Resumen de métodos multivariados
- Clasificación de técnicas
- Ordenación sin restricción:
- Análisis aglomerativo (cluster):
- Discriminación:
- Ordenación con restricción;
- Escalamiento multidimensional o Análisis de Coordenadas Principales.
- Análisis de correspondencia (CA).
- Análisis de correspondencia sin tendencia DCA.
- Análisis de redundancia
- Análisis de correspondencia canónico
La clave del uso de los métodos multivariados está en:
- El tipo de problema para el cuál el método está propuesto.
- El objetivo de cada técnica.
- La estructura de datos requerida para utilizar cada técnica.
- El muestreo realizado para cada técnica.
- Entender el concepto subyacentes a cada técnica.
Clasificación de técnicas
- Modelo: \[ y_1 + y_2 + \cdots + y_i \]
- Técnicas:
- Ordenación no restringida.
- Análisis aglomerativo (cluter analisis).
- Modelo: \[
y_1 + y_2 + \cdots + y_i = x
\]
- Técnicas:
- Anova multivariado (MANOVA).
- Prueba de Mantel.
- Análisis discriminante.
- Regresión logística.
- Árboles de clasifiación.
- Modelo: \[ y_1 + y_2 + \cdots + y_i = x_1 + x_2 + \cdots + x_j \]
- Técnicas:
- Ordenación con restricción.
- Correlación Canónico.
- Árboles de regresión multivariados.
Ordenación sin restricción:
- PCA (Componentes principales)
- MDS o PCoA (Escalamiento multidimensional métrico)
- CA (Análsis de correspondencia)
- DCA (Análisis de correspondencia segmentado o análisis de correspodencia sin tendencia)
- NMDS (Escalamiento multidimensional no-métrico)
Objetivo: Estraer gradientes de máxima variación.
Análisis aglomerativo (cluster):
- Varias ténicas, jerárquicas, divisivas, etc.
Objetivo: Establecer grupos de entes similares.
Discriminación:
- MANOVA (Anova multivariado)
- ANOSIM (Análisis de similitud)
- Mantel (Prueba de Mantel)
- LR (Regresión logística)
- DA (Análisis discriminante)
Objetivo: Prueba para diferenciar entre grupos de entidades y predecir la pertenencia a un grupo.
Ordenación con restricción;
- RDA (Análisis de redundancia)
- CCA (Análisis de correspondencia canónico)
Objetivo: Extraer gradientes de variación en variables dependientes explicadas por variables independientes.
Escalamiento multidimensional o Análisis de Coordenadas Principales.
MDS o PCoA
peces <- read.csv2("peces.csv", row.names = 1)
sumEsp <- apply(peces,1,sum)
peces <- peces[sumEsp!=0,]
require(vegan)
peces.perfil <- decostand(peces, method = "total")
mat_dist <- dist(peces.perfil, method = "manhattan")
print(mat_dist) 1 2 3 4 5 6 7 9 10 11
2 1.1666667
3 1.3750000 0.2500000
4 1.6190476 0.6666667 0.5416667
5 1.8823529 1.5882353 1.4632353 0.9215686
6 1.7142857 0.8571429 0.7619048 0.3809524 0.8179272
7 1.3750000 0.3750000 0.2500000 0.5714286 1.3455882 0.6369048
9 2.0000000 1.4285714 1.4285714 1.2380952 1.1848739 1.0000000 1.3035714
10 1.8571429 0.7857143 0.7142857 0.7142857 1.0672269 0.6190476 0.5357143 1.1428571
11 1.4545455 0.6060606 0.6477273 0.8658009 1.4705882 0.9696970 0.6477273 1.4935065 0.9220779
12 1.4444444 0.5555556 0.5555556 0.6349206 1.4771242 0.7777778 0.4444444 1.3174603 0.8571429 0.3535354
13 1.4736842 0.7368421 0.7368421 0.9323308 1.5882353 1.1228070 0.7631579 1.6466165 1.1203008 0.4019139
14 1.6428571 1.0000000 0.9285714 0.7857143 1.3739496 0.8571429 0.9285714 1.5000000 1.0714286 0.6688312
15 1.7575758 1.2121212 1.2121212 0.9610390 1.1105169 0.7792208 0.9621212 1.3116883 0.8268398 0.8484848
16 1.8500000 1.4500000 1.4000000 1.1095238 0.9647059 0.9595238 1.2250000 1.4071429 1.0071429 1.3181818
17 1.9090909 1.5454545 1.5000000 1.2272727 1.0695187 1.0411255 1.3295455 1.4480519 1.2727273 1.3636364
18 1.9523810 1.6666667 1.6190476 1.2380952 1.0504202 1.0476190 1.4464286 1.4285714 1.3333333 1.4285714
19 2.0000000 1.6521739 1.6086957 1.3395445 1.0690537 1.1573499 1.5217391 1.3043478 1.3788820 1.6442688
20 2.0000000 1.8928571 1.8214286 1.4642857 1.0609244 1.2380952 1.7142857 1.4642857 1.5714286 1.7857143
21 2.0000000 1.9354839 1.8387097 1.4869432 1.1404175 1.2964670 1.8064516 1.5806452 1.6635945 1.8709677
22 2.0000000 1.9722222 1.8888889 1.4920635 1.1601307 1.2976190 1.7777778 1.6111111 1.6388889 1.8611111
23 2.0000000 2.0000000 2.0000000 1.9047619 1.5882353 1.7142857 1.8750000 1.0000000 1.7142857 1.8181818
24 2.0000000 2.0000000 2.0000000 1.8095238 1.4980392 1.6190476 1.8750000 1.4666667 1.6000000 1.8181818
25 2.0000000 2.0000000 1.8750000 1.6277056 1.1016043 1.4372294 1.7500000 1.6363636 1.4935065 1.8181818
26 2.0000000 1.9534884 1.8604651 1.5304540 1.1846785 1.3444075 1.8139535 1.5348837 1.6744186 1.8604651
27 2.0000000 1.9682540 1.8432540 1.5238095 1.1839402 1.3333333 1.8095238 1.5714286 1.6825397 1.8730159
28 2.0000000 1.9714286 1.8857143 1.5428571 1.2285714 1.3523810 1.8000000 1.6000000 1.6857143 1.8571429
29 1.9770115 1.9310345 1.8160920 1.4679803 1.2183908 1.3234811 1.7701149 1.6781609 1.6551724 1.8160920
30 2.0000000 2.0000000 1.9101124 1.5398609 1.2134831 1.3772071 1.8651685 1.7078652 1.7528090 1.9325843
12 13 14 15 16 17 18 19 20 21
2
3
4
5
6
7
9
10
11
12
13 0.3859649
14 0.4920635 0.3684211
15 0.7979798 0.7910686 0.4978355
16 1.2500000 1.1789474 0.8714286 0.5757576
17 1.3636364 1.3636364 1.1298701 0.9242424 0.5545455
18 1.4603175 1.5238095 1.2619048 1.0216450 0.6976190 0.2835498
19 1.6086957 1.6155606 1.3788820 1.2094862 0.8369565 0.6284585 0.5196687
20 1.7857143 1.8928571 1.6071429 1.4112554 1.1142857 0.8084416 0.6190476 0.4596273
21 1.8709677 1.9354839 1.6566820 1.5034213 1.1919355 0.9120235 0.7373272 0.5287518 0.2419355
22 1.8611111 1.9722222 1.6865079 1.4747475 1.2055556 0.9419192 0.7420635 0.6219807 0.3492063 0.2123656
23 1.8888889 2.0000000 1.9285714 1.8181818 1.8500000 1.7272727 1.6666667 1.6086957 1.5357143 1.6129032
24 1.8888889 2.0000000 1.8571429 1.6969697 1.7000000 1.5909091 1.4285714 1.2579710 1.1166667 1.1569892
25 1.8888889 2.0000000 1.7857143 1.5151515 1.5181818 1.5000000 1.3809524 1.2529644 1.1071429 1.1290323
26 1.8604651 1.9534884 1.6677741 1.5391121 1.2813953 1.0845666 0.9180509 0.6622851 0.3770764 0.3098275
27 1.8730159 1.9682540 1.6825397 1.5064935 1.2642857 1.0598846 0.8888889 0.7211870 0.4126984 0.2754736
28 1.8603175 1.9714286 1.6857143 1.5393939 1.2714286 1.0948052 0.9047619 0.7465839 0.4714286 0.3622120
29 1.8160920 1.8850575 1.5993432 1.4336468 1.1511494 0.8589342 0.6896552 0.6786607 0.4503284 0.3018168
30 1.9325843 2.0000000 1.7223114 1.6247872 1.3028090 1.0270684 0.8389513 0.7650220 0.4991974 0.3581008
22 23 24 25 26 27 28 29
2
3
4
5
6
7
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23 1.6111111
24 1.0888889 0.8000000
25 1.1388889 1.0909091 0.7757576
