Análisis multivariante en R

Diego Nieto Lugilde

Universidad de Córdoba (España)

Preparación de datos

Análisis multivariante usa datos tabulados

Matriz de comunidades (sitios x especies)

	sp_1	sp_2	…	sp_n
site_1	1	0	…	1
site_2	0	0	…	1
…	…	…	…	…
site_n	0	1	…	1

También los datos de las variables ambientales

Matriz de variables (sitios x variables)

	v_1	v_2	…	v_n
site_1	1	0	…	1
site_2	0	0	…	1
…	…	…	…	…
site_n	0	1	…	1

Cargando de datos en R

library(openxlsx)
com <- read.xlsx("data/Wilson_Latorre/Data_multi_bio_R_course.xlsx", sheet = 1, rowNames = TRUE)
head(com)

         Acanthagrion Alluaudomyia Anchytarsus Aquarius Axarus Brechmorhoga
SC1_SU20            1            0           0        0      1            0
SC2_SU20            0            0           0        0      0            0
SC3_SU20            2            0           0        0      0            0
SC4_SU20           13            0           0        0      0           15
BA1_SU20           11            0           0        0      0            0
BA2_SU20            6            0           0        0      0            0
         Buenoa Charmatometra Cylloepus Erythemis Eurygerris Halobatopsis
SC1_SU20      0             0         0         0          3            0
SC2_SU20      0             0         0         1         50            0
SC3_SU20      0             0         0         2         24            0
SC4_SU20      0             0         0         0          1            0
BA1_SU20     50             0         0         0          0            0
BA2_SU20     19             0         0         0          0            0
         Hebrus Helochares Hetaerina Heterelmis Hexatoma Husseyella Hydrometra
SC1_SU20      0          0         0          0        0          0          0
SC2_SU20      0          0         0          0        0          0          0
SC3_SU20      0          0         0          0        0          0          0
SC4_SU20      0          0         0          0        0          0          0
BA1_SU20      0          0         1          0        0          0          0
BA2_SU20      0          0         3          0        0          0          0
         Hydroscapha Laccodytes Leptohyphes Leptonema Limnocoris Limnogonus
SC1_SU20           0          0           0         0          0          0
SC2_SU20           0          0           0         0          0          0
SC3_SU20           0          0           0         0          0          0
SC4_SU20           0          0           0         0          0          0
BA1_SU20           0         46           1         1          3          0
BA2_SU20           0         70           0         1          3          0
         Macrogynoplax Macrothemis Mesovelia Microvelia Paracloeodes Pelocoris
SC1_SU20             0           1         0          0            0         9
SC2_SU20             0           0         0          0            0         3
SC3_SU20             0           0         0          0            0         6
SC4_SU20             0           0         0          0            0         0
BA1_SU20             1           0         0          0            0         5
BA2_SU20             0           0         0          0            0         1
         Phyllogomphoides Phylloicus Rhagovelia Scirtes Simulium Stridulivelia
SC1_SU20                0          8          0       0        0             0
SC2_SU20                0          0          0       0        0             0
SC3_SU20                0          1          0       0        0             0
SC4_SU20                0          0          0       0        0             0
BA1_SU20                4         11         32       0        0             0
BA2_SU20                0          9          0       0        0             0
         Telmatometra Telmatometroides Thraulodes Tipula Tricorythodes
SC1_SU20            0                0          0      0             0
SC2_SU20            0                0          0      0             0
SC3_SU20            0                0          0      0             0
SC4_SU20            0                0          0      0             0
BA1_SU20            0                0         26      0             1
BA2_SU20            0                0         56      0             5
         Melanoides Lymnaea Pomacea Pseudothelphusidae Hyalella
SC1_SU20         69      13       8                  0        0
SC2_SU20          0       0       5                  0        0
SC3_SU20          0       1       0                  0        0
SC4_SU20          0       0       0                  2        0
BA1_SU20          0       0       0                  0        0
BA2_SU20          0       0       0                  3        0

env <- read.xlsx("data/Wilson_Latorre/Data_multi_env_R_course.xlsx", sheet = 1, rowNames = TRUE)
head(env)

         N-NO3- N-NH3 N-NO2- PO43-    pH    DO    EC   NTU    T°C
SC1_SU20   0.02  0.09  0.003  1.20 9.165 1.840 489.0  8.10 22.180
SC2_SU20   0.02  0.10  0.003  1.12 9.230 1.860 489.0  8.55 22.495
SC3_SU20   0.02  0.13  0.005  3.86 9.115 1.905 472.0  7.70 23.035
SC4_SU20   0.02  0.18  0.003  4.09 8.745 1.985 483.5  8.15 22.445
BA1_SU20   0.05  0.03  0.006  0.73 8.200 5.950 441.5 11.40 19.300
BA2_SU20   0.04  0.10  0.005  0.72 8.940 5.950 166.5 11.85 19.945
         Current.velocity Average.depth Average.width
SC1_SU20        0.3454020         0.055         0.300
SC2_SU20        0.1731571         0.055         0.400
SC3_SU20        0.1848344         0.050         0.825
SC4_SU20        0.4827096         0.025         0.130
BA1_SU20        0.2882227         0.065         0.140
BA2_SU20        0.2490695         0.025         0.255

Los nombres de especies largos pueden saturar los gráficos

• Si la identidad es irrelevante: usar nombres genéricos
  • Quercus ilex: SP_1
• Si la identidad de la especie es relevante: acortar
  • Quercus ilex: Q_ILEX
• Cornell Ecology Program (CEP) proporciona una abreviatura estandarizada:
  • 8 caracteres: 4 primeros del género y 4 de la especie:
  • Quercus ilex: QUERILEX

Transformación de valores de dominancia-abundancia

Índice Braun-Blanquet	Valor de Van deer Maarel
ausencia	0
r	1
+	2
1	3
2m	4
2a	5
2b	6
3	7
4	8
5	9

Datos de presencia-ausencia

Los análisis con datos de presencia-ausencia suelen ser más robustos que los de abundancia o cobertura

pres <- ifelse(com > 0, 1, 0)
head(pres)

         Acanthagrion Alluaudomyia Anchytarsus Aquarius Axarus Brechmorhoga
SC1_SU20            1            0           0        0      1            0
SC2_SU20            0            0           0        0      0            0
SC3_SU20            1            0           0        0      0            0
SC4_SU20            1            0           0        0      0            1
BA1_SU20            1            0           0        0      0            0
BA2_SU20            1            0           0        0      0            0
         Buenoa Charmatometra Cylloepus Erythemis Eurygerris Halobatopsis
SC1_SU20      0             0         0         0          1            0
SC2_SU20      0             0         0         1          1            0
SC3_SU20      0             0         0         1          1            0
SC4_SU20      0             0         0         0          1            0
BA1_SU20      1             0         0         0          0            0
BA2_SU20      1             0         0         0          0            0
         Hebrus Helochares Hetaerina Heterelmis Hexatoma Husseyella Hydrometra
SC1_SU20      0          0         0          0        0          0          0
SC2_SU20      0          0         0          0        0          0          0
SC3_SU20      0          0         0          0        0          0          0
SC4_SU20      0          0         0          0        0          0          0
BA1_SU20      0          0         1          0        0          0          0
BA2_SU20      0          0         1          0        0          0          0
         Hydroscapha Laccodytes Leptohyphes Leptonema Limnocoris Limnogonus
SC1_SU20           0          0           0         0          0          0
SC2_SU20           0          0           0         0          0          0
SC3_SU20           0          0           0         0          0          0
SC4_SU20           0          0           0         0          0          0
BA1_SU20           0          1           1         1          1          0
BA2_SU20           0          1           0         1          1          0
         Macrogynoplax Macrothemis Mesovelia Microvelia Paracloeodes Pelocoris
SC1_SU20             0           1         0          0            0         1
SC2_SU20             0           0         0          0            0         1
SC3_SU20             0           0         0          0            0         1
SC4_SU20             0           0         0          0            0         0
BA1_SU20             1           0         0          0            0         1
BA2_SU20             0           0         0          0            0         1
         Phyllogomphoides Phylloicus Rhagovelia Scirtes Simulium Stridulivelia
SC1_SU20                0          1          0       0        0             0
SC2_SU20                0          0          0       0        0             0
SC3_SU20                0          1          0       0        0             0
SC4_SU20                0          0          0       0        0             0
BA1_SU20                1          1          1       0        0             0
BA2_SU20                0          1          0       0        0             0
         Telmatometra Telmatometroides Thraulodes Tipula Tricorythodes
SC1_SU20            0                0          0      0             0
SC2_SU20            0                0          0      0             0
SC3_SU20            0                0          0      0             0
SC4_SU20            0                0          0      0             0
BA1_SU20            0                0          1      0             1
BA2_SU20            0                0          1      0             1
         Melanoides Lymnaea Pomacea Pseudothelphusidae Hyalella
SC1_SU20          1       1       1                  0        0
SC2_SU20          0       0       1                  0        0
SC3_SU20          0       1       0                  0        0
SC4_SU20          0       0       0                  1        0
BA1_SU20          0       0       0                  0        0
BA2_SU20          0       0       0                  1        0

Eliminar especies con pocas presencias

Puede ser recomendable eliminar especies poco prevalentes que aportan “ruido” y poca señal al análisis.

apply(com, MARGIN = 2, FUN = sum)

      Acanthagrion       Alluaudomyia        Anchytarsus           Aquarius 
                52                 10                 29                  8 
            Axarus       Brechmorhoga             Buenoa      Charmatometra 
                10                 26                107                 75 
         Cylloepus          Erythemis         Eurygerris       Halobatopsis 
                44                  7                185                222 
            Hebrus         Helochares          Hetaerina         Heterelmis 
               144                  9                 13                  6 
          Hexatoma         Husseyella         Hydrometra        Hydroscapha 
                20                668                  7                 22 
        Laccodytes        Leptohyphes          Leptonema         Limnocoris 
               397                223                203                 19 
        Limnogonus      Macrogynoplax        Macrothemis          Mesovelia 
                46                 50                  5                 25 
        Microvelia       Paracloeodes          Pelocoris   Phyllogomphoides 
               140                 39                 64                 65 
        Phylloicus         Rhagovelia            Scirtes           Simulium 
                74               1859                  6                 17 
     Stridulivelia       Telmatometra   Telmatometroides         Thraulodes 
               240                 47                 30                441 
            Tipula      Tricorythodes         Melanoides            Lymnaea 
                 6                 25                 69                 14 
           Pomacea Pseudothelphusidae           Hyalella 
                13                  9                717 

species_abundance <- apply(com, MARGIN = 2, FUN = sum)

which(species_abundance < 5)

named integer(0)

Estandarización de los datos ambientales

Suele ser recomendable para evitar falsas dominancias de unas variables sobre otras por sus diferencias de rangos de valores.

env <- scale(env)
head(env)

             N-NO3-       N-NH3      N-NO2-      PO43-         pH         DO
SC1_SU20 -0.7648842 -0.42121733 -0.83185846  0.2149981  1.4675714 -1.4774632
SC2_SU20 -0.7648842 -0.07065934 -0.83185846  0.1187752  1.5955475 -1.4673644
SC3_SU20 -0.7648842  0.98101460 -0.29136159  3.4144111  1.3691283 -1.4446421
SC4_SU20 -0.7648842  2.73380451 -0.83185846  3.6910521  0.6406493 -1.4042469
BA1_SU20 -0.4582918 -2.52456522 -0.02111316 -0.3503117 -0.4323806  0.5978414
BA2_SU20 -0.5604893 -0.07065934 -0.29136159 -0.3623395  1.0245774  0.5978414
                 EC        NTU        T°C Current.velocity Average.depth
SC1_SU20 -0.1316708 -0.5229457  0.5869094       -0.5270000     0.4145403
SC2_SU20 -0.1316708 -0.5024451  0.8937583       -0.5359574     0.4145403
SC3_SU20 -0.1740674 -0.5411686  1.4197850       -0.5353502     0.2341829
SC4_SU20 -0.1453873 -0.5206679  0.8450522       -0.5198595    -0.6676043
BA1_SU20 -0.2501317 -0.3726073 -2.2185663       -0.5299736     0.7752552
BA2_SU20 -0.9359579 -0.3521066 -1.5902567       -0.5320097    -0.6676043
         Average.width
SC1_SU20   -0.52030131
SC2_SU20   -0.41396478
SC3_SU20    0.03796546
SC4_SU20   -0.70107341
BA1_SU20   -0.69043976
BA2_SU20   -0.56815275

Análisis de ordenación en R

Para el análisis de vegetación en R hay un paquete muy útil: vegan

#install.packages("vegan")
library(vegan)

Análisis de componentes principales (PCA)

Aunque parezca confuso, se usa la función rda.

