel-name[PLOT CCA]
] .panel[.panel-name[Resultado CA + Envfit]
## ## ***VECTORS ## ## CA1 CA2 r2 Pr(>r) ## ele 0.81159 0.58423 0.8078 0.001 *** ## slo 0.73753 0.67531 0.2976 0.006 ** ## dis -0.92837 -0.37166 0.4440 0.002 ** ## pH 0.50723 -0.86181 0.0908 0.248 ## har -0.71728 -0.69678 0.4722 0.004 ** ## pho -0.99897 0.04533 0.1757 0.070 . ## nit -0.94906 -0.31511 0.4510 0.001 *** ## amm -0.97495 0.22241 0.1762 0.068 . ## oxy 0.93352 -0.35854 0.6263 0.001 *** ## bod -0.94094 0.33857 0.2237 0.032 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## Permutation: free ## Number of permutations: 999 ] .panel[.panel-name[PLOt CA + Envfit]
]]

class: center, middle # Dúvidas

Felipe P.L. Melo
Felipe P.L. Melo
Associate Professor in Applied Ecology

Biologist and eco-socialist. Another world is possible!