26 0.3488372 1.4883721 0.9364341 0.9852008
27 0.2738095 1.5873016 1.0476190 1.0793651 0.2148394
28 0.2650794 1.6000000 1.0666667 1.1428571 0.3023256 0.2158730
29 0.3045977 1.6781609 1.1954023 1.2183908 0.3838546 0.3108922 0.2866995
30 0.3258427 1.7078652 1.2808989 1.2134831 0.4724327 0.4080614 0.2783307 0.2985923mds <- cmdscale(mat_dist)
row.names(peces.perfil) [1] "1" "2" "3" "4" "5" "6" "7" "9" "10" "11" "12" "13" "14" "15" "16" "17" "18" "19" "20" "21"
[21] "22" "23" "24" "25" "26" "27" "28" "29" "30"plot(mds, type = "n")
abline(h = 0, col = "red", lty = 2)abline(v = 0, col = "red", lty = 2)
text(mds[,1], mds[,2], labels = row.names(peces.perfil))
nMDS
peces <- read.csv2("peces.csv", row.names = 1)
sumEsp <- apply(peces,1,sum)
peces <- peces[sumEsp!=0,]
require(vegan)
peces.perfil <- decostand(peces, method = "normalize")
mat_dist <- dist(peces.perfil, method = "minkowski", p = 1/3)
print(mat_dist) 1 2 3 4 5 6 7 9
2 11.277923
3 24.396166 5.144579
4 136.642143 63.686838 37.578332
5 417.235145 407.424089 399.973315 280.309993
6 247.254359 161.500267 115.361353 86.481289 241.094158
7 37.762409 14.779360 16.809063 73.208578 368.626035 89.704459
9 90.426484 67.431567 113.292446 186.553314 315.040862 220.402706 109.784208
10 93.355680 48.971249 56.030138 103.771646 276.310942 104.889295 32.130348 139.251561
11 61.628072 40.165985 52.069600 166.197245 453.767565 291.576364 54.400825 171.804575
12 66.794399 27.782106 41.068761 128.691115 599.641426 245.147683 20.986309 157.816810
13 71.338729 36.129811 49.423584 229.104362 747.278948 421.161832 83.211561 255.316235
14 241.342063 144.495084 135.810470 210.193947 826.854341 364.390230 165.039463 406.539486
15 375.997453 273.111645 340.466297 360.411886 672.488199 339.970461 243.433876 404.046438
16 957.352022 782.124391 801.331881 729.080071 740.858338 643.231159 767.916493 848.140607
17 1951.222791 1678.330758 1665.840804 1430.509736 1613.933936 1342.135864 1598.472950 1703.861281
18 2375.530339 2193.158505 2118.844807 1867.572443 1914.750778 1701.589150 2094.174844 1975.157279
19 2419.703575 2117.992654 2140.778037 2054.771834 1808.874098 1865.716656 2055.158998 1608.167657
20 2434.966881 2640.526730 2553.932847 2330.808533 1687.229611 1825.162319 2458.542666 1909.032506
21 2710.097683 3051.214855 2986.011752 2390.560100 1999.304652 2331.557239 2756.584351 2337.157360
22 2529.499546 3152.489528 3070.509221 2577.486485 2159.175474 2199.134109 2973.872358 2406.729633
23 39.943048 116.763599 157.179982 337.250832 452.070003 364.326638 149.685491 59.395393
24 228.146659 435.480428 529.248915 719.087687 924.968689 729.331640 508.434569 326.172789
25 253.304115 473.929078 455.375467 542.838067 465.386260 512.003484 427.684828 396.499614
26 2058.868823 2558.899428 2491.818032 2257.399191 1731.245449 1917.530141 2396.585202 1911.619214
27 2310.209913 2889.138056 2841.199118 2569.463347 2111.714635 2198.957681 2639.285418 2218.958613
28 2426.102351 3031.816653 2952.797510 2652.592737 2216.934108 1889.367550 2737.493297 2303.387043
29 3263.562622 3712.188183 3652.449535 2956.391564 2694.604200 2916.497120 3474.277269 3088.617232
30 2366.694410 3239.023848 3159.089024 2563.939895 2227.772163 2386.745644 2954.104971 2613.002595
10 11 12 13 14 15 16 17
2
3
4
5
6
7
9
10
11 113.753118
12 111.154597 23.757193
13 176.276092 37.615994 32.235014
14 267.612395 139.764695 80.799805 86.295463
15 180.643392 212.758253 178.152540 233.175051 183.902116
16 661.944231 868.619474 873.301097 969.256635 713.019154 472.250730
17 1412.164358 1545.655482 1668.098939 1747.594700 1348.107522 1094.633962 729.431647
18 1653.031658 2099.272982 2178.916458 2267.347830 1995.407457 1543.551422 1183.937262 494.192271
19 2100.226025 2996.098518 2735.483427 3082.163619 2547.541233 2404.543699 1158.739211 1400.143340
20 2354.260940 2981.463451 3311.117757 3741.604809 3574.304481 3248.758604 2440.503256 2011.910391
21 2877.428664 3563.274931 3696.238907 4297.580732 4064.564324 3910.677396 2919.518078 2420.396457
22 2749.076457 3626.530835 3907.334567 4426.975545 4230.411376 3732.859735 3055.670132 2638.432509
23 174.811895 187.395179 217.957196 296.101117 533.024352 637.635882 1268.562117 1948.783957
24 355.923898 587.244517 656.107977 819.316114 1052.693680 1117.807147 1754.855708 2363.787254
25 358.281757 615.720449 698.378486 877.597546 968.098052 978.879215 1565.323396 2291.021824
26 2395.029837 2810.100412 3193.136290 3666.623999 3450.492473 3145.389274 2453.890904 2438.887728
27 2630.902337 3261.672779 3581.951639 4094.028693 3906.411636 3592.581287 2823.413024 2720.041560
28 2696.910263 3495.450125 3768.668490 4275.291836 4037.593811 3496.022827 2942.247608 3069.871215
29 3306.028767 3866.723252 4190.041392 4410.850458 4219.422939 3732.366137 3257.639483 2356.709442
30 2996.818287 3774.441134 3925.458459 4552.268870 4221.941442 4051.938534 3134.685702 2861.449320
18 19 20 21 22 23 24 25
2
3
4
5
6
7
9
10
11
12
13
14
15
16
17
18
19 1208.800093
20 1557.358769 863.968142
21 2044.299574 1053.711148 424.484807
22 1989.806154 1231.218575 611.498595 454.534902
23 2140.073653 1907.754175 1733.849475 2099.047866 1938.388215
24 2044.335085 1800.396503 1225.315366 1576.408281 1315.445173 67.771831
25 2147.829189 1837.101027 1372.746876 1553.554374 1364.813165 114.160032 203.733414
26 2396.240349 1138.990921 711.510651 587.826658 551.250198 1440.243385 1052.375778 1241.769487
27 2380.288031 1478.898975 836.685595 531.441812 446.314934 1751.564182 1269.053833 1415.740838
28 2589.102320 1566.740296 935.246765 750.070052 315.691188 1846.607655 1282.019979 1454.256036
29 1942.429106 1572.161363 1157.365497 698.737222 773.986237 2898.966461 2208.232157 2136.578940
30 2339.574321 1622.441593 939.264761 683.681526 489.065599 1976.685623 1516.951374 1284.534819
26 27 28 29
2
3
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5
6
7
9
10
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12
13
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25
26
27 372.331702
28 452.803346 341.753748
29 1062.206121 698.068939 789.558094
30 825.847492 706.563907 383.698694 808.054338require(MASS)
nMDS <- isoMDS(mat_dist)initial value 14.528956
final value 14.528914
convergedplot(nMDS$points[,1], nMDS$points[,2], type = "n")
abline(h = 0, col = "red", lty = 2)abline(v = 0, col = "red", lty = 2)
text(nMDS$points[,1], nMDS$points[,2], labels = row.names(peces.perfil))
Análisis de correspondencia (CA).
- MDS: Escalamiento multidmensional.
- PCoA: Análisis de coordenadas principales,
- CCA: Análisis de correspondencia canónico.
- CVA: Análisis de variable canónico.