Note

Así se juntan la aproximación unconstrained y su equivalente constrained en la misma función. Si se especifican variables ambientales se ejecuta la versión constrained. Si no se especifican se ejecuta la versión unconstrained.

library(vegan)
com_pca <- rda(com)
summary(com_pca)

Call:
rda(X = com) 

Partitioning of variance:
              Inertia Proportion
Total            4519          1
Unconstrained    4519          1

Eigenvalues, and their contribution to the variance 

Importance of components:
                            PC1     PC2       PC3       PC4       PC5       PC6
Eigenvalue            2187.4619 799.757 384.62383 301.25474 213.50619 170.54819
Proportion Explained     0.4841   0.177   0.08511   0.06666   0.04725   0.03774
Cumulative Proportion    0.4841   0.661   0.74614   0.81280   0.86005   0.89779
                            PC7      PC8      PC9    PC10      PC11     PC12
Eigenvalue            121.86627 78.76660 63.64766 51.5328 41.933627 30.81886
Proportion Explained    0.02697  0.01743  0.01408  0.0114  0.009279  0.00682
Cumulative Proportion   0.92475  0.94218  0.95627  0.9677  0.976950  0.98377
                           PC13      PC14     PC15     PC16     PC17     PC18
Eigenvalue            19.293953 13.977440 7.478486 6.301116 5.325404 4.895010
Proportion Explained   0.004269  0.003093 0.001655 0.001394 0.001178 0.001083
Cumulative Proportion  0.988039  0.991132 0.992787 0.994181 0.995360 0.996443
                           PC19      PC20      PC21      PC22      PC23
Eigenvalue            2.9642153 1.9436469 1.8133701 1.5310380 1.1604214
Proportion Explained  0.0006559 0.0004301 0.0004013 0.0003388 0.0002568
Cumulative Proportion 0.9970987 0.9975288 0.9979301 0.9982689 0.9985257
                           PC24     PC25      PC26      PC27      PC28     PC29
Eigenvalue            0.9742495 0.881045 0.8053291 0.7310154 0.6134854 0.560428
Proportion Explained  0.0002156 0.000195 0.0001782 0.0001618 0.0001358 0.000124
Cumulative Proportion 0.9987413 0.998936 0.9991144 0.9992762 0.9994119 0.999536
                           PC30      PC31      PC32      PC33      PC34
Eigenvalue            0.4692335 3.608e-01 3.350e-01 2.496e-01 0.1893600
Proportion Explained  0.0001038 7.985e-05 7.413e-05 5.523e-05 0.0000419
Cumulative Proportion 0.9996398 9.997e-01 9.998e-01 9.998e-01 0.9998909
                           PC35      PC36      PC37      PC38      PC39
Eigenvalue            0.1608567 7.868e-02 6.290e-02 5.185e-02 3.865e-02
Proportion Explained  0.0000356 1.741e-05 1.392e-05 1.147e-05 8.552e-06
Cumulative Proportion 0.9999265 9.999e-01 1.000e+00 1.000e+00 1.000e+00
                           PC40      PC41      PC42      PC43      PC44
Eigenvalue            2.666e-02 2.308e-02 2.147e-02 1.152e-02 1.093e-02
Proportion Explained  5.899e-06 5.108e-06 4.750e-06 2.549e-06 2.419e-06
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
                           PC45      PC46      PC47
Eigenvalue            4.245e-03 1.759e-03 4.155e-04
Proportion Explained  9.395e-07 3.892e-07 9.193e-08
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00

Análisis de componentes principales (PCA)

Recordad que se puede aplicar sobre las variables ambientales.

env_pca <- rda(env)
summary(env_pca)

Call:
rda(X = env) 

Partitioning of variance:
              Inertia Proportion
Total              12          1
Unconstrained      12          1

Eigenvalues, and their contribution to the variance 

Importance of components:
                         PC1    PC2    PC3    PC4     PC5    PC6     PC7
Eigenvalue            2.3173 1.8963 1.7049 1.4959 0.96866 0.9204 0.68192
Proportion Explained  0.1931 0.1580 0.1421 0.1247 0.08072 0.0767 0.05683
Cumulative Proportion 0.1931 0.3511 0.4932 0.6179 0.69859 0.7753 0.83212
                          PC8     PC9    PC10   PC11    PC12
Eigenvalue            0.61606 0.48107 0.36300 0.3000 0.25449
Proportion Explained  0.05134 0.04009 0.03025 0.0250 0.02121
Cumulative Proportion 0.88345 0.92354 0.95379 0.9788 1.00000

Check also further results with the summary() function

summary(env_pca)

Call:
rda(X = env) 

Partitioning of variance:
              Inertia Proportion
Total              12          1
Unconstrained      12          1

Eigenvalues, and their contribution to the variance 

Importance of components:
                         PC1    PC2    PC3    PC4     PC5    PC6     PC7
Eigenvalue            2.3173 1.8963 1.7049 1.4959 0.96866 0.9204 0.68192
Proportion Explained  0.1931 0.1580 0.1421 0.1247 0.08072 0.0767 0.05683
Cumulative Proportion 0.1931 0.3511 0.4932 0.6179 0.69859 0.7753 0.83212
                          PC8     PC9    PC10   PC11    PC12
Eigenvalue            0.61606 0.48107 0.36300 0.3000 0.25449
Proportion Explained  0.05134 0.04009 0.03025 0.0250 0.02121
Cumulative Proportion 0.88345 0.92354 0.95379 0.9788 1.00000

env_pca$CA$v

                         PC1         PC2         PC3        PC4         PC5
N-NO3-            0.32031223 -0.30211892 -0.20115934 -0.3011722  0.07352871
N-NH3             0.38055599 -0.10874414  0.06674836  0.1737745 -0.34671681
N-NO2-            0.14216941 -0.24123068  0.07215036 -0.6265295  0.03294995
PO43-             0.22040311  0.33312846  0.37683614  0.1266316 -0.33052524
pH                0.34428190  0.15555771  0.22097160  0.2252069  0.49254123
DO               -0.29005123  0.17856591 -0.41796570 -0.2692005 -0.23762856
EC                0.54134932 -0.11407844 -0.13751211 -0.1652052  0.05638408
NTU               0.13289053 -0.09044532 -0.56364492  0.2927723 -0.03682056
T°C               0.34207065  0.39796985 -0.03942349 -0.1940970 -0.44656615
Current.velocity  0.20839179  0.31631306 -0.48151546  0.2107636  0.23052042
Average.depth     0.04695159  0.33376375  0.08051027 -0.2934169  0.45351453
Average.width    -0.08811863  0.52973732 -0.08857890 -0.2571751  0.04704061
                         PC6         PC7          PC8         PC9        PC10
N-NO3-            0.18279920 -0.52856946  0.192354225  0.44790260  0.21963829
N-NH3            -0.59741653  0.08862608  0.248271756  0.24949366 -0.42719362
N-NO2-           -0.01951778  0.22508183 -0.432599283 -0.23392763 -0.27557405
PO43-             0.07077806 -0.45981202 -0.378863735 -0.19106715 -0.02789961
pH                0.13994132  0.23679338 -0.388190667  0.52034972 -0.09622764
DO               -0.26047421  0.10513758 -0.368178185  0.40362889  0.02234876
EC                0.11383982  0.18180895  0.149577125 -0.31550699 -0.04185242
NTU               0.07827562 -0.35387712 -0.363885722 -0.16045071 -0.30357964
T°C               0.12514753  0.19636776  0.002753015  0.08331696  0.41705874
Current.velocity -0.11407622  0.22242606  0.057290713 -0.22033095  0.18596813
Average.depth    -0.58530829 -0.36398905  0.031335050 -0.14771722  0.11328142
Average.width     0.35568161 -0.06885220  0.354084910  0.09813438 -0.60623340
                        PC11        PC12
N-NO3-           -0.26170681  0.04897385
N-NH3            -0.08368694  0.10169295
N-NO2-           -0.23121896  0.31694592
PO43-            -0.33981809 -0.24581334
pH                0.09255617 -0.01383574
DO               -0.03612001 -0.44852716
EC                0.23162854 -0.64900704
NTU               0.36829809  0.22820022
T°C               0.34146368  0.36640352
Current.velocity -0.60273149  0.12213400
Average.depth     0.27497155  0.04275909
Average.width    -0.03014773  0.02703834

Draw the biplot

plot(env_pca)

Análisis de redundancia (RDA)

com_rda <- rda(com, env)
summary(com_rda)

Call:
rda(X = com, Y = env) 

Partitioning of variance:
              Inertia Proportion
Total            4519     1.0000
Constrained      1615     0.3574
Unconstrained    2904     0.6426

Eigenvalues, and their contribution to the variance 

Importance of components:
                           RDA1      RDA2     RDA3    RDA4      RDA5      RDA6
Eigenvalue            1021.6237 260.56676 177.1408 43.8355 35.169916 25.584748
Proportion Explained     0.2261   0.05766   0.0392  0.0097  0.007783  0.005662
Cumulative Proportion    0.2261   0.28373   0.3229  0.3326  0.340410  0.346072
                           RDA7      RDA8      RDA9     RDA10     RDA11
Eigenvalue            18.341747 13.369385 11.040412 3.7617208 2.5882886
Proportion Explained   0.004059  0.002958  0.002443 0.0008324 0.0005727
Cumulative Proportion  0.350131  0.353089  0.355532 0.3563647 0.3569374
                          RDA12       PC1      PC2       PC3       PC4
Eigenvalue            2.2840683 1262.9045 637.6078 223.08199 212.75033
Proportion Explained  0.0005054    0.2795   0.1411   0.04936   0.04708
Cumulative Proportion 0.3574428    0.6369   0.7780   0.82736   0.87444
                            PC5     PC6      PC7      PC8      PC9      PC10
Eigenvalue            151.67398 94.0099 73.16352 70.33941 50.33677 33.160450
Proportion Explained    0.03356  0.0208  0.01619  0.01557  0.01114  0.007338
Cumulative Proportion   0.90800  0.9288  0.94500  0.96056  0.97170  0.979038
                           PC11      PC12      PC13    PC14     PC15     PC16
Eigenvalue            24.367712 19.710238 15.384744 8.54049 6.047435 4.672616
Proportion Explained   0.005392  0.004362  0.003404 0.00189 0.001338 0.001034
Cumulative Proportion  0.984430  0.988792  0.992196 0.99409 0.995424 0.996458
                           PC17      PC18      PC19      PC20     PC21
Eigenvalue            3.4286141 2.3151886 1.8779793 1.6322417 1.052929
Proportion Explained  0.0007587 0.0005123 0.0004156 0.0003612 0.000233
Cumulative Proportion 0.9972170 0.9977293 0.9981449 0.9985061 0.998739
                           PC22      PC23    PC24      PC25      PC26      PC27
Eigenvalue            0.8519737 0.8149331 0.67776 0.5757515 0.4997553 4.234e-01
Proportion Explained  0.0001885 0.0001803 0.00015 0.0001274 0.0001106 9.369e-05
Cumulative Proportion 0.9989276 0.9991079 0.99926 0.9993853 0.9994959 9.996e-01
                           PC28      PC29      PC30      PC31      PC32
Eigenvalue            3.780e-01 3.652e-01 2.692e-01 2.006e-01 1.576e-01
Proportion Explained  8.365e-05 8.082e-05 5.958e-05 4.439e-05 3.489e-05
Cumulative Proportion 9.997e-01 9.998e-01 9.998e-01 9.999e-01 9.999e-01
                           PC33      PC34      PC35      PC36      PC37
Eigenvalue            0.1288085 1.083e-01 6.710e-02 0.0492444 4.341e-02
Proportion Explained  0.0000285 2.396e-05 1.485e-05 0.0000109 9.605e-06
Cumulative Proportion 0.9999214 9.999e-01 1.000e+00 0.9999711 1.000e+00
                           PC38      PC39      PC40      PC41      PC42
Eigenvalue            2.286e-02 2.151e-02 1.764e-02 1.220e-02 6.451e-03
Proportion Explained  5.058e-06 4.759e-06 3.903e-06 2.699e-06 1.428e-06
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
                           PC43      PC44      PC45      PC46      PC47
Eigenvalue            2.971e-03 2.318e-03 1.145e-03 9.616e-05 4.021e-05
Proportion Explained  6.575e-07 5.130e-07 2.533e-07 2.128e-08 8.898e-09
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00

Accumulated constrained eigenvalues
Importance of components:
                           RDA1     RDA2     RDA3     RDA4     RDA5     RDA6
Eigenvalue            1021.6237 260.5668 177.1408 43.83553 35.16992 25.58475
Proportion Explained     0.6325   0.1613   0.1097  0.02714  0.02177  0.01584
Cumulative Proportion    0.6325   0.7938   0.9034  0.93058  0.95235  0.96819
                          RDA7      RDA8      RDA9    RDA10    RDA11    RDA12
Eigenvalue            18.34175 13.369385 11.040412 3.761721 2.588289 2.284068
Proportion Explained   0.01135  0.008277  0.006835 0.002329 0.001602 0.001414
Cumulative Proportion  0.97954  0.987820  0.994655 0.996984 0.998586 1.000000

Análisis de correspondencia (CA)

Aunque parezca confuso, para CA y CCA se usa la función cca.

Note

Así se juntan la aproximación unconstrained y su equivalente constrained en la misma función. Si se especifican variables ambientales se ejecuta la versión constrained. Si no se especifican se ejecuta la versión unconstrained.

com_ca <- cca(com)
summary(com_ca)

Call:
cca(X = com) 

Partitioning of scaled Chi-square:
              Inertia Proportion
Total           5.615          1
Unconstrained   5.615          1

Eigenvalues, and their contribution to the scaled Chi-square 

Importance of components:
                         CA1    CA2     CA3     CA4     CA5     CA6     CA7
Eigenvalue            0.7913 0.5869 0.54980 0.50433 0.43309 0.39883 0.37028
Proportion Explained  0.1409 0.1045 0.09791 0.08981 0.07713 0.07103 0.06594
Cumulative Proportion 0.1409 0.2454 0.34335 0.43316 0.51029 0.58132 0.64726
                          CA8     CA9    CA10    CA11    CA12    CA13   CA14
Eigenvalue            0.34145 0.21422 0.20194 0.16032 0.14161 0.11605 0.1022
Proportion Explained  0.06081 0.03815 0.03596 0.02855 0.02522 0.02067 0.0182
Cumulative Proportion 0.70807 0.74622 0.78218 0.81073 0.83595 0.85662 0.8748
                         CA15    CA16    CA17    CA18     CA19     CA20
Eigenvalue            0.08694 0.07948 0.07266 0.05866 0.053491 0.043814
Proportion Explained  0.01548 0.01415 0.01294 0.01045 0.009526 0.007803
Cumulative Proportion 0.89030 0.90445 0.91739 0.92784 0.937364 0.945166
                          CA21     CA22     CA23     CA24     CA25     CA26
Eigenvalue            0.038661 0.036152 0.030367 0.026522 0.025407 0.022898
Proportion Explained  0.006885 0.006438 0.005408 0.004723 0.004525 0.004078
Cumulative Proportion 0.952051 0.958490 0.963897 0.968621 0.973145 0.977223
                         CA27     CA28     CA29     CA30     CA31     CA32
Eigenvalue            0.01965 0.016691 0.015062 0.012925 0.012160 0.009854
Proportion Explained  0.00350 0.002972 0.002682 0.002302 0.002166 0.001755
Cumulative Proportion 0.98072 0.983696 0.986378 0.988680 0.990846 0.992600
                          CA33     CA34     CA35      CA36      CA37      CA38
Eigenvalue            0.007995 0.006898 0.005684 0.0053291 0.0037969 0.0034624
Proportion Explained  0.001424 0.001228 0.001012 0.0009491 0.0006762 0.0006166
Cumulative Proportion 0.994024 0.995253 0.996265 0.9972139 0.9978901 0.9985067
                           CA39      CA40      CA41      CA42      CA43
Eigenvalue            0.0024043 0.0019048 0.0016968 0.0010102 0.0007473
Proportion Explained  0.0004282 0.0003392 0.0003022 0.0001799 0.0001331
Cumulative Proportion 0.9989349 0.9992741 0.9995763 0.9997562 0.9998893
                           CA44      CA45      CA46
Eigenvalue            4.539e-04 1.402e-04 2.761e-05
Proportion Explained  8.084e-05 2.497e-05 4.917e-06
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00

Análisis de correspondencia sin tendencia (DCA)

Para DCA se usa la función decorana

com_dca <- decorana(com)
summary(com_dca)

Call:
decorana(veg = com) 

Detrended correspondence analysis with 26 segments.
Rescaling of axes with 4 iterations.
Total inertia (scaled Chi-square): 5.6152 

                       DCA1   DCA2   DCA3   DCA4
Eigenvalues          0.6267 0.4767 0.4001 0.2539
Additive Eigenvalues 0.6267 0.4770 0.4038 0.2426
Decorana values      0.7913 0.5363 0.2942 0.1418
Axis lengths         5.9777 3.7231 2.6577 2.9976

Species scores:

                       DCA1     DCA2     DCA3     DCA4 Totals
Acanthagrion        1.60694  0.80799 -0.94470  1.62819     52
Alluaudomyia       -0.94294 -1.57088 -0.02629  0.31808     10
Anchytarsus        -0.07506 -1.72338  0.70040 -0.45851     29
Aquarius            0.40296 -1.33548  1.00732  1.82158      8
Axarus              3.04490 -1.11159  1.99289  3.99533     10
Brechmorhoga        1.34984  0.89799 -1.64998  2.84341     26
Buenoa              0.77981  1.47284 -0.85987 -0.59710    107
Charmatometra       0.05812 -1.81577  2.19881  2.05810     75
Cylloepus          -0.44157  0.89475 -1.37892 -0.61169     44
Erythemis           2.29913  0.48441 -0.04217 -0.37551      7
Eurygerris          2.90304 -0.75832  0.43202 -0.07082    185
Halobatopsis        0.14318 -2.39065 -0.30604 -0.71264    222
Hebrus             -0.09256  2.27250  0.07982  0.48632    144
Helochares          0.46612 -1.34812 -1.45841 -2.27319      9
Hetaerina           0.36145  0.54776  0.20102  1.11532     13
Heterelmis          0.46851 -1.50301  1.28216  1.36257      6
Hexatoma           -0.76598 -0.37341 -0.98501  0.25350     20
Husseyella         -0.29053 -0.28605  0.81614  1.20557    668
Hydrometra          0.73719 -2.23726 -0.13384  2.07685      7
Hydroscapha        -0.90082 -0.04279  0.55010  0.08175     22
Laccodytes          0.36264  1.84142  0.20581 -1.34126    397
Leptohyphes        -0.02827 -1.55136 -1.47960 -0.39479    223
Leptonema          -0.33461 -1.30580 -2.27743 -0.23598    203
Limnocoris          0.44083  0.32063 -0.38631 -0.58065     19
Limnogonus          0.17554  0.92849  0.35293  0.72238     46
Macrogynoplax      -0.11301 -0.75510 -1.40697 -1.51651     50
Macrothemis         3.96646 -1.13131 -0.60431 -1.32666      5
Mesovelia          -0.08900 -1.73325 -0.32911 -1.22189     25
Microvelia         -0.30466  0.39074 -0.86141 -0.15164    140
Paracloeodes        0.50196 -2.44066 -0.55938  0.40920     39
Pelocoris           3.76501  0.83904  0.77848 -0.89325     64
Phyllogomphoides    0.53340  0.85773 -0.71772  1.11416     65
Phylloicus          3.17723  1.54971 -0.07132 -0.28145     74
Rhagovelia         -0.42625  0.22386  0.37998  0.28794   1859
Scirtes            -0.19769 -0.93088 -0.00465 -0.30551      6
Simulium            0.45319 -2.75161 -0.20844  0.98919     17
Stridulivelia       0.13763 -0.60301  2.24422 -2.09489    240
Telmatometra        0.81657 -1.69430  1.73028 -1.32355     47
Telmatometroides    0.63431 -1.82980  1.73766  1.26768     30
Thraulodes          0.10002 -0.46048 -1.81090 -0.59927    441
Tipula              0.07223 -0.11959 -0.15818 -1.33345      6
Tricorythodes       0.17402  1.00406 -0.06125 -1.59211     25
Melanoides          5.30945  0.43094 -0.10991  0.06094     69
Lymnaea             5.25643  0.45234 -0.15279 -0.06937     14
Pomacea             5.03341  0.36062  0.03959  0.49634     13
Pseudothelphusidae  1.00717  1.35258 -1.15401  1.85759      9
Hyalella           -1.42548  0.42734 -0.21153  0.05697    717

Site scores:

              DCA1      DCA2      DCA3      DCA4 Totals
SC1_SU20  4.881265  0.484420 -0.009538  0.009446    113
SC2_SU20  3.117171 -0.561206  0.408340 -0.069736     59
SC3_SU20  3.014132 -0.238291  0.356707 -0.136238     36
SC4_SU20  1.485652  0.836144 -1.255054  2.176194     31
BA1_SU20  0.619685  0.963733 -0.439317 -0.453271    193
BA2_SU20  0.532770  0.915387 -0.656103 -0.758346    176
BA3_SU20  0.596017  0.590823 -0.994171 -0.267610     57
BA4_SU20  0.569482  1.020375 -0.587405 -0.581567     71
PH1_SU20  0.612069 -0.087539 -0.432800  0.605615     45
PH2_SU20  0.273793 -0.187887 -0.297560  0.305555     36
PH3_SU20  0.444733  0.088630 -0.130518  0.359987     68
PH4_SU20  0.408826 -0.178944 -0.820253 -0.064872     26
SR1_SU20 -0.289085  0.318665  0.231492  0.158066    122
SR2_SU20 -0.143621  0.270827  0.287180  0.388874    124
SR3_SU20 -0.421506  0.036679  0.389022  0.554321    119
SR4_SU20 -0.392087  0.112754  0.438001  0.459636     75
SC1_WI21  0.478049 -1.561851 -0.580123 -0.227748     46
SC2_WI21  0.092825 -1.697692 -0.502059 -0.379706     68
SC3_WI21  0.294940 -2.078195 -0.374144 -0.464317     71
SC4_WI21  0.456235 -1.845152 -0.274663  0.166801     55
BA1_WI21  0.122181  0.250342  0.077459  0.031001     95
BA2_WI21 -0.110741  0.396852  0.387949  0.502887     96
BA3_WI21 -0.018977  1.644910  0.061230  0.196557    195
BA4_WI21 -0.232392  0.206557 -0.070286  0.042573    188
PH1_WI21 -0.063850 -0.443013 -0.779542 -0.220375    153
PH2_WI21 -0.087027 -0.626780 -1.325982 -0.328634    139
PH3_WI21 -0.134874 -0.752580 -1.465623 -0.231757    282
PH4_WI21 -0.124711 -0.662093 -1.175691 -0.296573    132
SR1_WI21 -1.096447  0.355960 -0.142925  0.088298    416
SR2_WI21 -0.636019  0.208604  0.182509  0.228090    315
SR3_WI21 -0.815715  0.324273 -0.007004  0.133088    213
SR4_WI21 -1.021240  0.244713 -0.030755  0.146740    220
SC1_SU21  1.300748 -0.657675  0.645779 -0.345399     65
SC2_SU21  0.480190 -0.937748  0.944185  0.508444     76
SC3_SU21  0.200722 -0.523454  1.086678 -0.492217    253
SC4_SU21  0.018660 -1.137162  0.310454 -0.136963    254
BA1_SU21  0.046227  0.124825  0.910566 -0.703536    215
BA2_SU21  0.340772  1.124662  0.260768 -0.821367    143
BA3_SU21  0.231572  0.778929  0.063940 -0.606947    128
BA4_SU21  0.223190 -0.109423 -0.114672 -0.070884     45
PH1_SU21  0.209328 -0.440538  0.764086  1.181556     60
PH2_SU21 -0.122650 -0.794680  1.192092  1.126296     68
PH3_SU21 -0.108634 -0.099184  0.309374  0.605623     70
PH4_SU21  0.135386 -0.324744  0.118454  0.313624     77
SR1_SU21 -0.596473  0.157355  0.331782  0.317332    165
SR2_SU21 -0.368040  0.124007  0.518913  0.256252    125
SR3_SU21 -0.640269  0.194007  0.206711  0.417934     27
SR4_SU21 -0.492074  0.119603  0.287259  0.373501     39
SC1_WI22 -0.130760 -0.541553 -1.204252 -0.264670      7
SC2_WI22  0.139095 -0.661341 -0.653872 -0.054844      8
SC3_WI22  0.942667 -1.642773  0.093241  0.313043     16
SC4_WI22  0.022940 -1.163443  0.519261  0.764566     11
BA1_WI22 -0.340531 -0.098189  0.655451  0.867493     19
BA2_WI22 -0.127921 -0.055474  0.707236  0.143585    148
BA3_WI22 -0.208027 -0.031350  0.833026 -0.154347     41
BA4_WI22  0.000322 -0.257762 -0.290759 -0.494023     34
PH1_WI22 -0.203525 -0.432576  0.201056  0.697941     56
PH2_WI22  0.194818 -0.145982 -0.161855 -0.074275     26
PH3_WI22 -0.095700 -0.465690 -1.066300 -0.374549     31
PH4_WI22 -0.350005 -0.102587  0.176635  0.321496      7
SR1_WI22 -0.385484 -0.013953  0.108685  0.281442     73
SR2_WI22 -0.364401 -0.070880  0.221186  0.340095     78
SR3_WI22 -0.371338  0.047677  0.328371  0.384036     70
SR4_WI22 -0.229623 -0.186450  0.122452  0.194482     37