- ANOSIM: Análisis de similitud.
t1 <- read.csv2("tablaCont.csv", row.names = 1)
t1margin.table(as.matrix(t1), 1)Bacter Microb Plant Fung Fish Bird Insect
1144 179 3334 563 1466 429 637 margin.table(as.matrix(t1), 2)Cluster PCA MDS PCoA CCA RDA MANOVA Mantel ANOSIM CVA
3246 2277 432 82 968 247 169 170 75 86 chi1 <- chisq.test(t1)Chi-squared approximation may be incorrectprint(chi1)
Pearson's Chi-squared test
data: t1
X-squared = 578.16, df = 54, p-value < 2.2e-16print(chi1$observed) Cluster PCA MDS PCoA CCA RDA MANOVA Mantel ANOSIM CVA
Bacter 553 434 51 5 37 21 15 5 10 13
Microb 82 72 7 2 4 4 2 3 1 2
Plant 1344 950 153 57 517 123 63 77 20 30
Fung 304 153 16 6 48 16 5 6 1 8
Fish 441 493 143 4 198 40 53 42 34 18
Bird 176 88 23 3 91 15 9 18 2 4
Insect 346 87 39 5 73 28 22 19 7 11print(chi1$expected) Cluster PCA MDS PCoA CCA RDA MANOVA Mantel ANOSIM
Bacter 479.02786 336.02786 63.752322 12.101135 142.85243 36.450980 24.940144 25.087719 11.068111
Microb 74.95279 52.57779 9.975232 1.893447 22.35191 5.703431 3.902348 3.925439 1.731811
Plant 1396.04799 979.29799 185.795666 35.266770 416.31992 106.230392 72.683953 73.114035 32.256192
Fung 235.74536 165.37036 31.374613 5.955366 70.30237 17.938725 12.273865 12.346491 5.446981
Fish 613.85913 430.60913 81.696594 15.507224 183.06089 46.710784 31.960010 32.149123 14.183437
Bird 179.63545 126.01045 23.907121 4.537926 53.56966 13.669118 9.352554 9.407895 4.150542
Insect 266.73142 187.10642 35.498452 6.738132 79.54283 20.296569 13.887126 13.969298 6.162926
CVA
Bacter 12.691434
Microb 1.985810
Plant 36.987100
Fung 6.245872
Fish 16.263674
Bird 4.759288
Insect 7.066821require(ca)
ca_t1 <- ca(t1)
ca_t1
Principal inertias (eigenvalues):
1 2 3 4 5 6
Value 0.035233 0.026746 0.011064 0.001164 0.000318 5.6e-05
Percentage 47.24% 35.86% 14.83% 1.56% 0.43% 0.08%
Rows:
Bacter Microb Plant Fung Fish Bird Insect
Mass 0.147575 0.023091 0.430083 0.072626 0.189112 0.055341 0.082172
ChiDist 0.364326 0.379370 0.130142 0.289552 0.329517 0.332658 0.376355
Inertia 0.019588 0.003323 0.007284 0.006089 0.020534 0.006124 0.011639
Dim. 1 1.841903 1.814691 -0.334880 1.253003 -0.910201 -1.358911 -0.162620
Dim. 2 -0.689812 -0.717055 0.437299 0.993077 -1.680987 1.065769 1.424732
Columns:
Cluster PCA MDS PCoA CCA RDA MANOVA Mantel ANOSIM CVA
Mass 0.418731 0.293731 0.055728 0.010578 0.124871 0.031863 0.021801 0.021930 0.009675 0.011094
ChiDist 0.180789 0.221392 0.382311 0.574617 0.397353 0.237501 0.414914 0.436890 0.708188 0.224016
Inertia 0.013686 0.014397 0.008145 0.003493 0.019716 0.001797 0.003753 0.004186 0.004852 0.000557
Dim. 1 0.658768 0.517444 -1.138329 -0.471807 -1.944623 -0.788318 -1.501268 -2.174671 -1.421668 0.244303
Dim. 2 0.731977 -1.059702 -1.666058 2.207099 0.717044 1.014040 -0.992172 0.348263 -3.499596 0.024122plot(ca_t1)
plot(ca_t1, lines = TRUE)
plot(ca_t1, arrows = c(TRUE, TRUE))
Análisis de correspondencia sin tendencia DCA.
ejemplo1 <- read.csv2("ejemplo1_sitio.csv", row.names = 1)
row.names(ejemplo1) <- paste("Sitio", row.names(ejemplo1))
ejemplo1require(ca)
ca1 <- ca(ejemplo1)
ca1
Principal inertias (eigenvalues):
1 2 3 4 5 6 7 8 9 10
Value 0.945428 0.79626 0.590795 0.377372 0.198258 0.078079 0.057411 0.056247 0.041075 0.038788
Percentage 28.59% 24.08% 17.86% 11.41% 5.99% 2.36% 1.74% 1.7% 1.24% 1.17%
11 12 13 14 15 16 17 18 19
Value 0.036979 0.024534 0.019418 0.017685 0.017089 0.006671 0.002179 0.001904 0.001052
Percentage 1.12% 0.74% 0.59% 0.53% 0.52% 0.2% 0.07% 0.06% 0.03%
Rows:
Sitio 1 Sitio 2 Sitio 3 Sitio 4 Sitio 5 Sitio 6 Sitio 7 Sitio 8 Sitio 9 Sitio 10
Mass 0.031915 0.042553 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191
ChiDist 2.679829 2.185654 1.857238 1.716974 1.661325 1.661325 1.661325 1.661325 1.661325 1.661325
Inertia 0.229196 0.203280 0.183475 0.156809 0.146809 0.146809 0.146809 0.146809 0.146809 0.146809
Dim. 1 -1.426828 -1.391228 -1.343991 -1.248889 -1.123087 -0.964471 -0.779625 -0.572853 -0.350233 -0.117831
Dim. 2 1.465127 1.319301 1.137720 0.786881 0.367102 -0.100200 -0.553615 -0.947228 -1.236105 -1.389072
Sitio 11 Sitio 12 Sitio 13 Sitio 14 Sitio 15 Sitio 16 Sitio 17 Sitio 18 Sitio 19 Sitio 20
Mass 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.042553 0.031915
ChiDist 1.661325 1.661325 1.661325 1.661325 1.661325 1.661325 1.716974 1.857238 2.185654 2.679829
Inertia 0.146809 0.146809 0.146809 0.146809 0.146809 0.146809 0.156809 0.183475 0.203280 0.229196
Dim. 1 0.117831 0.350233 0.572853 0.779625 0.964471 1.123087 1.248889 1.343991 1.391228 1.426828
Dim. 2 -1.389072 -1.236105 -0.947228 -0.553615 -0.100200 0.367102 0.786881 1.137720 1.319301 1.465127
Columns:
SP1 SP2 SP3 SP4 SP5 SP6 SP7 SP8 SP9 SP10
Mass 0.031915 0.042553 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191
ChiDist 2.679829 2.185654 1.857238 1.716974 1.661325 1.661325 1.661325 1.661325 1.661325 1.661325
Inertia 0.229196 0.203280 0.183475 0.156809 0.146809 0.146809 0.146809 0.146809 0.146809 0.146809
Dim. 1 -1.426828 -1.391228 -1.343991 -1.248889 -1.123087 -0.964471 -0.779625 -0.572853 -0.350233 -0.117831
Dim. 2 1.465127 1.319301 1.137720 0.786881 0.367102 -0.100200 -0.553615 -0.947228 -1.236105 -1.389072
SP11 SP12 SP13 SP14 SP15 SP16 SP17 SP18 SP19 SP20
Mass 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.053191 0.042553 0.031915
ChiDist 1.661325 1.661325 1.661325 1.661325 1.661325 1.661325 1.716974 1.857238 2.185654 2.679829
Inertia 0.146809 0.146809 0.146809 0.146809 0.146809 0.146809 0.156809 0.183475 0.203280 0.229196
Dim. 1 0.117831 0.350233 0.572853 0.779625 0.964471 1.123087 1.248889 1.343991 1.391228 1.426828
Dim. 2 -1.389072 -1.236105 -0.947228 -0.553615 -0.100200 0.367102 0.786881 1.137720 1.319301 1.465127plot(ca1)
plot(ca1, lines = c(TRUE, FALSE))
plot(ca1, arrows = c(TRUE, FALSE))
require(vegan)
dca1 <- decorana(ejemplo1)
dca1
Call:
decorana(veg = ejemplo1)
Detrended correspondence analysis with 26 segments.
Rescaling of axes with 4 iterations.