Análisis de correspondencia canónica (CCA)

com_cca <- cca(com, env)
summary(com_cca)

Call:
cca(X = com, Y = env) 

Partitioning of scaled Chi-square:
              Inertia Proportion
Total           5.615     1.0000
Constrained     1.834     0.3266
Unconstrained   3.781     0.6734

Eigenvalues, and their contribution to the scaled Chi-square 

Importance of components:
                         CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
Eigenvalue            0.41771 0.34006 0.29475 0.23066 0.18126 0.13352 0.08256
Proportion Explained  0.07439 0.06056 0.05249 0.04108 0.03228 0.02378 0.01470
Cumulative Proportion 0.07439 0.13495 0.18744 0.22852 0.26080 0.28458 0.29928
                          CCA8     CCA9    CCA10    CCA11    CCA12    CA1
Eigenvalue            0.055432 0.041867 0.026178 0.016834 0.013166 0.6144
Proportion Explained  0.009872 0.007456 0.004662 0.002998 0.002345 0.1094
Cumulative Proportion 0.309150 0.316606 0.321268 0.324266 0.326611 0.4360
                          CA2     CA3     CA4     CA5     CA6     CA7     CA8
Eigenvalue            0.43728 0.42637 0.36174 0.33740 0.20865 0.17322 0.14728
Proportion Explained  0.07788 0.07593 0.06442 0.06009 0.03716 0.03085 0.02623
Cumulative Proportion 0.51390 0.58983 0.65425 0.71434 0.75150 0.78234 0.80857
                          CA9    CA10    CA11    CA12    CA13    CA14    CA15
Eigenvalue            0.13437 0.12059 0.10943 0.09414 0.08171 0.07113 0.05999
Proportion Explained  0.02393 0.02148 0.01949 0.01676 0.01455 0.01267 0.01068
Cumulative Proportion 0.83250 0.85398 0.87347 0.89023 0.90478 0.91745 0.92813
                          CA16     CA17     CA18     CA19     CA20     CA21
Eigenvalue            0.053018 0.043691 0.040397 0.039451 0.033512 0.028671
Proportion Explained  0.009442 0.007781 0.007194 0.007026 0.005968 0.005106
Cumulative Proportion 0.937576 0.945357 0.952551 0.959576 0.965544 0.970650
                          CA22    CA23     CA24     CA25     CA26     CA27
Eigenvalue            0.025489 0.02004 0.017119 0.015422 0.013192 0.012564
Proportion Explained  0.004539 0.00357 0.003049 0.002747 0.002349 0.002237
Cumulative Proportion 0.975190 0.97876 0.981808 0.984555 0.986904 0.989141
                          CA28     CA29     CA30     CA31     CA32      CA33
Eigenvalue            0.009859 0.009241 0.007809 0.007374 0.005651 0.0045789
Proportion Explained  0.001756 0.001646 0.001391 0.001313 0.001006 0.0008154
Cumulative Proportion 0.990897 0.992543 0.993934 0.995247 0.996253 0.9970687
                           CA34      CA35      CA36     CA37      CA38
Eigenvalue            0.0039677 0.0032689 0.0026354 0.001713 0.0016206
Proportion Explained  0.0007066 0.0005821 0.0004693 0.000305 0.0002886
Cumulative Proportion 0.9977753 0.9983574 0.9988268 0.999132 0.9994204
                           CA39      CA40      CA41      CA42      CA43
Eigenvalue            0.0012195 0.0008813 4.327e-04 3.753e-04 2.676e-04
Proportion Explained  0.0002172 0.0001569 7.706e-05 6.683e-05 4.766e-05
Cumulative Proportion 0.9996376 0.9997945 9.999e-01 9.999e-01 1.000e+00
                           CA44      CA45      CA46
Eigenvalue            5.434e-05 2.205e-05 1.826e-06
Proportion Explained  9.678e-06 3.926e-06 3.252e-07
Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00

Accumulated constrained eigenvalues
Importance of components:
                        CCA1   CCA2   CCA3   CCA4    CCA5   CCA6    CCA7
Eigenvalue            0.4177 0.3401 0.2948 0.2307 0.18126 0.1335 0.08256
Proportion Explained  0.2278 0.1854 0.1607 0.1258 0.09883 0.0728 0.04501
Cumulative Proportion 0.2278 0.4132 0.5739 0.6997 0.79850 0.8713 0.91632
                         CCA8    CCA9   CCA10    CCA11    CCA12
Eigenvalue            0.05543 0.04187 0.02618 0.016834 0.013166
Proportion Explained  0.03022 0.02283 0.01427 0.009179 0.007179
Cumulative Proportion 0.94654 0.96937 0.98364 0.992821 1.000000

PCA basado en transformaciones

Para ello se transforman los datos con la función decostand

com_hel <- decostand(com, 'hellinger')

com_tbpca <- rda(com_hel)
summary(com_tbpca)

Call:
rda(X = com_hel) 

Partitioning of variance:
              Inertia Proportion
Total          0.5544          1
Unconstrained  0.5544          1

Eigenvalues, and their contribution to the variance 

Importance of components:
                         PC1     PC2     PC3     PC4     PC5     PC6     PC7
Eigenvalue            0.1180 0.07567 0.05877 0.04761 0.03591 0.02468 0.02146
Proportion Explained  0.2129 0.13649 0.10600 0.08588 0.06477 0.04451 0.03871
Cumulative Proportion 0.2129 0.34939 0.45539 0.54127 0.60604 0.65055 0.68926
                          PC8     PC9    PC10    PC11    PC12    PC13     PC14
Eigenvalue            0.02019 0.01874 0.01605 0.01528 0.01348 0.01087 0.009842
Proportion Explained  0.03642 0.03380 0.02894 0.02757 0.02432 0.01960 0.017753
Cumulative Proportion 0.72569 0.75948 0.78843 0.81599 0.84031 0.85991 0.877662
                          PC15     PC16     PC17     PC18     PC19     PC20
Eigenvalue            0.008896 0.007634 0.007179 0.005634 0.004923 0.004014
Proportion Explained  0.016045 0.013771 0.012950 0.010162 0.008880 0.007241
Cumulative Proportion 0.893708 0.907478 0.920428 0.930590 0.939470 0.946710
                          PC21     PC22     PC23     PC24     PC25     PC26
Eigenvalue            0.003356 0.003065 0.002973 0.002440 0.002090 0.001947
Proportion Explained  0.006053 0.005528 0.005363 0.004402 0.003769 0.003511
Cumulative Proportion 0.952763 0.958291 0.963655 0.968056 0.971826 0.975337
                          PC27     PC28     PC29     PC30     PC31     PC32
Eigenvalue            0.001762 0.001668 0.001425 0.001291 0.001233 0.001150
Proportion Explained  0.003178 0.003008 0.002570 0.002329 0.002225 0.002074
Cumulative Proportion 0.978515 0.981523 0.984093 0.986422 0.988647 0.990720
                           PC33      PC34      PC35      PC36      PC37
Eigenvalue            0.0008938 0.0008634 0.0006126 0.0005303 0.0004952
Proportion Explained  0.0016121 0.0015574 0.0011049 0.0009566 0.0008933
Cumulative Proportion 0.9923325 0.9938899 0.9949947 0.9959513 0.9968446
                           PC38      PC39      PC40      PC41      PC42
Eigenvalue            0.0004198 0.0003663 0.0002457 0.0001914 0.0001737
Proportion Explained  0.0007572 0.0006607 0.0004432 0.0003452 0.0003134
Cumulative Proportion 0.9976018 0.9982625 0.9987057 0.9990509 0.9993642
                           PC43      PC44      PC45      PC46      PC47
Eigenvalue            0.0001343 0.0001012 8.084e-05 2.953e-05 6.686e-06
Proportion Explained  0.0002422 0.0001825 1.458e-04 5.326e-05 1.206e-05
Cumulative Proportion 0.9996064 0.9997889 9.999e-01 1.000e+00 1.000e+00

PCA basado en transformaciones

Para ello se transforman los datos con la función decostand

com_tbrda <- rda(com_hel, env)
summary(com_tbrda)

Call:
rda(X = com_hel, Y = env) 

Partitioning of variance:
              Inertia Proportion
Total          0.5544     1.0000
Constrained    0.1984     0.3579
Unconstrained  0.3560     0.6421