DCA1 DCA2 DCA3 DCA4
Eigenvalues 0.9351 0.23818 0.11471 0.05417
Decorana values 0.9454 0.06092 0.04539 0.02980
Axis lengths 11.0826 1.85490 1.28126 0.98343plot(dca1)
Análisis de redundancia
peces <- read.csv2("peces.csv", row.names = 1)
ambient <- read.csv2("ambientales.csv",enc="latin1",row.names=1)
sumEsp <- apply(peces,1,sum)
peces <- peces[sumEsp!=0,]
ambient <- ambient[sumEsp!=0,]
require(vegan)
peces.hell <- decostand(peces, "hell")
pca <- rda(peces.hell)
print(summary(pca))
Call:
rda(X = peces.hell)
Partitioning of variance:
Inertia Proportion
Total 0.5025 1
Unconstrained 0.5025 1
Eigenvalues, and their contribution to the variance
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
Eigenvalue 0.2580 0.06424 0.04632 0.03850 0.02197 0.01675 0.01472 0.01156 0.006936 0.006019
Proportion Explained 0.5133 0.12784 0.09218 0.07662 0.04371 0.03334 0.02930 0.02300 0.013800 0.011980
Cumulative Proportion 0.5133 0.64118 0.73337 0.80999 0.85370 0.88704 0.91634 0.93934 0.953140 0.965120
PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19
Eigenvalue 0.004412 0.002982 0.002713 0.001835 0.001455 0.001118 0.0008309 0.0005415 0.0004755
Proportion Explained 0.008780 0.005930 0.005400 0.003650 0.002890 0.002220 0.0016500 0.0010800 0.0009500
Cumulative Proportion 0.973900 0.979840 0.985240 0.988890 0.991780 0.994010 0.9956600 0.9967400 0.9976900
PC20 PC21 PC22 PC23 PC24 PC25 PC26 PC27
Eigenvalue 0.000368 0.0002765 0.0002253 0.0001429 7.618e-05 4.99e-05 1.526e-05 9.118e-06
Proportion Explained 0.000730 0.0005500 0.0004500 0.0002800 1.500e-04 1.00e-04 3.000e-05 2.000e-05
Cumulative Proportion 0.998420 0.9989700 0.9994200 0.9997000 9.999e-01 1.00e+00 1.000e+00 1.000e+00
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores: 1.93676
Species scores
PC1 PC2 PC3 PC4 PC5 PC6
Cogo 0.17336 0.08295 -0.064963 0.2539861 -0.0285801 0.019057
Satr 0.64860 0.01162 -0.261994 -0.1606020 -0.0745819 -0.088616
Phph 0.51810 0.14773 0.165304 0.0241017 0.1012928 0.104748
Neba 0.38606 0.16615 0.242995 -0.0275216 0.1258011 0.048299
Thth 0.16893 0.06274 -0.096143 0.2426514 0.0140574 0.062117
Teso 0.07786 0.14644 -0.031402 0.2339394 -0.1032338 -0.040810
Chna -0.18491 0.04901 -0.045107 0.0199377 0.0687305 0.009650
Chto -0.14644 0.17834 -0.010937 0.0649955 -0.0006229 -0.106955
Lele -0.11436 0.15673 0.142223 -0.0127266 -0.1989404 0.013897
Lece -0.09682 -0.15449 0.242943 0.1124210 0.0233830 -0.039996
Baba -0.19826 0.21211 -0.053980 0.0969899 0.0067098 -0.035442
Spbi -0.17689 0.16250 -0.033112 0.0397113 0.0323159 -0.072908
Gogo -0.23138 0.09782 0.064144 -0.0013887 -0.1503303 0.130575
Eslu -0.15129 0.12804 0.040303 -0.1203826 -0.1006077 0.066242
Pefl -0.15719 0.18144 0.057029 -0.0940032 -0.0412984 -0.060409
Rham -0.22853 0.13870 -0.062197 -0.0125024 0.0798647 -0.006907
Legi -0.22790 0.08231 -0.065797 0.0172143 0.0611434 -0.001407
Scer -0.19221 0.03090 -0.006264 -0.0739133 -0.0731548 0.074581
Cyca -0.18699 0.13388 -0.050804 0.0001803 0.0403961 -0.031005
Titi -0.19169 0.15719 0.114415 -0.0818330 0.0142624 -0.072024
Abbr -0.20174 0.08807 -0.067086 -0.0529106 0.0737228 0.037312
Icme -0.14717 0.05829 -0.067311 -0.0458414 0.0501013 0.031605
Acce -0.30155 -0.01785 -0.084333 -0.0181797 0.0226500 0.126639
Ruru -0.35245 -0.14076 0.168014 0.0185946 0.0213462 -0.129788
Blbj -0.24317 0.03679 -0.082731 -0.0384489 0.0939828 0.063369
Alal -0.42536 -0.26155 -0.054190 0.1021959 -0.0078085 0.044540
Anan -0.20631 0.11889 -0.062079 -0.0175733 0.0718743 -0.001956
Site scores (weighted sums of species scores)
PC1 PC2 PC3 PC4 PC5 PC6
1 0.367401 -0.39935 -1.08857 -0.63304 -0.512027 -0.858378
2 0.503582 -0.05683 -0.19259 -0.43441 0.389533 0.069451
3 0.461709 0.02262 -0.06522 -0.49798 0.309425 0.270577
4 0.298336 0.15130 0.26748 -0.53196 0.003088 0.184821
5 -0.002222 0.07631 0.54769 -0.50936 -0.780261 -0.169353
6 0.212816 0.08345 0.55091 -0.42210 -0.139518 -0.104278
7 0.438055 -0.06114 0.15590 -0.31150 0.158686 0.036565
9 0.040794 -0.44269 0.89022 0.09609 0.641193 -0.646943
10 0.298011 -0.01094 0.56837 -0.10013 -0.088124 0.515072
11 0.467609 -0.12622 -0.15505 0.29459 0.325464 0.200912
12 0.476845 -0.07691 -0.16329 0.29384 0.360112 0.194576
13 0.483620 0.06649 -0.44723 0.53734 0.048587 0.182565
14 0.371728 0.16555 -0.21939 0.62130 -0.183604 0.364847
15 0.277048 0.23525 0.08928 0.61773 -0.475769 0.124107
16 0.077024 0.47455 0.17116 0.34361 -0.570434 -0.572740
17 -0.053860 0.42290 0.02810 0.42376 -0.059203 -0.586419
18 -0.135418 0.37780 0.03233 0.39706 -0.007199 -0.347064
19 -0.269281 0.30751 0.18022 0.09354 0.178657 -0.016299
20 -0.378830 0.19764 0.04939 -0.03438 0.157660 -0.056696
21 -0.409369 0.22888 -0.08401 -0.12823 0.152787 0.096105
22 -0.443679 0.17698 -0.13708 -0.13152 0.103294 0.030004
23 -0.242292 -1.11711 0.15254 0.40512 0.045573 -0.576778
24 -0.358333 -0.83372 -0.17314 0.27200 0.181192 0.347231
25 -0.325288 -0.61983 0.10487 0.01059 -1.034438 0.750325
26 -0.441703 0.02111 -0.13742 -0.14346 0.200775 0.244356
27 -0.444529 0.12735 -0.15915 -0.14112 0.179240 0.123487
28 -0.446407 0.12774 -0.18830 -0.15467 0.239617 0.117101
29 -0.355788 0.28044 -0.28006 -0.02003 0.110181 0.079568
30 -0.467578 0.20086 -0.29797 -0.21269 0.065512 0.003276plot(pca)
rda1 <- rda(peces.hell ~ das, data = ambient)
print(summary(rda1))
Call:
rda(formula = peces.hell ~ das, data = ambient)
Partitioning of variance:
Inertia Proportion
Total 0.5025 1.0000
Constrained 0.1958 0.3897
Unconstrained 0.3067 0.6103
Eigenvalues, and their contribution to the variance
Importance of components:
RDA1 PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9
Eigenvalue 0.1958 0.09117 0.06422 0.04311 0.02416 0.02106 0.01481 0.01254 0.009112 0.006351
Proportion Explained 0.3897 0.18142 0.12779 0.08580 0.04808 0.04191 0.02948 0.02496 0.018130 0.012640
Cumulative Proportion 0.3897 0.57115 0.69894 0.78473 0.83282 0.87473 0.90421 0.92917 0.947300 0.959940
PC10 PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18
Eigenvalue 0.005495 0.003709 0.002727 0.001898 0.001581 0.001325 0.0008844 0.0006854 0.00051
Proportion Explained 0.010940 0.007380 0.005430 0.003780 0.003150 0.002640 0.0017600 0.0013600 0.00101
Cumulative Proportion 0.970880 0.978260 0.983680 0.987460 0.990600 0.993240 0.9950000 0.9963600 0.99738
PC19 PC20 PC21 PC22 PC23 PC24 PC25 PC26
Eigenvalue 0.0004486 0.0002837 0.000226 0.0001584 9.257e-05 5.608e-05 3.792e-05 9.552e-06
Proportion Explained 0.0008900 0.0005600 0.000450 0.0003200 1.800e-04 1.100e-04 8.000e-05 2.000e-05
Cumulative Proportion 0.9982700 0.9988400 0.999290 0.9996000 9.998e-01 9.999e-01 1.000e+00 1.000e+00