Eigenvalues, and their contribution to the variance 

Importance of components:
                         RDA1    RDA2    RDA3    RDA4    RDA5    RDA6     RDA7
Eigenvalue            0.06767 0.04142 0.02755 0.01876 0.01296 0.00891 0.006814
Proportion Explained  0.12207 0.07470 0.04970 0.03385 0.02338 0.01607 0.012291
Cumulative Proportion 0.12207 0.19677 0.24646 0.28031 0.30369 0.31976 0.332051
                          RDA8     RDA9    RDA10    RDA11    RDA12     PC1
Eigenvalue            0.005452 0.003318 0.002643 0.001841 0.001067 0.08044
Proportion Explained  0.009835 0.005985 0.004767 0.003321 0.001925 0.14509
Cumulative Proportion 0.341886 0.347871 0.352638 0.355959 0.357884 0.50297
                          PC2     PC3     PC4     PC5     PC6     PC7     PC8
Eigenvalue            0.03865 0.03026 0.02626 0.02523 0.01885 0.01734 0.01398
Proportion Explained  0.06971 0.05457 0.04736 0.04550 0.03401 0.03128 0.02521
Cumulative Proportion 0.57269 0.62726 0.67463 0.72013 0.75414 0.78542 0.81063
                          PC9    PC10    PC11     PC12     PC13     PC14
Eigenvalue            0.01318 0.01189 0.01046 0.009137 0.008639 0.007416
Proportion Explained  0.02376 0.02144 0.01886 0.016481 0.015582 0.013376
Cumulative Proportion 0.83440 0.85584 0.87470 0.891182 0.906765 0.920140
                          PC15     PC16     PC17     PC18     PC19     PC20
Eigenvalue            0.006094 0.004674 0.004182 0.003798 0.003389 0.002718
Proportion Explained  0.010991 0.008430 0.007542 0.006850 0.006114 0.004903
Cumulative Proportion 0.931132 0.939562 0.947104 0.953954 0.960067 0.964970
                          PC21     PC22     PC23     PC24     PC25     PC26
Eigenvalue            0.002365 0.002185 0.001972 0.001631 0.001582 0.001310
Proportion Explained  0.004265 0.003941 0.003556 0.002941 0.002853 0.002363
Cumulative Proportion 0.969236 0.973177 0.976733 0.979675 0.982528 0.984891
                          PC27     PC28      PC29      PC30      PC31      PC32
Eigenvalue            0.001244 0.001061 0.0009535 0.0008724 0.0007685 0.0006355
Proportion Explained  0.002244 0.001914 0.0017198 0.0015736 0.0013862 0.0011462
Cumulative Proportion 0.987136 0.989050 0.9907694 0.9923430 0.9937292 0.9948754
                           PC33      PC34      PC35      PC36      PC37
Eigenvalue            0.0005467 0.0005054 0.0004099 0.0003714 0.0002355
Proportion Explained  0.0009860 0.0009116 0.0007393 0.0006698 0.0004249
Cumulative Proportion 0.9958614 0.9967730 0.9975123 0.9981821 0.9986070
                           PC38      PC39      PC40      PC41      PC42
Eigenvalue            0.0001761 0.0001596 0.0001406 0.0001099 9.131e-05
Proportion Explained  0.0003177 0.0002878 0.0002536 0.0001982 1.647e-04
Cumulative Proportion 0.9989247 0.9992125 0.9994661 0.9996643 9.998e-01
                           PC43      PC44      PC45      PC46      PC47
Eigenvalue            4.389e-05 2.746e-05 1.381e-05 7.831e-06 1.820e-06
Proportion Explained  7.917e-05 4.954e-05 2.490e-05 1.413e-05 3.283e-06
Cumulative Proportion 9.999e-01 1.000e+00 1.000e+00 1.000e+00 1.000e+00

Accumulated constrained eigenvalues
Importance of components:
                         RDA1    RDA2    RDA3    RDA4    RDA5    RDA6     RDA7
Eigenvalue            0.06767 0.04142 0.02755 0.01876 0.01296 0.00891 0.006814
Proportion Explained  0.34108 0.20873 0.13886 0.09457 0.06533 0.04491 0.034344
Cumulative Proportion 0.34108 0.54981 0.68867 0.78324 0.84857 0.89347 0.927817
                          RDA8     RDA9    RDA10    RDA11    RDA12
Eigenvalue            0.005452 0.003318 0.002643 0.001841 0.001067
Proportion Explained  0.027480 0.016723 0.013321 0.009279 0.005379
Cumulative Proportion 0.955297 0.972020 0.985341 0.994621 1.000000

Visualizar ordenación

Es interesante observar como se disponen especies y sitios en el espacio bidimensional.

Para ello usamos la función plot sobre cualquiera de los objetos de ordenación.

plot(com_cca)

¿Gráficos sobrecargados?

Puedes representar solo ‘especies’ o ‘sitios’ con el argumento display

plot(com_cca, display = "sites")

plot(com_cca, display = "species")