PC27
Eigenvalue 3.924e-06
Proportion Explained 1.000e-05
Cumulative Proportion 1.000e+00
Accumulated constrained eigenvalues
Importance of components:
RDA1
Eigenvalue 0.1958
Proportion Explained 1.0000
Cumulative Proportion 1.0000
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores: 1.93676
Species scores
RDA1 PC1 PC2 PC3 PC4 PC5
Cogo -0.054132 -0.26670 0.072574 -0.118965 0.106809 -0.0092829
Satr -0.563253 -0.34682 0.002396 0.285639 0.039973 0.0387857
Phph -0.453769 -0.22134 0.145793 -0.171021 -0.171870 -0.0008564
Neba -0.382083 -0.07689 0.169537 -0.189650 -0.189145 -0.0330382
Thth -0.038674 -0.28506 0.051343 -0.091509 0.063509 -0.0238737
Teso -0.006115 -0.16481 0.139501 -0.119248 0.187036 0.0130230
Chna 0.156045 0.07766 0.049611 0.034025 0.017828 -0.0871564
Chto 0.123202 0.05978 0.178890 -0.015869 0.112737 -0.0846815
Lele 0.066149 0.13027 0.162331 -0.094654 0.063977 0.1897790
Lece 0.065344 0.11122 -0.149219 -0.256890 -0.019550 -0.0187035
Baba 0.200088 0.02637 0.210338 -0.006774 0.089524 -0.0597238
Spbi 0.160102 0.06094 0.162736 0.013448 0.065122 -0.0874777
Gogo 0.186926 0.14132 0.101802 -0.040207 0.035095 0.1744898
Eslu 0.090870 0.15212 0.133539 0.051232 -0.016236 0.1289982
Pefl 0.075648 0.17860 0.187890 0.030826 0.028736 0.0111957
Rham 0.212821 0.07728 0.139039 0.063477 -0.017498 -0.0804411
Legi 0.218037 0.06567 0.081990 0.048383 0.009392 -0.0729919
Scer 0.157697 0.11562 0.033883 0.055059 -0.018099 0.1066249
Cyca 0.182597 0.05232 0.133759 0.044959 0.006184 -0.0528951
Titi 0.098267 0.21472 0.165208 -0.021798 -0.014714 -0.0265350
Abbr 0.198039 0.06101 0.088221 0.084953 -0.072427 -0.0324701
Icme 0.166663 0.01609 0.057266 0.075136 -0.074418 -0.0038267
Acce 0.292661 0.09091 -0.017930 0.079826 -0.041147 0.0247274
Ruru 0.230053 0.30620 -0.130915 -0.114718 0.066907 -0.0915881
Blbj 0.234965 0.07384 0.036746 0.090127 -0.070914 -0.0515381
Alal 0.405078 0.14062 -0.261311 -0.007415 0.084857 -0.0279890
Anan 0.199828 0.06079 0.118864 0.063470 -0.028011 -0.0637102
Site scores (weighted sums of species scores)
RDA1 PC1 PC2 PC3 PC4 PC5
1 -0.40668 -0.065821 -0.407807 1.312429 0.77785 -0.05002
2 -0.57998 -0.134813 -0.057311 0.395158 -0.37960 -0.24293
3 -0.54086 -0.058244 0.026460 0.328167 -0.48406 -0.05987
4 -0.38105 0.255766 0.169243 0.116491 -0.34313 0.18667
5 -0.06567 0.773673 0.113233 -0.038417 0.29829 0.64123
6 -0.29850 0.402236 0.108700 -0.159995 -0.20399 0.22232
7 -0.51559 -0.081633 -0.056764 0.030035 -0.40480 0.04585
9 -0.09653 0.528062 -0.414208 -0.719433 -0.23337 -0.72142
10 -0.36181 -0.016846 -0.001888 -0.444843 -0.53594 0.50470
11 -0.49424 -0.596733 -0.147467 -0.124483 -0.24943 -0.15582
12 -0.50461 -0.637646 -0.099507 -0.124287 -0.28459 -0.17548
13 -0.48695 -0.799590 0.033361 -0.026249 0.18035 -0.08636
14 -0.36742 -0.628544 0.139621 -0.240333 0.26155 0.16656
15 -0.28047 -0.439398 0.219177 -0.470599 0.37290 0.39517
16 -0.08806 -0.097701 0.472382 -0.320512 0.63894 0.18043
17 0.07154 -0.001907 0.420440 -0.226331 0.61156 -0.39984
18 0.16512 0.076867 0.377426 -0.210080 0.51255 -0.35684
19 0.29492 0.325021 0.318340 -0.146884 0.11912 -0.29882
20 0.41926 0.410196 0.209720 0.043049 0.12501 -0.28197
21 0.46157 0.328809 0.236827 0.184337 -0.01809 -0.15575
22 0.50374 0.327608 0.183949 0.229166 0.02125 -0.12546
23 0.27559 0.034710 -1.118655 -0.358632 0.32228 -0.33338
24 0.42607 0.080491 -0.838217 -0.009696 0.10633 -0.20429
25 0.36405 0.113298 -0.617354 -0.107446 0.19297 1.20923
26 0.50398 0.139969 0.021783 0.187543 -0.26562 -0.02284
27 0.50836 0.093350 0.126264 0.197870 -0.24491 -0.02795
28 0.51366 0.024389 0.124019 0.213270 -0.33913 -0.03695
29 0.42158 -0.232392 0.266901 0.180625 -0.23607 0.04984
30 0.53897 -0.123176 0.191332 0.310080 -0.31820 0.13401
Site constraints (linear combinations of constraining variables)
RDA1 PC1 PC2 PC3 PC4 PC5
1 -0.50684 -0.065821 -0.407807 1.312429 0.77785 -0.05002
2 -0.50184 -0.134813 -0.057311 0.395158 -0.37960 -0.24293
3 -0.48080 -0.058244 0.026460 0.328167 -0.48406 -0.05987
4 -0.45898 0.255766 0.169243 0.116491 -0.34313 0.18667
5 -0.45109 0.773673 0.113233 -0.038417 0.29829 0.64123
6 -0.42242 0.402236 0.108700 -0.159995 -0.20399 0.22232
7 -0.41085 -0.081633 -0.056764 0.030035 -0.40480 0.04585
9 -0.32223 0.528062 -0.414208 -0.719433 -0.23337 -0.72142
10 -0.24728 -0.016846 -0.001888 -0.444843 -0.53594 0.50470
11 -0.18312 -0.596733 -0.147467 -0.124483 -0.24943 -0.15582
12 -0.15945 -0.637646 -0.099507 -0.124287 -0.28459 -0.17548
13 -0.13000 -0.799590 0.033361 -0.026249 0.18035 -0.08636
14 -0.10738 -0.628544 0.139621 -0.240333 0.26155 0.16656
15 -0.07504 -0.439398 0.219177 -0.470599 0.37290 0.39517
16 -0.01876 -0.097701 0.472382 -0.320512 0.63894 0.18043
17 0.01437 -0.001907 0.420440 -0.226331 0.61156 -0.39984
18 0.04724 0.076867 0.377426 -0.210080 0.51255 -0.35684
19 0.08301 0.325021 0.318340 -0.146884 0.11912 -0.29882
20 0.14375 0.410196 0.209720 0.043049 0.12501 -0.28197
21 0.23185 0.328809 0.236827 0.184337 -0.01809 -0.15575
22 0.26551 0.327608 0.183949 0.229166 0.02125 -0.12546
23 0.29260 0.034710 -1.118655 -0.358632 0.32228 -0.33338
24 0.31995 0.080491 -0.838217 -0.009696 0.10633 -0.20429
25 0.35440 0.113298 -0.617354 -0.107446 0.19297 1.20923
26 0.43355 0.139969 0.021783 0.187543 -0.26562 -0.02284
27 0.47378 0.093350 0.126264 0.197870 -0.24491 -0.02795
28 0.53032 0.024389 0.124019 0.213270 -0.33913 -0.03695
29 0.60212 -0.232392 0.266901 0.180625 -0.23607 0.04984
30 0.68364 -0.123176 0.191332 0.310080 -0.31820 0.13401
Biplot scores for constraining variables
RDA1 PC1 PC2 PC3 PC4 PC5
das 1 0 0 0 0 0plot(rda1)
rda2 <- rda(peces.hell ~ ., data = ambient)
print(summary(rda2))
Call:
rda(formula = peces.hell ~ das + alt + slo + flo + pH + har + pho + nit + amm + oxy + bdo, data = ambient)
Partitioning of variance:
Inertia Proportion
Total 0.5025 1.0000
Constrained 0.3676 0.7314
Unconstrained 0.1350 0.2686
Eigenvalues, and their contribution to the variance
Importance of components:
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6 RDA7 RDA8 RDA9 RDA10
Eigenvalue 0.2302 0.05347 0.03396 0.02762 0.006804 0.006271 0.003154 0.003017 0.001417 0.0008703
Proportion Explained 0.4581 0.10640 0.06758 0.05496 0.013540 0.012480 0.006280 0.006000 0.002820 0.0017300
Cumulative Proportion 0.4581 0.56451 0.63208 0.68704 0.700580 0.713060 0.719340 0.725340 0.728160 0.7298900
RDA11 PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
Eigenvalue 0.0007768 0.04383 0.02270 0.01774 0.01413 0.009321 0.008515 0.005219 0.004581
Proportion Explained 0.0015500 0.08722 0.04518 0.03529 0.02811 0.018550 0.016940 0.010390 0.009120