Análisis de clasificación en R

Medida de disimilitud

Para calcular la disimilitud entre todos los ‘sitios’ usamos la función vegdist

dist <- vegdist(com)
dist

          SC1_SU20  SC2_SU20  SC3_SU20  SC4_SU20  BA1_SU20  BA2_SU20  BA3_SU20
SC2_SU20 0.8720930                                                            
SC3_SU20 0.8389262 0.4105263                                                  
SC4_SU20 0.9722222 0.9777778 0.9104478                                        
BA1_SU20 0.9084967 0.9761905 0.9301310 0.9017857                              
BA2_SU20 0.9307958 0.9914894 0.9622642 0.9227053 0.3875339                    
BA3_SU20 0.9529412 0.9482759 0.9139785 0.9545455 0.5920000 0.6738197          
BA4_SU20 0.9456522 0.9846154 0.9626168 0.9215686 0.5151515 0.5060729 0.5000000
PH1_SU20 0.9620253 0.8653846 0.8271605 0.8157895 0.8403361 0.9185520 0.7058824
PH2_SU20 0.9597315 0.9157895 0.8888889 0.9701493 0.8515284 0.9528302 0.6774194
PH3_SU20 0.9337017 0.8425197 0.8076923 0.9595960 0.7164751 0.9098361 0.6320000
PH4_SU20 0.9568345 0.9294118 0.9032258 0.9298246 0.8173516 0.8712871 0.5662651
SR1_SU20 0.9829787 0.9889503 0.9746835 0.9869281 0.6317460 0.8322148 0.9106145
SR2_SU20 0.9409283 0.9781421 0.9375000 0.9483871 0.6593060 0.8533333 0.8895028
SR3_SU20 0.9827586 1.0000000 0.9741935 0.9866667 0.7756410 0.9796610 0.9431818
SR4_SU20 1.0000000 1.0000000 1.0000000 1.0000000 0.7537313 0.9920319 0.9393939
SC1_WI21 0.9496855 0.9047619 0.8536585 0.9480519 0.9246862 0.9279279 0.8058252
SC2_WI21 0.9889503 0.9842520 0.9807692 0.9797980 0.9616858 0.9918033 0.9360000
SC3_WI21 0.9565217 0.9538462 0.9252336 0.9607843 0.9696970 0.9757085 0.9062500
SC4_WI21 0.9642857 0.8947368 0.8681319 0.9767442 0.9919355 1.0000000 0.9464286
BA1_WI21 0.9134615 0.9740260 0.9541985 0.9841270 0.6041667 0.8154982 0.8947368
BA2_WI21 0.9521531 0.9741935 0.9545455 0.9842520 0.7301038 0.9485294 0.9346405
BA3_WI21 0.9675325 0.9763780 0.9653680 0.9911504 0.7268041 0.8706199 0.9603175
BA4_WI21 0.9800664 1.0000000 0.9910714 1.0000000 0.7375328 0.9010989 0.9591837
PH1_WI21 0.9699248 0.9716981 0.9576720 1.0000000 0.6184971 0.8115502 0.8000000
PH2_WI21 1.0000000 1.0000000 1.0000000 1.0000000 0.7228916 0.6380952 0.7959184
PH3_WI21 0.9848101 0.9882698 0.9748428 0.9872204 0.7305263 0.7248908 0.8702065
PH4_WI21 0.9918367 0.9895288 0.9880952 1.0000000 0.7353846 0.7727273 0.7883598
SR1_WI21 0.9886578 0.9957895 0.9867257 0.9955257 0.8489327 0.9594595 0.9577167
SR2_WI21 0.9953271 1.0000000 0.9943020 1.0000000 0.8543307 0.9796334 0.9784946
SR3_WI21 0.9693252 1.0000000 0.9839357 0.9918033 0.7733990 0.9177378 0.9259259
SR4_WI21 0.9939940 1.0000000 0.9921875 0.9920319 0.8353511 0.9949495 0.9711191
SC1_SU21 0.9325843 0.5967742 0.5049505 0.9583333 0.8837209 0.9834025 0.9016393
SC2_SU21 0.9365079 0.8962963 0.8571429 0.9813084 0.8884758 0.9761905 0.9097744
SC3_SU21 0.9289617 0.9358974 0.9031142 0.9859155 0.8161435 0.9813520 0.9483871
SC4_SU21 0.9782016 0.9872204 0.9793103 0.9789474 0.8478747 0.9953488 0.9614148
BA1_SU21 0.9573171 0.9781022 0.9601594 0.9837398 0.6225490 0.7698210 0.9044118
BA2_SU21 0.9375000 0.9603960 0.9441341 0.9885057 0.5535714 0.4858934 0.8700000
BA3_SU21 0.9585062 0.9358289 0.9268293 0.9874214 0.4579439 0.5526316 0.7945946
BA4_SU21 0.9367089 0.9807692 0.9259259 0.9736842 0.7815126 0.9366516 0.7843137
PH1_SU21 0.9884393 1.0000000 1.0000000 1.0000000 0.8102767 1.0000000 0.9145299
PH2_SU21 0.9889503 0.9842520 0.9807692 0.9797980 0.8467433 1.0000000 0.9360000
PH3_SU21 0.9781421 0.9689922 0.9433962 0.9603960 0.7338403 0.9674797 0.7952756
PH4_SU21 0.9473684 0.9117647 0.8584071 0.9444444 0.6666667 0.9209486 0.7462687
SR1_SU21 0.9928058 1.0000000 0.9900498 1.0000000 0.8044693 0.9824047 0.9639640
SR2_SU21 0.9915966 1.0000000 1.0000000 1.0000000 0.7798742 0.9800664 0.9670330
SR3_SU21 0.9857143 1.0000000 0.9682540 1.0000000 0.9181818 0.9901478 0.9285714
SR4_SU21 1.0000000 1.0000000 1.0000000 1.0000000 0.7413793 0.9906977 0.9166667
SC1_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.9300000 0.9562842 0.8125000
SC2_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.9402985 0.9456522 0.8461538
SC3_WI22 0.9534884 0.8933333 0.8461538 0.9574468 0.9904306 1.0000000 0.8904110
SC4_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.9509804 0.9893048 0.9117647
BA1_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.9339623 1.0000000 0.9210526
BA2_WI22 0.9540230 0.9420290 0.9347826 0.9888268 0.7653959 0.9814815 0.9024390
BA3_WI22 0.9870130 0.9800000 0.9740260 0.9722222 0.7692308 1.0000000 0.9183673
BA4_WI22 0.9863946 0.9784946 0.9714286 1.0000000 0.8061674 0.9238095 0.7582418
PH1_WI22 0.9881657 0.9826087 0.9782609 0.9770115 0.8554217 0.9568966 0.8407080
PH2_WI22 0.9568345 0.9529412 0.9354839 0.9649123 0.7990868 0.9405941 0.8072289
PH3_WI22 0.9861111 1.0000000 0.9701493 0.9677419 0.8125000 0.8840580 0.6590909
PH4_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.9400000 1.0000000 0.9062500
SR1_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.7293233 0.9759036 0.9076923
SR2_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.7490775 0.9842520 0.9407407
SR3_WI22 1.0000000 1.0000000 1.0000000 1.0000000 0.7262357 0.9756098 0.9055118
SR4_WI22 0.9866667 0.9791667 0.9726027 0.9705882 0.8000000 0.9718310 0.8510638
          BA4_SU20  PH1_SU20  PH2_SU20  PH3_SU20  PH4_SU20  SR1_SU20  SR2_SU20
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20 0.7413793                                                            
PH2_SU20 0.7943925 0.3333333                                                  
PH3_SU20 0.7410072 0.4690265 0.4038462                                        
PH4_SU20 0.6494845 0.5774648 0.5161290 0.4893617                              
SR1_SU20 0.7305699 0.7844311 0.7848101 0.6631579 0.8783784                    
SR2_SU20 0.7743590 0.7514793 0.7500000 0.6354167 0.8666667 0.1544715          
SR3_SU20 0.9578947 0.8414634 0.8322581 0.7112299 0.9310345 0.2116183 0.1934156
SR4_SU20 0.9726027 0.8000000 0.7657658 0.6083916 0.8811881 0.2893401 0.3467337
SC1_WI21 0.8974359 0.6923077 0.6097561 0.7368421 0.7500000 0.9166667 0.9058824
SC2_WI21 0.9712230 0.8053097 0.7692308 0.8823529 0.8510638 0.9473684 0.9479167
SC3_WI21 0.9577465 0.8275862 0.8317757 0.8848921 0.8556701 0.9792746 0.9589744
SC4_WI21 1.0000000 0.7600000 0.7142857 0.8211382 0.9259259 0.9435028 0.9329609
BA1_WI21 0.7349398 0.6857143 0.6488550 0.5705521 0.7851240 0.3548387 0.3515982
BA2_WI21 0.8922156 0.7730496 0.7575758 0.5975610 0.8360656 0.3761468 0.3090909
BA3_WI21 0.7894737 0.8416667 0.8095238 0.7566540 0.9004525 0.6656151 0.6990596
BA4_WI21 0.8532819 0.8369099 0.7857143 0.7187500 0.9065421 0.4516129 0.4551282
PH1_WI21 0.8214286 0.7575758 0.7142857 0.5927602 0.7653631 0.5709091 0.5812274
PH2_WI21 0.8190476 0.7608696 0.7371429 0.6618357 0.7696970 0.7701149 0.7946768
PH3_WI21 0.8810198 0.8715596 0.8553459 0.7542857 0.8636364 0.7227723 0.7339901
PH4_WI21 0.8029557 0.7514124 0.7261905 0.6300000 0.7341772 0.7401575 0.7656250
SR1_WI21 0.9466119 0.9045553 0.9070796 0.8471074 0.9411765 0.6802974 0.7000000
SR2_WI21 0.9585492 0.9111111 0.9145299 0.8381201 0.9472141 0.5560641 0.5808656
SR3_WI21 0.8873239 0.8837209 0.8634538 0.7580071 0.8995816 0.5044776 0.5370920
SR4_WI21 0.9725086 0.8943396 0.8906250 0.8055556 0.9430894 0.5614035 0.6046512
SC1_SU21 0.9411765 0.6181818 0.6435644 0.6090226 0.7802198 0.8609626 0.8201058
SC2_SU21 0.9319728 0.6033058 0.6071429 0.5555556 0.7647059 0.7575758 0.7300000
SC3_SU21 0.9814815 0.8523490 0.8339100 0.7258567 0.9211470 0.5680000 0.5649867
SC4_SU21 0.9692308 0.8528428 0.8482759 0.7888199 0.9214286 0.5957447 0.5767196
BA1_SU21 0.7132867 0.8307692 0.8247012 0.7031802 0.8589212 0.4005935 0.4572271
BA2_SU21 0.6355140 0.7872340 0.7541899 0.6682464 0.8224852 0.6528302 0.6853933
BA3_SU21 0.6080402 0.7225434 0.7073171 0.5510204 0.8181818 0.5120000 0.5952381
BA4_SU21 0.8103448 0.5777778 0.5061728 0.5221239 0.7464789 0.7125749 0.7041420
PH1_SU21 0.9541985 0.6761905 0.6458333 0.5000000 0.8139535 0.5824176 0.5760870
PH2_SU21 0.9856115 0.7699115 0.7500000 0.5882353 0.8723404 0.5894737 0.5937500
PH3_SU21 0.8865248 0.6173913 0.5849057 0.4492754 0.7916667 0.4375000 0.4226804
PH4_SU21 0.8378378 0.5901639 0.4690265 0.3655172 0.6699029 0.5477387 0.5223881
SR1_SU21 0.9661017 0.8666667 0.8507463 0.7510730 0.9476440 0.3449477 0.3564014
SR2_SU21 0.9591837 0.8705882 0.8509317 0.7202073 0.9337748 0.3927126 0.4377510
SR3_SU21 0.9387755 0.6944444 0.6190476 0.6842105 0.8113208 0.6375839 0.6423841
SR4_SU21 0.9454545 0.7142857 0.6533333 0.5700935 0.8461538 0.5155280 0.5214724
SC1_WI22 0.8717949 0.7307692 0.6744186 0.8400000 0.6363636 0.9069767 0.9236641
SC2_WI22 0.8734177 0.7735849 0.7727273 0.8684211 0.7058824 0.9230769 0.9393939
SC3_WI22 0.9770115 0.7049180 0.7307692 0.8571429 0.8571429 0.9565217 0.9428571
SC4_WI22 0.9756098 0.7500000 0.8297872 0.8987342 0.7837838 0.9398496 0.9407407
BA1_WI22 0.9777778 0.6875000 0.5636364 0.6321839 0.7777778 0.7304965 0.7342657
BA2_WI22 0.9452055 0.7927461 0.7826087 0.6388889 0.8735632 0.3777778 0.3455882
BA3_WI22 0.9821429 0.7209302 0.6883117 0.5779817 0.8208955 0.6073620 0.6121212
BA4_WI22 0.7904762 0.5696203 0.5428571 0.5882353 0.5666667 0.7564103 0.7974684
PH1_WI22 0.9055118 0.6237624 0.5652174 0.5645161 0.7317073 0.4943820 0.4888889
PH2_WI22 0.8556701 0.5774648 0.5161290 0.5319149 0.5769231 0.7027027 0.7333333
PH3_WI22 0.7647059 0.6052632 0.6119403 0.6161616 0.4736842 0.7908497 0.8193548
PH4_WI22 0.9743590 0.7307692 0.6744186 0.8133333 0.6363636 0.9069767 0.9083969
SR1_WI22 0.9444444 0.7457627 0.7247706 0.5744681 0.8585859 0.3025641 0.3705584
SR2_WI22 0.9597315 0.7886179 0.7719298 0.6301370 0.9038462 0.3000000 0.3366337
SR3_WI22 0.9432624 0.7391304 0.6981132 0.5507246 0.8541667 0.2916667 0.3092784
SR4_WI22 0.9259259 0.6097561 0.5616438 0.4285714 0.7460317 0.5723270 0.6024845
          SR3_SU20  SR4_SU20  SC1_WI21  SC2_WI21  SC3_WI21  SC4_WI21  BA1_WI21
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20 0.2371134                                                            
SC1_WI21 0.9515152 0.9338843                                                  
SC2_WI21 0.9465241 0.9440559 0.4736842                                        
SC3_WI21 0.9894737 0.9863014 0.5726496 0.4244604                              
SC4_WI21 0.9425287 0.9384615 0.3465347 0.5447154 0.6349206                    
BA1_WI21 0.5046729 0.4235294 0.7588652 0.7546012 0.9036145 0.8266667          
BA2_WI21 0.3488372 0.3801170 0.9436620 0.8780488 0.9401198 0.9072848 0.3507853
BA3_WI21 0.7898089 0.7703704 0.9336100 0.8859316 0.9548872 0.9120000 0.6000000
BA4_WI21 0.4723127 0.4524715 0.8888889 0.7968750 0.9536680 0.8930041 0.4487633
PH1_WI21 0.5955882 0.5350877 0.7688442 0.7104072 0.8839286 0.8173077 0.5161290
PH2_WI21 0.7984496 0.7850467 0.8162162 0.7487923 0.9333333 0.8556701 0.6666667
PH3_WI21 0.7456359 0.7535014 0.8963415 0.8571429 0.9546742 0.9347181 0.6763926
PH4_WI21 0.7768924 0.7681159 0.7528090 0.6900000 0.8817734 0.7967914 0.6475771
SR1_WI21 0.6635514 0.7107943 0.9480519 0.9421488 0.9712526 0.9617834 0.7651663
SR2_WI21 0.5299539 0.6153846 0.9556787 0.9268930 0.9585492 0.9405405 0.6829268
SR3_WI21 0.4879518 0.5208333 0.9150579 0.9572954 0.9788732 0.9701493 0.6493506
SR4_WI21 0.5162242 0.5525424 0.9699248 0.9305556 0.9793814 0.9490909 0.7206349
SC1_SU21 0.8695652 0.8285714 0.8018018 0.8646617 0.9264706 0.8166667 0.7750000
SC2_SU21 0.7641026 0.7086093 0.7868852 0.8194444 0.8775510 0.7557252 0.6140351
SC3_SU21 0.5053763 0.5487805 0.8127090 0.8130841 0.8827160 0.8116883 0.6379310
SC4_SU21 0.5871314 0.6109422 0.7933333 0.6149068 0.6061538 0.8187702 0.5988539
BA1_SU21 0.4790419 0.4827586 0.9080460 0.9222615 0.9580420 0.9555556 0.4838710
BA2_SU21 0.8244275 0.7889908 0.8518519 0.9336493 0.9439252 0.8888889 0.6134454
BA3_SU21 0.7004049 0.6650246 0.8620690 0.9183673 0.9597990 0.9125683 0.5246637
BA4_SU21 0.7317073 0.6833333 0.8461538 0.8407080 0.9310345 0.8600000 0.6571429
PH1_SU21 0.5642458 0.4666667 0.8679245 0.8593750 0.9389313 0.8434783 0.4709677
PH2_SU21 0.5935829 0.5104895 0.8947368 0.8970588 0.9568345 0.8861789 0.5092025
PH3_SU21 0.4497354 0.4344828 0.8448276 0.8695652 0.9290780 0.8720000 0.4060606
PH4_SU21 0.5816327 0.4605263 0.6097561 0.7931034 0.8378378 0.7272727 0.4186047
SR1_SU21 0.2535211 0.3833333 0.9620853 0.9570815 1.0000000 0.9636364 0.5846154
SR2_SU21 0.3360656 0.2600000 0.9649123 0.9585492 1.0000000 0.9555556 0.5090909
SR3_SU21 0.6438356 0.7058824 0.9178082 0.9157895 1.0000000 0.9024390 0.7377049
SR4_SU21 0.5189873 0.4035088 0.9294118 0.9252336 1.0000000 0.9148936 0.4925373
SC1_WI22 0.9523810 0.9268293 0.8490566 0.9200000 0.9487179 0.9677419 0.8823529
SC2_WI22 0.9842520 0.9518072 0.8148148 0.9473684 0.9493671 0.9682540 0.9029126
SC3_WI22 0.9703704 0.9560440 0.6129032 0.7619048 0.7471264 0.6619718 0.9099099
SC4_WI22 0.9538462 0.9302326 0.8947368 0.8481013 0.9024390 0.9090909 0.9056604
BA1_WI22 0.7246377 0.5957447 0.9076923 0.9080460 1.0000000 0.8918919 0.6666667
BA2_WI22 0.2359551 0.3273543 0.9072165 0.9444444 0.9543379 0.9211823 0.5308642
BA3_WI22 0.6125000 0.4655172 0.9080460 0.9082569 0.9821429 0.8958333 0.5294118
BA4_WI22 0.8169935 0.7798165 0.8250000 0.9019608 0.9619048 0.9550562 0.7519380
PH1_WI22 0.4971429 0.5725191 0.8039216 0.8709677 0.9212598 0.8558559 0.5099338
PH2_WI22 0.7793103 0.6831683 0.8055556 0.8510638 0.9175258 0.9012346 0.6528926
PH3_WI22 0.8266667 0.8113208 0.7662338 0.8989899 0.9411765 0.9534884 0.7936508
PH4_WI22 0.9047619 0.8536585 0.9245283 0.8666667 0.9743590 0.9354839 0.8627451
SR1_WI22 0.3229167 0.1486486 0.9159664 0.9432624 0.9861111 0.9375000 0.4761905
SR2_WI22 0.2893401 0.1372549 0.9516129 0.9178082 1.0000000 0.9248120 0.4335260
SR3_WI22 0.3333333 0.1310345 0.9137931 0.9420290 0.9858156 0.9360000 0.4060606
SR4_WI22 0.6153846 0.5000000 0.8554217 0.9047619 0.9629630 0.8913043 0.5454545
          BA2_WI21  BA3_WI21  BA4_WI21  PH1_WI21  PH2_WI21  PH3_WI21  PH4_WI21
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21 0.6219931                                                            
BA4_WI21 0.5492958 0.6762402                                                  
PH1_WI21 0.5742972 0.7068966 0.5307918                                        
PH2_WI21 0.7702128 0.7844311 0.7125382 0.3287671                              
PH3_WI21 0.7248677 0.8155136 0.7234043 0.4804598 0.3634204                    
PH4_WI21 0.7368421 0.7981651 0.6875000 0.2280702 0.2693727 0.4589372          
SR1_WI21 0.7695312 0.8428805 0.6523179 0.7328647 0.8486486 0.8338109 0.8248175
SR2_WI21 0.6399027 0.8196078 0.4990060 0.7136752 0.8546256 0.8157454 0.8165548
SR3_WI21 0.6569579 0.8137255 0.5112219 0.6775956 0.8295455 0.7979798 0.8144928
SR4_WI21 0.6898734 0.8265060 0.6176471 0.6943700 0.8384401 0.8167331 0.8352273
SC1_SU21 0.8136646 0.8461538 0.8577075 0.7981651 0.8529412 0.9020173 0.8172589
SC2_SU21 0.6511628 0.8007380 0.7575758 0.7467249 0.7767442 0.8379888 0.7019231
SC3_SU21 0.6045845 0.8214286 0.5736961 0.6403941 0.8316327 0.7794393 0.7922078
SC4_SU21 0.6114286 0.7951002 0.5520362 0.5921376 0.7709924 0.7425373 0.7305699
BA1_SU21 0.5241158 0.6780488 0.4937965 0.6250000 0.8135593 0.7545272 0.7925072
BA2_SU21 0.6652720 0.6568047 0.7280967 0.7837838 0.7801418 0.8541176 0.7963636
BA3_SU21 0.6696429 0.6532508 0.6962025 0.6441281 0.7453184 0.7609756 0.7384615
BA4_SU21 0.6879433 0.7916667 0.7939914 0.7070707 0.7391304 0.8165138 0.6949153
PH1_SU21 0.5000000 0.7647059 0.7096774 0.6713615 0.7487437 0.7660819 0.7083333
PH2_SU21 0.5243902 0.8022814 0.7500000 0.7285068 0.7777778 0.7885714 0.7500000
PH3_SU21 0.3734940 0.7358491 0.6744186 0.6322870 0.7320574 0.7215909 0.7128713
PH4_SU21 0.5028902 0.7058824 0.6377358 0.5043478 0.6759259 0.7047354 0.6363636
SR1_SU21 0.4712644 0.8055556 0.4050992 0.6477987 0.8355263 0.7807606 0.8181818
SR2_SU21 0.4751131 0.7875000 0.3610224 0.6258993 0.8333333 0.7788698 0.8210117
SR3_SU21 0.7398374 0.8648649 0.8046512 0.8333333 0.8313253 0.8834951 0.7735849
SR4_SU21 0.4962963 0.7264957 0.6740088 0.6354167 0.7303371 0.7694704 0.7426901
SC1_WI22 0.9611650 0.9702970 0.9487179 0.9125000 0.9041096 0.9515571 0.8992806
SC2_WI22 0.9807692 0.9901478 0.9693878 0.9254658 0.9183673 0.9655172 0.9142857
SC3_WI22 0.9464286 0.9715640 0.9803922 0.9171598 0.9612903 0.9865772 0.9189189
SC4_WI22 0.9439252 0.9611650 0.9597990 0.9268293 0.9333333 0.9726962 0.9160839
BA1_WI22 0.6695652 0.8878505 0.8164251 0.8255814 0.8481013 0.8737542 0.7748344
BA2_WI22 0.4098361 0.7900875 0.4642857 0.5946844 0.8188153 0.7674419 0.8000000
BA3_WI22 0.5328467 0.7372881 0.7292576 0.6804124 0.7666667 0.8080495 0.8034682
BA4_WI22 0.8000000 0.8689956 0.8648649 0.7112299 0.7341040 0.8354430 0.6987952
PH1_WI22 0.4473684 0.8406375 0.7704918 0.7033493 0.7128205 0.7633136 0.6489362
PH2_WI22 0.7049180 0.8280543 0.8224299 0.7430168 0.7454545 0.8571429 0.7341772
PH3_WI22 0.8582677 0.9203540 0.8995434 0.6847826 0.6941176 0.8146965 0.6687117
PH4_WI22 0.8834951 0.9306931 0.9282051 0.9125000 0.9041096 0.9515571 0.8992806
SR1_WI22 0.4437870 0.7686567 0.5095785 0.4513274 0.6981132 0.7352113 0.6878049
SR2_WI22 0.3793103 0.7655678 0.5187970 0.4805195 0.7235023 0.7166667 0.7047619
SR3_WI22 0.3614458 0.7584906 0.5116279 0.4887892 0.7511962 0.7272727 0.7227723
SR4_WI22 0.5789474 0.7844828 0.7422222 0.6421053 0.6704545 0.7868339 0.6686391
          SR1_WI21  SR2_WI21  SR3_WI21  SR4_WI21  SC1_SU21  SC2_SU21  SC3_SU21
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21                                                                      
BA4_WI21                                                                      
PH1_WI21                                                                      
PH2_WI21                                                                      
PH3_WI21                                                                      
PH4_WI21                                                                      
SR1_WI21                                                                      
SR2_WI21 0.5157319                                                            