Cumulative Proportion 0.7314400 0.81865 0.86384 0.89913 0.92724 0.945790 0.962730 0.973120 0.982240
PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 PC17
Eigenvalue 0.002958 0.002013 0.001342 0.0009585 0.0007297 0.0003818 0.000334 0.0001299 7.886e-05
Proportion Explained 0.005890 0.004010 0.002670 0.0019100 0.0014500 0.0007600 0.000660 0.0002600 1.600e-04
Cumulative Proportion 0.988130 0.992130 0.994800 0.9967100 0.9981600 0.9989200 0.999580 0.9998400 1.000e+00
Accumulated constrained eigenvalues
Importance of components:
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6 RDA7 RDA8 RDA9 RDA10
Eigenvalue 0.2302 0.05347 0.03396 0.02762 0.006804 0.006271 0.003154 0.003017 0.001417 0.0008703
Proportion Explained 0.6263 0.14547 0.09239 0.07513 0.018510 0.017060 0.008580 0.008210 0.003850 0.0023700
Cumulative Proportion 0.6263 0.77178 0.86417 0.93930 0.957810 0.974870 0.983460 0.991660 0.995520 0.9978900
RDA11
Eigenvalue 0.0007768
Proportion Explained 0.0021100
Cumulative Proportion 1.0000000
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores: 1.93676
Species scores
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
Cogo 0.14261 0.1180253 -0.22904 0.086458 -0.028042 -0.013691
Satr 0.63485 0.0273682 0.20085 0.163764 0.019805 0.005858
Phph 0.48361 0.1077673 -0.07980 -0.133313 0.034833 -0.004144
Neba 0.36118 0.1090800 -0.01143 -0.219383 0.029874 0.037263
Thth 0.14244 0.1122444 -0.22054 0.106069 -0.044501 -0.008622
Teso 0.07292 0.1280078 -0.18815 0.059441 -0.008623 -0.001556
Chna -0.17236 0.0784750 -0.01415 -0.012202 0.024412 0.062130
Chto -0.12548 0.1660939 -0.03644 0.002070 0.087969 0.023223
Lele -0.07912 0.0398662 -0.02835 -0.050439 0.011284 -0.093644
Lece -0.09581 -0.1434198 -0.13995 -0.122810 -0.079051 -0.011121
Baba -0.17975 0.2151163 -0.04819 0.043810 0.015552 0.014657
Spbi -0.15589 0.1641509 -0.01369 0.003517 0.059083 0.001573
Gogo -0.20301 0.0348690 -0.03783 -0.027001 0.044723 -0.081508
Eslu -0.11339 0.0291095 0.06240 -0.048558 0.031607 -0.069690
Pefl -0.09975 0.1120913 0.04452 -0.095320 0.011882 0.011139
Rham -0.21017 0.1602633 0.04184 0.021526 0.010718 0.001693
Legi -0.23232 0.1103727 0.01809 -0.005716 -0.011545 0.043028
Scer -0.16516 -0.0006841 0.03199 0.006260 0.013625 -0.098070
Cyca -0.18069 0.1411915 0.03496 0.016758 -0.006660 0.003324
Titi -0.14230 0.1179099 0.05249 -0.141851 -0.032298 0.007223
Abbr -0.19435 0.1092121 0.07605 0.033536 -0.055275 0.006789
Icme -0.15512 0.0727019 0.07999 0.034135 -0.088141 -0.009924
Acce -0.31286 0.0113937 0.03276 0.017709 -0.001507 -0.043683
Ruru -0.31310 -0.1517049 -0.05604 -0.140122 0.004038 0.040470
Blbj -0.24750 0.0837801 0.06250 0.012999 -0.059178 0.048588
Alal -0.43297 -0.2232880 -0.09319 0.124580 0.089120 0.048742
Anan -0.19684 0.1387592 0.04844 0.020291 -0.007706 -0.002579
Site scores (weighted sums of species scores)
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
1 0.39199 -0.31267 0.98240 1.29491 -0.1258591 0.32865
2 0.52860 -0.04444 0.49719 0.10778 0.4259551 0.63121
3 0.48740 -0.02096 0.49331 -0.07076 0.5699500 0.29678
4 0.32937 0.02809 0.38254 -0.51181 0.2540256 -0.18083
5 0.02656 -0.18286 0.21678 -0.72427 0.0467813 -1.40635
6 0.24215 -0.08873 0.21046 -0.77964 -0.0138240 -0.32595
7 0.46183 -0.11999 0.28437 -0.18382 0.0403432 0.11466
9 0.04221 -0.52153 -0.30776 -1.06830 -1.1177967 0.90976
10 0.31401 -0.14722 -0.08142 -0.55441 0.0004456 -0.69622
11 0.48177 -0.03460 -0.30084 0.30647 -0.6211610 0.24013
12 0.49116 0.01863 -0.28336 0.28353 -0.5526465 0.38811
13 0.49826 0.19287 -0.45932 0.66506 -0.3554733 0.30170
14 0.38432 0.23745 -0.61472 0.44511 -0.3586002 -0.25255
15 0.29122 0.24047 -0.65399 0.13806 -0.5744138 -0.61858
16 0.09316 0.42148 -0.35490 -0.15339 0.5215487 -0.37988
17 -0.04925 0.45811 -0.39677 -0.01491 0.9780228 0.37292
18 -0.13761 0.42321 -0.38275 -0.05496 0.8161603 0.16502
19 -0.27972 0.31288 -0.11236 -0.33397 0.8933487 0.22061
20 -0.39479 0.22514 0.04995 -0.18906 0.5524046 0.07848
21 -0.42845 0.27228 0.18669 -0.06116 0.1685934 -0.05714
22 -0.46606 0.23214 0.22711 0.01341 -0.2537680 -0.02033
23 -0.27461 -1.14655 -0.45652 0.29007 -0.0135080 1.25334
24 -0.40481 -0.76490 -0.22822 0.37504 -0.0609283 1.09137
25 -0.34882 -0.79890 -0.18120 0.26592 0.6572636 -1.77138
26 -0.46948 0.07575 0.22954 0.02782 -0.3290586 -0.01789
27 -0.47071 0.19146 0.25713 0.03821 -0.3683865 -0.05750
28 -0.47379 0.20692 0.28560 0.06099 -0.5260879 -0.05532
29 -0.37500 0.36927 0.15499 0.19260 -0.2675599 -0.13575
30 -0.49089 0.27719 0.35606 0.19549 -0.3857710 -0.41707
Site constraints (linear combinations of constraining variables)
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
1 0.56175 -0.1760841 0.88764 0.754729 0.05699 -0.024789
2 0.27817 0.0278236 0.64854 -0.186273 0.71868 0.103142
3 0.40029 -0.1410937 0.44478 0.093254 0.06243 0.159225
4 0.38057 0.0304488 0.27060 -0.451187 0.11348 -0.163639
5 0.28434 -0.4313776 -0.07763 -0.624922 -0.31890 -0.121072
6 0.32365 -0.1717502 0.33216 -0.239434 0.10094 0.430241
7 0.43342 -0.1878085 0.23023 -0.249967 -0.43848 -0.112702
9 0.03876 -0.2453624 -0.06488 -1.063159 -0.28405 -0.165997
10 0.20896 -0.1304587 0.09944 -0.029712 -0.15900 -0.003754
11 0.40310 0.2072872 -0.38689 0.263810 -0.34896 -0.675910
12 0.31060 0.1676808 -0.35285 0.131850 0.23982 0.374171
13 0.36401 0.1083071 -0.45977 0.254110 -0.16169 0.154682
14 0.37243 0.1568990 -0.54561 0.280403 -0.29513 0.137795
15 0.30217 0.2952073 -0.51539 0.302620 -0.26909 -0.210679
16 -0.03361 0.2527439 -0.16089 -0.109020 0.07654 -0.063949
17 -0.04798 0.2826767 -0.42392 -0.163557 0.50606 0.277953
18 -0.04201 0.3220218 -0.27114 -0.101241 0.36862 -0.205147
19 -0.04238 0.3815154 -0.25768 -0.005306 0.34826 -0.051361
20 -0.22510 0.3772267 -0.06452 0.029576 0.73223 0.129096
21 -0.36748 0.2531034 0.06637 -0.113143 0.22778 0.340391
22 -0.31101 0.0588354 0.04318 0.184265 -0.22087 0.507177
23 -0.23685 -1.0546821 -0.31876 0.653124 -0.04596 0.560361
24 -0.50645 -0.5459548 -0.31521 -0.311281 -0.17450 0.594229
25 -0.37598 -0.9060399 -0.21468 0.249405 0.74559 -1.161192
26 -0.50636 0.0003718 0.12134 -0.254528 -0.36086 -0.278472
27 -0.57930 0.0667865 0.37489 0.211246 -0.22598 0.098458
28 -0.60704 0.3723919 0.35636 -0.090151 -0.04124 -0.118013
29 -0.34377 0.3294603 0.26629 0.309673 -0.30573 -0.235032
30 -0.43691 0.2998244 0.28800 0.274817 -0.64698 -0.275212
Biplot scores for constraining variables
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
das -0.9128 0.12530 -0.14564 0.28559 -0.14025 -0.08596
alt 0.8174 -0.19940 0.42653 -0.31363 0.04070 0.04191