SR3_WI21 0.3577107 0.3636364                                                  
SR4_WI21 0.3427673 0.4280374 0.1593533                                        
SC1_SU21 0.9376299 0.9263158 0.8992806 0.9087719                              
SC2_SU21 0.8780488 0.8516624 0.8408304 0.8581081 0.4893617                    
SC3_SU21 0.7488789 0.6408451 0.6652361 0.6955603 0.7169811 0.6231003          
SC4_SU21 0.7791045 0.6695958 0.7259101 0.7130802 0.7617555 0.6242424 0.4398422
BA1_SU21 0.7083994 0.6264151 0.5887850 0.6597701 0.8428571 0.7938144 0.2905983
BA2_SU21 0.8783542 0.8689956 0.8089888 0.8787879 0.7884615 0.7534247 0.7979798
BA3_SU21 0.8308824 0.8239278 0.7419355 0.7873563 0.7720207 0.7843137 0.7690289
BA4_SU21 0.8785249 0.8666667 0.8139535 0.8188679 0.6909091 0.6528926 0.8187919
PH1_SU21 0.8487395 0.7813333 0.7728938 0.7928571 0.7600000 0.5147059 0.6805112
PH2_SU21 0.8677686 0.7859008 0.7935943 0.8125000 0.7744361 0.5000000 0.6760125
PH3_SU21 0.8189300 0.7350649 0.7385159 0.7448276 0.7629630 0.6164384 0.6346749
PH4_SU21 0.7931034 0.7704082 0.6827586 0.7373737 0.6619718 0.5294118 0.6363636
SR1_SU21 0.5662651 0.3500000 0.3544974 0.4441558 0.8347826 0.8008299 0.5167464
SR2_SU21 0.6857671 0.4636364 0.4970414 0.6000000 0.8315789 0.7810945 0.5185185
SR3_SU21 0.8781038 0.8421053 0.7750000 0.7894737 0.7826087 0.6893204 0.8928571
SR4_SU21 0.8285714 0.7853107 0.6984127 0.7065637 0.7692308 0.7217391 0.7671233
SC1_WI22 0.9669031 0.9813665 0.9545455 0.9823789 0.9166667 0.9277108 0.9769231
SC2_WI22 0.9716981 0.9814241 0.9547511 0.9912281 0.9452055 0.9285714 0.9770115
SC3_WI22 0.9861111 0.9637462 0.9825328 0.9830508 0.8271605 0.8043478 0.9182156
SC4_WI22 0.9765808 0.9693252 0.9732143 0.9740260 0.8947368 0.7931034 0.9318182
BA1_WI22 0.9172414 0.8862275 0.8620690 0.8828452 0.7857143 0.6210526 0.8602941
BA2_WI22 0.6879433 0.5421166 0.5346260 0.6195652 0.7840376 0.7500000 0.3815461
BA3_WI22 0.8643326 0.8146067 0.7559055 0.7624521 0.6792453 0.7264957 0.7210884
BA4_WI22 0.9066667 0.9140401 0.8623482 0.8976378 0.6565657 0.7636364 0.8745645
PH1_WI22 0.8728814 0.7843666 0.8141264 0.8623188 0.7520661 0.5909091 0.7152104
PH2_WI22 0.9004525 0.9002933 0.8410042 0.8699187 0.6923077 0.7058824 0.8709677
PH3_WI22 0.9149888 0.9364162 0.8688525 0.9043825 0.8125000 0.8130841 0.9225352
PH4_WI22 0.9669031 0.9627329 0.9454545 0.9471366 0.8055556 0.8313253 0.9461538
SR1_WI22 0.7259714 0.6701031 0.5524476 0.5767918 0.8260870 0.7315436 0.6196319
SR2_WI22 0.7327935 0.6539440 0.5807560 0.5973154 0.8181818 0.7142857 0.5830816
SR3_WI22 0.7325103 0.6623377 0.5689046 0.6000000 0.7925926 0.6849315 0.6037152
SR4_WI22 0.8587196 0.8295455 0.7680000 0.7898833 0.7058824 0.6460177 0.7931034
          SC4_SU21  BA1_SU21  BA2_SU21  BA3_SU21  BA4_SU21  PH1_SU21  PH2_SU21
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21                                                                      
BA4_WI21                                                                      
PH1_WI21                                                                      
PH2_WI21                                                                      
PH3_WI21                                                                      
PH4_WI21                                                                      
SR1_WI21                                                                      
SR2_WI21                                                                      
SR3_WI21                                                                      
SR4_WI21                                                                      
SC1_SU21                                                                      
SC2_SU21                                                                      
SC3_SU21                                                                      
SC4_SU21                                                                      
BA1_SU21 0.5991471                                                            
BA2_SU21 0.8035264 0.6033520                                                  
BA3_SU21 0.7853403 0.5510204 0.3431734                                        
BA4_SU21 0.8193980 0.7923077 0.7340426 0.5953757                              
PH1_SU21 0.6878981 0.7090909 0.7635468 0.6702128 0.5619048                    
PH2_SU21 0.6397516 0.7173145 0.7725118 0.7040816 0.6637168 0.3125000          
PH3_SU21 0.6481481 0.6280702 0.7464789 0.5454545 0.4608696 0.2923077 0.4057971
PH4_SU21 0.6435045 0.6301370 0.6636364 0.5219512 0.5245902 0.3868613 0.4758621
SR1_SU21 0.6181384 0.5105263 0.8181818 0.7269625 0.7904762 0.6533333 0.6652361
SR2_SU21 0.6147757 0.4764706 0.7761194 0.6837945 0.7411765 0.5891892 0.5958549
SR3_SU21 0.8718861 0.8677686 0.8235294 0.8064516 0.5833333 0.6551724 0.6842105
SR4_SU21 0.7474403 0.7322835 0.7692308 0.6167665 0.5238095 0.4747475 0.5327103
SC1_WI22 0.9770115 0.9549550 0.9200000 0.9111111 0.8076923 0.9104478 0.9466667
SC2_WI22 0.9770992 0.9461883 0.9337748 0.9117647 0.9245283 0.9411765 0.9210526
SC3_WI22 0.9037037 0.9740260 0.9245283 0.9305556 0.9344262 0.8947368 0.8571429
SC4_WI22 0.9245283 0.9646018 0.9480519 0.9424460 0.8571429 0.7464789 0.7974684
BA1_WI22 0.8608059 0.8376068 0.8395062 0.8095238 0.6250000 0.5189873 0.5632184
BA2_WI22 0.5522388 0.3774105 0.7388316 0.6594203 0.7409326 0.5961538 0.6203704
BA3_WI22 0.7220339 0.6796875 0.6739130 0.5857988 0.5581395 0.5049505 0.5229358
BA4_WI22 0.8819444 0.8072289 0.7401130 0.6049383 0.3924051 0.7021277 0.7647059
PH1_WI22 0.7419355 0.7121771 0.7587940 0.6847826 0.5841584 0.4310345 0.4677419
PH2_WI22 0.8642857 0.8257261 0.7514793 0.7012987 0.4084507 0.6279070 0.6595745
PH3_WI22 0.9228070 0.8699187 0.8160920 0.7232704 0.5263158 0.7802198 0.7979798
PH4_WI22 0.9463602 0.9459459 0.9066667 0.9111111 0.7307692 0.7910448 0.8400000
SR1_WI22 0.6452599 0.5555556 0.7777778 0.5820896 0.6271186 0.5488722 0.5886525
SR2_WI22 0.5963855 0.5358362 0.7828054 0.5922330 0.6260163 0.4637681 0.5068493
SR3_WI22 0.6049383 0.5368421 0.7558685 0.6161616 0.6000000 0.4461538 0.4927536
SR4_WI22 0.7938144 0.7460317 0.7000000 0.5636364 0.4390244 0.4432990 0.4476190
          PH3_SU21  PH4_SU21  SR1_SU21  SR2_SU21  SR3_SU21  SR4_SU21  SC1_WI22
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21                                                                      
BA4_WI21                                                                      
PH1_WI21                                                                      
PH2_WI21                                                                      
PH3_WI21                                                                      
PH4_WI21                                                                      
SR1_WI21                                                                      
SR2_WI21                                                                      
SR3_WI21                                                                      
SR4_WI21                                                                      
SC1_SU21                                                                      
SC2_SU21                                                                      
SC3_SU21                                                                      
SC4_SU21                                                                      
BA1_SU21                                                                      
BA2_SU21                                                                      
BA3_SU21                                                                      
BA4_SU21                                                                      
PH1_SU21                                                                      
PH2_SU21                                                                      
PH3_SU21                                                                      
PH4_SU21 0.3333333                                                            
SR1_SU21 0.5659574 0.6363636                                                  
SR2_SU21 0.5589744 0.5841584 0.2413793                                        
SR3_SU21 0.6907216 0.7115385 0.7291667 0.8026316                              
SR4_SU21 0.4495413 0.4137931 0.6274510 0.5853659 0.4848485                    
SC1_WI22 0.8701299 0.8571429 0.9651163 0.9696970 0.8823529 0.8695652          
SC2_WI22 0.9230769 0.8588235 0.9884393 0.9849624 0.9428571 0.9574468 0.4666667
SC3_WI22 0.9302326 0.7634409 0.9779006 0.9716312 0.9069767 0.9272727 0.9130435
SC4_WI22 0.8518519 0.7954545 0.9659091 0.9558824 0.8421053 0.8800000 0.6666667
BA1_WI22 0.5730337 0.6458333 0.7934783 0.7361111 0.3913043 0.5862069 0.8461538
BA2_WI22 0.4770642 0.5288889 0.3035144 0.2820513 0.8285714 0.6363636 0.9483871
BA3_WI22 0.4594595 0.4237288 0.6601942 0.5662651 0.6470588 0.2250000 0.9166667
BA4_WI22 0.6538462 0.5855856 0.8291457 0.7861635 0.7049180 0.6712329 0.6585366
PH1_WI22 0.3015873 0.5338346 0.6108597 0.6685083 0.6385542 0.6210526 0.7777778
PH2_WI22 0.5833333 0.5533981 0.8324607 0.7748344 0.6603774 0.5076923 0.5757576
PH3_WI22 0.7227723 0.6481481 0.8877551 0.8846154 0.6896552 0.7142857 0.6842105
PH4_WI22 0.8181818 0.8333333 0.9302326 0.9090909 0.6470588 0.7391304 0.5714286
SR1_WI22 0.4685315 0.4400000 0.4537815 0.3636364 0.7000000 0.3750000 0.8750000
SR2_WI22 0.4324324 0.4709677 0.4320988 0.3300493 0.7142857 0.4017094 0.9294118
SR3_WI22 0.3857143 0.3877551 0.4468085 0.3538462 0.6701031 0.3394495 0.8701299
SR4_WI22 0.4205607 0.4210526 0.6930693 0.6419753 0.5312500 0.3421053 0.7727273
          SC2_WI22  SC3_WI22  SC4_WI22  BA1_WI22  BA2_WI22  BA3_WI22  BA4_WI22
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21                                                                      
BA4_WI21                                                                      
PH1_WI21                                                                      
PH2_WI21                                                                      
PH3_WI21                                                                      
PH4_WI21                                                                      
SR1_WI21                                                                      
SR2_WI21                                                                      
SR3_WI21                                                                      
SR4_WI21                                                                      
SC1_SU21                                                                      
SC2_SU21                                                                      
SC3_SU21                                                                      
SC4_SU21                                                                      
BA1_SU21                                                                      
BA2_SU21                                                                      
BA3_SU21                                                                      
BA4_SU21                                                                      
PH1_SU21                                                                      
PH2_SU21                                                                      
PH3_SU21                                                                      
PH4_SU21                                                                      
SR1_SU21                                                                      
SR2_SU21                                                                      
SR3_SU21                                                                      
SR4_SU21                                                                      
SC1_WI22                                                                      
SC2_WI22                                                                      
SC3_WI22 0.7500000                                                            
SC4_WI22 0.6842105 0.7037037                                                  
BA1_WI22 0.9259259 0.8857143 0.8000000                                        
BA2_WI22 0.9487179 0.9268293 0.9496855 0.7724551                              
BA3_WI22 0.9591837 0.8947368 0.8846154 0.6333333 0.5661376                    
BA4_WI22 0.7619048 0.9200000 0.8222222 0.6981132 0.7582418 0.5733333          
PH1_WI22 0.8437500 0.9166667 0.8208955 0.4933333 0.5686275 0.6494845 0.5555556
PH2_WI22 0.7647059 0.8095238 0.7837838 0.6444444 0.7701149 0.5223881 0.3666667
PH3_WI22 0.6923077 0.8723404 0.8095238 0.6800000 0.8547486 0.7500000 0.3230769
PH4_WI22 0.8666667 0.8260870 0.5555556 0.5384615 0.9225806 0.7500000 0.6585366
SR1_WI22 0.9259259 0.9550562 0.9285714 0.6521739 0.4117647 0.4561404 0.6448598
SR2_WI22 0.9767442 0.9574468 0.9325843 0.6082474 0.4070796 0.4621849 0.6964286
SR3_WI22 0.9230769 0.9534884 0.9259259 0.5730337 0.3853211 0.4234234 0.6923077
SR4_WI22 0.8666667 0.8867925 0.8750000 0.4642857 0.6432432 0.3333333 0.4366197
          PH1_WI22  PH2_WI22  PH3_WI22  PH4_WI22  SR1_WI22  SR2_WI22  SR3_WI22
SC2_SU20                                                                      
SC3_SU20                                                                      
SC4_SU20                                                                      
BA1_SU20                                                                      
BA2_SU20                                                                      
BA3_SU20                                                                      
BA4_SU20                                                                      
PH1_SU20                                                                      
PH2_SU20                                                                      
PH3_SU20                                                                      
PH4_SU20                                                                      
SR1_SU20                                                                      
SR2_SU20                                                                      
SR3_SU20                                                                      
SR4_SU20                                                                      
SC1_WI21                                                                      
SC2_WI21                                                                      
SC3_WI21                                                                      
SC4_WI21                                                                      
BA1_WI21                                                                      
BA2_WI21                                                                      
BA3_WI21                                                                      
BA4_WI21                                                                      
PH1_WI21                                                                      
PH2_WI21                                                                      
PH3_WI21                                                                      
PH4_WI21                                                                      
SR1_WI21                                                                      
SR2_WI21                                                                      
SR3_WI21                                                                      
SR4_WI21                                                                      
SC1_SU21                                                                      
SC2_SU21                                                                      
SC3_SU21                                                                      
SC4_SU21                                                                      
BA1_SU21                                                                      
BA2_SU21                                                                      
BA3_SU21                                                                      
BA4_SU21                                                                      
PH1_SU21                                                                      
PH2_SU21                                                                      
PH3_SU21                                                                      
PH4_SU21                                                                      
SR1_SU21                                                                      
SR2_SU21                                                                      
SR3_SU21                                                                      
SR4_SU21                                                                      
SC1_WI22                                                                      
SC2_WI22                                                                      
SC3_WI22                                                                      
SC4_WI22                                                                      
BA1_WI22                                                                      
BA2_WI22                                                                      
BA3_WI22                                                                      
BA4_WI22                                                                      
PH1_WI22                                                                      
PH2_WI22 0.5365854                                                            
PH3_WI22 0.6091954 0.5087719                                                  
PH4_WI22 0.7777778 0.5757576 0.6842105                                        
SR1_WI22 0.5658915 0.6161616 0.6730769 0.8500000                              
SR2_WI22 0.5223881 0.6730769 0.7614679 0.8588235 0.1258278                    
SR3_WI22 0.5396825 0.6041667 0.7425743 0.8441558 0.1468531 0.1351351          
SR4_WI22 0.4193548 0.3650794 0.5294118 0.7272727 0.3818182 0.4434783 0.4018692