slo 0.7304 -0.18160 0.44131 0.12857 -0.03275 0.05724
flo -0.7734 0.22945 -0.11776 0.35275 -0.20906 -0.20090
pH 0.1032 0.17963 -0.23622 0.15717 -0.27998 -0.00646
har -0.5651 0.06594 -0.58956 0.05411 -0.38278 -0.21829
pho -0.4885 -0.66510 -0.22158 0.20580 0.19624 -0.37929
nit -0.7699 -0.21306 -0.25074 0.19239 0.30094 -0.31772
amm -0.4700 -0.70062 -0.19662 0.17917 0.34014 -0.29055
oxy 0.7593 0.57745 -0.03543 0.21067 0.03237 0.15692
bdo -0.5124 -0.80242 -0.19822 0.12204 0.05668 -0.05770plot(rda2)
Análisis de correspondencia canónico
peces <- read.csv2("peces.csv", row.names = 1)
ambient <- read.csv2("ambientales.csv",enc="latin1",row.names=1)
sumEsp <- apply(peces,1,sum)
peces <- peces[sumEsp!=0,]
ambient <- ambient[sumEsp!=0,]
require(vegan)
cca1 <- cca(peces)
print(summary(cca1))
Call:
cca(X = peces)
Partitioning of mean squared contingency coefficient:
Inertia Proportion
Total 1.167 1
Unconstrained 1.167 1
Eigenvalues, and their contribution to the mean squared contingency coefficient
Importance of components:
CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10 CA11
Eigenvalue 0.601 0.1444 0.10729 0.08337 0.05158 0.04185 0.03389 0.02883 0.01684 0.01083 0.01014
Proportion Explained 0.515 0.1237 0.09195 0.07145 0.04420 0.03586 0.02904 0.02470 0.01443 0.00928 0.00869
Cumulative Proportion 0.515 0.6388 0.73069 0.80214 0.84634 0.88220 0.91124 0.93594 0.95038 0.95965 0.96835
CA12 CA13 CA14 CA15 CA16 CA17 CA18 CA19 CA20
Eigenvalue 0.007886 0.006123 0.004867 0.004606 0.003844 0.003067 0.001823 0.001642 0.001295
Proportion Explained 0.006760 0.005250 0.004170 0.003950 0.003290 0.002630 0.001560 0.001410 0.001110
Cumulative Proportion 0.975100 0.980350 0.984520 0.988470 0.991760 0.994390 0.995950 0.997360 0.998470
CA21 CA22 CA23 CA24 CA25 CA26
Eigenvalue 0.0008775 0.0004217 0.0002149 0.0001528 8.949e-05 2.695e-05
Proportion Explained 0.0007500 0.0003600 0.0001800 0.0001300 8.000e-05 2.000e-05
Cumulative Proportion 0.9992200 0.9995900 0.9997700 0.9999000 1.000e+00 1.000e+00
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
Species scores
CA1 CA2 CA3 CA4 CA5 CA6
Cogo 1.50075 -1.410293 0.26049 -0.307203 0.271777 -0.003465
Satr 1.66167 0.444129 0.57571 0.166073 -0.261870 -0.326590
Phph 1.28545 0.285328 -0.04768 0.018126 0.043847 0.200732
Neba 0.98662 0.360900 -0.35265 -0.009021 -0.012231 0.253429
Thth 1.55554 -1.389752 0.80505 -0.468471 0.471301 0.225409
Teso 0.99709 -1.479902 -0.48035 0.079397 -0.105715 -0.332445
Chna -0.54916 -0.051534 0.01123 -0.096004 -0.382763 0.134807
Chto -0.18478 -0.437710 -0.57438 0.424267 -0.587150 0.091866
Lele 0.01337 -0.095342 -0.57672 0.212017 0.126668 -0.389103
Lece 0.01078 0.140577 -0.34811 -0.538268 0.185286 0.167087
Baba -0.33363 -0.300682 -0.04929 0.170961 -0.157203 0.103068
Spbi -0.38357 -0.255310 -0.20136 0.374057 -0.385866 0.239001
Gogo -0.32152 -0.034382 -0.07423 -0.031236 0.014417 -0.156351
Eslu -0.26165 0.187282 0.00617 0.183771 0.295142 -0.262808
Pefl -0.28913 0.121044 -0.18919 0.367615 0.218087 -0.163675
Rham -0.60298 -0.057369 0.20341 0.214299 -0.050977 0.211926
Legi -0.58669 -0.082467 0.21198 0.050175 -0.120456 0.108724
Scer -0.61815 0.124733 0.13339 0.147190 0.317736 -0.340380
Cyca -0.57951 -0.110732 0.20173 0.308547 0.006854 0.153224
Titi -0.37880 0.138023 -0.07825 0.095793 0.256285 -0.029245
Abbr -0.70235 0.011155 0.40242 0.211582 0.138186 0.132297
Icme -0.73238 -0.009098 0.55678 0.321852 0.281812 0.172271
Acce -0.69300 0.038971 0.37688 -0.183965 -0.051945 -0.011126
Ruru -0.44181 0.176915 -0.23691 -0.345104 0.129676 -0.043802
Blbj -0.70928 0.032317 0.40924 0.030224 0.049050 0.114560
Alal -0.63114 0.053594 0.15204 -0.661381 -0.414796 -0.206611
Anan -0.63578 -0.041894 0.30093 0.224044 0.030444 0.203160
Site scores (weighted averages of species scores)
CA1 CA2 CA3 CA4 CA5 CA6
1 2.76488 3.076306 5.3657489 1.99192 -5.07714 -7.80447
2 2.27540 2.565531 1.2659130 0.87538 -1.89139 -0.13887
3 2.01823 2.441224 0.5144079 0.79436 -1.03741 0.56015
4 1.28485 1.935664 -0.2509482 0.76470 0.54752 0.10579
5 0.08875 1.015182 -1.4555434 0.47672 2.69249 -2.92498
6 1.03188 1.712163 -0.9544059 0.01584 0.91932 0.39856
7 1.91427 2.256208 -0.0001407 0.39844 -1.07017 0.32127
9 0.25591 1.443008 -2.5777721 -3.41400 2.36613 2.71741
10 1.24517 1.526391 -1.9635663 -0.41230 0.69647 1.51859
11 2.14501 0.110278 1.6108693 -0.82023 0.53918 1.01153
12 2.17418 -0.251649 1.5845397 -0.81483 0.52623 1.05501
13 2.30944 -2.034439 1.9181448 -0.60481 0.64435 -0.14844
14 1.87141 -2.262503 1.1066796 -0.80840 1.09542 0.11038
15 1.34659 -1.805967 -0.6441505 -0.52803 0.76871 -0.67165
16 0.70214 -1.501167 -1.9735888 0.98502 -0.93585 -1.27168
17 0.28775 -0.836803 -1.2259108 0.73302 -1.57036 0.57315
18 0.05299 -0.647950 -0.9234228 0.35770 -0.95401 0.77738
19 -0.20584 -0.007252 -1.0154343 0.07041 -1.03450 0.51442
20 -0.57879 0.042849 -0.3660551 -0.15019 -0.61357 0.10115
21 -0.67320 0.038875 0.1194956 0.17256 -0.14686 -0.12018
22 -0.71933 0.014694 0.2204186 0.13598 0.09459 -0.02068
23 -0.70438 0.735398 -0.6546250 -6.61523 -2.49441 -1.73215
24 -0.83976 0.390120 0.5605295 -4.38864 -2.56916 -0.96702
25 -0.68476 0.418842 -0.2860819 -2.80336 -0.37540 -3.93791
26 -0.75808 0.210204 0.5894091 -0.70004 -0.01880 -0.10779
27 -0.75046 0.100869 0.5531191 -0.12946 0.29164 0.11280
28 -0.77878 0.088976 0.7379012 0.05204 0.40940 0.43236
29 -0.60815 -0.203235 0.5522726 0.43621 0.15010 0.25618
30 -0.80860 -0.019592 0.6686542 0.88136 0.52744 0.16456plot(cca1)
cca2 <- cca(peces, ambient)
print(summary(cca2))
Call:
cca(X = peces, Y = ambient)
Partitioning of mean squared contingency coefficient:
Inertia Proportion
Total 1.1669 1.0000
Constrained 0.8377 0.7179
Unconstrained 0.3292 0.2821
Eigenvalues, and their contribution to the mean squared contingency coefficient
Importance of components:
CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7 CCA8 CCA9 CCA10
Eigenvalue 0.5345 0.1227 0.06876 0.04886 0.02746 0.01295 0.009775 0.00545 0.003523 0.00217
Proportion Explained 0.4580 0.1052 0.05892 0.04187 0.02353 0.01110 0.008380 0.00467 0.003020 0.00186
Cumulative Proportion 0.4580 0.5632 0.62211 0.66399 0.68752 0.69862 0.707000 0.71167 0.714690 0.71655
CCA11 CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9
Eigenvalue 0.001596 0.10182 0.05329 0.05021 0.03452 0.03000 0.01456 0.01226 0.008865 0.007317
Proportion Explained 0.001370 0.08726 0.04567 0.04303 0.02958 0.02571 0.01248 0.01050 0.007600 0.006270
Cumulative Proportion 0.717910 0.80517 0.85084 0.89387 0.92345 0.94917 0.96165 0.97215 0.979740 0.986010
CA10 CA11 CA12 CA13 CA14 CA15 CA16 CA17