Tipos de distancias

La disimilitud entre ‘sitios’ se puede calcular de varias maneras: euclidean, manhattan, gower, canberra, bray, jaccard…

Para ello usamos el argumento method

dist <- vegdist(com, method="euclidean")
dist <- vegdist(com, method="bray")
dist <- vegdist(com, method="jaccard")
head(dist)

[1] 0.9316770 0.9124088 0.9859155 0.9520548 0.9641577 0.9759036

Clasificación jerárquica

Para ello usamos la función hclust sobre la matriz de distancias

hc <- hclust(dist)
hc

Call:
hclust(d = dist)

Cluster method   : complete 
Distance         : jaccard 
Number of objects: 64 

Métodos de agrupación

Métodos para realizar la agrupación hay varios: single, complete, average, centroid…

Especificamos el método con el argumento method.

hc <- hclust(dist, method="single")
hc <- hclust(dist, method="centroid")
hc <- hclust(dist, method="average")
hc <- hclust(dist, method="complete")
hc

Call:
hclust(d = dist, method = "complete")

Cluster method   : complete 
Distance         : jaccard 
Number of objects: 64 

Visualizar clasificaciones

Las clasificaciones jerárquicas se pueden visualizar como un árbol filogenético con la función plot

plot(hc, hang=-1)

Interpretación

Establecer grupos en un árbol no es siempre trivial

• Se puede usar un umbral para determinar los grupos
• O establecer un número determinado de grupos

Visualizar clasificaciones con un umbral

plot(hc, hang=-1) 
rect.hclust(hc, h=0.8)

Visualizar clasificaciones con número de grupos

plot(hc, hang=-1)
rect.hclust(hc, k=4)

Extraer grupos

En ocasiones es interesante extraer la asignación de cada sitio a un grupo

Para ello podemos usar la función cutree

grp <- cutree(hc, h=0.7)
grp <- cutree(hc, k=4)
grp

SC1_SU20 SC2_SU20 SC3_SU20 SC4_SU20 BA1_SU20 BA2_SU20 BA3_SU20 BA4_SU20 
       1        1        1        1        2        2        2        2 
PH1_SU20 PH2_SU20 PH3_SU20 PH4_SU20 SR1_SU20 SR2_SU20 SR3_SU20 SR4_SU20 
       3        3        4        3        4        4        4        4 
SC1_WI21 SC2_WI21 SC3_WI21 SC4_WI21 BA1_WI21 BA2_WI21 BA3_WI21 BA4_WI21 
       3        3        3        3        4        4        4        4 
PH1_WI21 PH2_WI21 PH3_WI21 PH4_WI21 SR1_WI21 SR2_WI21 SR3_WI21 SR4_WI21 
       4        4        4        4        4        4        4        4 
SC1_SU21 SC2_SU21 SC3_SU21 SC4_SU21 BA1_SU21 BA2_SU21 BA3_SU21 BA4_SU21 
       4        4        4        4        4        2        2        4 
PH1_SU21 PH2_SU21 PH3_SU21 PH4_SU21 SR1_SU21 SR2_SU21 SR3_SU21 SR4_SU21 
       4        4        4        4        4        4        4        4 
SC1_WI22 SC2_WI22 SC3_WI22 SC4_WI22 BA1_WI22 BA2_WI22 BA3_WI22 BA4_WI22 
       3        3        3        3        4        4        4        4 
PH1_WI22 PH2_WI22 PH3_WI22 PH4_WI22 SR1_WI22 SR2_WI22 SR3_WI22 SR4_WI22 
       4        4        4        3        4        4        4        4 

Combinar ordenación y agrupamientos

Dibujar agrupamientos sobre los gráficos de ordenación

Para ello usamos la función ordihull

plot(com_cca, display="sites")
ordihull(com_cca, grp, lty=2, col="red")

Hay más opciones…

También se pueden usar las funciones ordispider y ordiellipse

plot(com_cca, display="sites")
ordispider(com_cca, grp, lty=2, col="red")

… que elegirás en función de tu necesidad

Para ello usamos las funciones ordispider y ordiellipse

plot(com_cca, display="sites")
ordiellipse(com_cca, grp, lty=2, col="red")