Eigenvalue 0.00457 0.003873 0.002968 0.002148 0.001493 0.0008308 0.0003886 4.723e-05
Proportion Explained 0.00392 0.003320 0.002540 0.001840 0.001280 0.0007100 0.0003300 4.000e-05
Cumulative Proportion 0.98993 0.993250 0.995790 0.997630 0.998910 0.9996300 0.9999600 1.000e+00
Accumulated constrained eigenvalues
Importance of components:
CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7 CCA8 CCA9 CCA10
Eigenvalue 0.5345 0.1227 0.06876 0.04886 0.02746 0.01295 0.009775 0.00545 0.003523 0.00217
Proportion Explained 0.6380 0.1465 0.08207 0.05833 0.03278 0.01546 0.011670 0.00651 0.004210 0.00259
Cumulative Proportion 0.6380 0.7845 0.86656 0.92489 0.95767 0.97313 0.984790 0.99130 0.995500 0.99809
CCA11
Eigenvalue 0.001596
Proportion Explained 0.001910
Cumulative Proportion 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 -1.276782 1.35155 -0.012375 0.22531 -0.179903 0.094379
Satr -1.525689 -0.43466 -0.328892 0.23630 0.144768 -0.007892
Phph -1.221136 -0.19104 0.007043 -0.05474 0.018108 -0.045958
Neba -0.966876 -0.29832 0.078083 -0.12854 0.052918 0.061401
Thth -1.324767 1.38168 -0.151752 0.48930 -0.180045 -0.293303
Teso -0.895169 1.18994 0.050588 -0.06064 -0.162988 0.235364
Chna 0.494080 0.18453 0.118825 -0.10125 0.356934 0.081358
Chto 0.151333 0.43227 0.125378 -0.53252 0.352606 -0.021676
Lele -0.119548 0.03933 0.260802 -0.15326 -0.191334 0.051822
Lece -0.003793 -0.08117 0.386934 0.01045 -0.255979 0.006033
Baba 0.305425 0.28556 -0.108575 -0.18426 0.185070 0.114957
Spbi 0.354748 0.31834 -0.044857 -0.41401 0.222240 -0.351709
Gogo 0.262245 0.02464 0.094701 0.07675 0.113405 0.065630
Eslu 0.166490 -0.28428 0.007552 0.02723 -0.130462 -0.084917
Pefl 0.144865 -0.16017 0.054768 -0.26509 -0.145556 -0.168154
Rham 0.578999 0.07021 -0.304787 -0.12841 0.100704 -0.052385
Legi 0.620722 0.04340 -0.207869 -0.01401 0.030758 0.011737
Scer 0.523613 -0.14218 -0.008426 0.13359 -0.163790 -0.216274
Cyca 0.592932 0.06934 -0.382972 -0.05516 -0.071659 0.034195
Titi 0.295852 -0.18634 -0.010118 -0.14245 -0.070774 0.152197
Abbr 0.700227 -0.04107 -0.444469 0.08575 -0.065584 0.126693
Icme 0.779693 -0.08488 -0.700727 0.17060 -0.349148 -0.167956
Acce 0.758681 -0.07352 -0.075256 0.26356 -0.009589 0.100114
Ruru 0.380007 -0.14619 0.392859 -0.05620 -0.128640 -0.006855
Blbj 0.744602 -0.05553 -0.330245 0.11600 -0.050556 0.140966
Alal 0.670437 0.01773 0.410319 0.53876 0.271721 -0.064363
Anan 0.651162 0.01894 -0.384970 -0.05095 -0.032570 -0.058778
Site scores (weighted averages of species scores)
CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
1 -2.85448 -3.542243 -4.78349 4.83584 5.271517 -0.6094
2 -2.40317 -2.602684 -1.67506 0.98386 2.897990 -0.2515
3 -2.15182 -2.498007 -1.10107 0.37389 2.158658 -0.2276
4 -1.41353 -2.063451 -0.20347 -0.48937 0.292725 -0.8701
5 -0.20080 -1.272187 1.69105 -1.16361 -3.297892 -1.4784
6 -1.14732 -1.793445 0.68997 -0.76727 -0.632502 1.0056
7 -2.04292 -2.277225 -0.52553 0.22641 1.396340 0.6832
9 -0.31069 -1.317289 3.88257 -1.10418 -4.391402 1.6171
10 -1.37143 -1.426835 1.45628 -1.03158 -0.916454 1.2974
11 -2.21687 0.211582 -0.86950 2.02128 -0.186283 -2.3797
12 -2.24382 0.567984 -1.00620 2.14659 0.064873 -1.5851
13 -2.36193 2.360284 -1.40230 2.63669 -0.585878 -1.4910
14 -1.91679 2.553732 -0.73172 2.02824 -1.054392 -0.2921
15 -1.40724 1.948920 0.38348 0.44007 -1.601560 3.3146
16 -0.76771 1.491747 0.73233 -2.02643 -0.161016 3.1721
17 -0.32180 1.012062 0.60116 -2.04569 1.611913 -1.7428
18 -0.07148 0.812691 0.63263 -1.62433 1.139577 -1.7708
19 0.19279 0.099176 0.90109 -1.25404 1.701956 0.4343
20 0.59825 0.003113 0.64635 -0.59114 1.200796 -0.4261
21 0.70530 -0.074133 -0.03580 -0.19148 0.618312 0.1850
22 0.76014 -0.073194 -0.23365 -0.06468 -0.005157 0.9481
23 0.80314 -0.390997 5.81927 5.27872 1.445825 -2.5009
24 0.96586 -0.171744 3.04080 4.37524 2.477896 0.9084
25 0.72138 -0.433817 3.15322 3.71187 0.536863 -1.4876
26 0.82289 -0.272389 0.06034 1.06446 0.175249 0.7865
27 0.81044 -0.213067 -0.44897 0.48279 -0.250576 1.4377
28 0.84855 -0.199638 -0.85082 0.48169 -0.742223 0.6115
29 0.65716 0.130297 -0.84172 0.01666 -0.336119 -0.6828
30 0.86319 -0.098907 -1.18924 -0.16484 -0.840025 -1.8059
Site constraints (linear combinations of constraining variables)
CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
1 -3.32694 -2.89515 -3.29235 2.20626 2.3060 1.19734
2 -1.14185 -3.48021 -0.43333 -1.28383 2.3367 -0.31102
3 -1.93997 -2.25021 -0.99858 0.51805 0.6466 0.28492
4 -1.52691 -1.99021 -0.02728 -0.74518 -0.0490 -0.11014
5 -0.88266 -1.27553 2.02571 -0.61079 -2.4324 -0.61528
6 -1.64941 -2.17812 -0.45378 0.86544 1.3469 -0.17736
7 -1.99263 -1.43304 -0.43014 0.89711 -1.5779 0.09591
9 0.13595 -1.35685 2.65394 -2.09948 -2.8253 -0.16589
10 -1.30135 -0.70616 0.02396 -0.02439 -0.2340 0.56841
11 -2.14664 1.68069 -0.44700 -0.32485 -1.5256 0.75702
12 -1.31891 0.71524 0.03340 0.39201 1.2446 -1.01908
13 -1.57343 1.39536 -0.04734 0.87388 -0.3098 -0.48242
14 -1.96408 1.99860 -0.50752 1.54706 -0.5462 -0.09997
15 -1.38328 1.80655 -0.17564 0.15301 -0.7491 0.98224
16 -0.44297 0.57049 0.29502 -0.89002 -0.1082 1.20984
17 -0.16066 1.13332 0.97402 -0.97270 0.5673 -1.34255
18 -0.13172 0.68153 0.77466 -1.17474 0.4923 -0.06227
19 -0.31662 0.78989 0.20453 -0.49484 1.1835 0.33682
20 0.27681 0.25870 0.29757 -0.98233 1.5082 -0.61280
21 0.72426 -0.11812 0.28673 -0.81779 0.9103 0.70093
22 0.42432 0.18792 -0.10587 0.69590 0.2200 1.32655
23 0.08867 0.16111 2.12318 6.90639 1.5586 -1.01857
24 1.67581 0.01813 3.09214 1.76719 -0.4168 -0.47757
25 0.82273 -0.77842 3.79368 4.54032 1.8147 -2.08635
26 0.91779 -0.27125 0.64570 0.49523 -0.2030 1.35326
27 0.99628 -0.45687 -0.45261 0.38428 -0.1698 1.18499
28 0.96393 -0.23682 -0.80926 0.09871 -0.3918 0.49065
29 0.54853 0.00564 -1.12139 -0.08810 -0.1117 -1.83093
30 0.89306 0.01746 -1.10304 0.25786 -1.0940 -0.84974
Biplot scores for constraining variables
CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
das 0.8505 0.20713 -0.36616 0.21848 -0.05812 -0.122225
alt -0.7829 -0.51983 0.20652 -0.15363 -0.12246 0.003771
slo -0.6757 -0.38134 0.06041 -0.02902 0.06942 0.276108
flo 0.6712 0.19931 -0.47854 0.18667 -0.15433 -0.386319
pH -0.1632 0.26541 -0.18504 0.17477 -0.34042 0.310417
har 0.5268 0.47813 -0.16715 0.19889 -0.43653 -0.386105
pho 0.4475 -0.02641 0.38275 0.58922 0.02700 -0.110983
nit 0.6805 0.19160 0.18329 0.15906 0.25741 0.115838
amm 0.4378 -0.08809 0.53506 0.47050 0.21034 -0.174471
oxy -0.7854 0.36744 -0.27958 -0.29226 0.23381 -0.052042
bdo 0.4819 -0.16869 0.50336 0.63234 -0.05626 -0.025082plot(cca2)
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