
R version 4.4.1 (2024-06-14) -- "Race for Your Life"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: aarch64-apple-darwin20

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> ## test the stability of cca object and its support functions
> suppressPackageStartupMessages(require(vegan))
> suppressPackageStartupMessages(require(parallel))
> set.seed(4711)
> op <- options(digits=5)
> ## models
> data(dune, dune.env)
> mcca <- cca(dune ~ Condition(Management) + Manure + A1, dune.env)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mrda <- rda(dune ~ Condition(Management) + Manure + A1, dune.env)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mrda1 <- rda(dune ~ Condition(Management) + Manure + A1, dune.env, scale=TRUE)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mcap <- capscale(dune ~ Condition(Management) + Manure + A1, dune.env,
+           dist = "bray")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mdb <- dbrda(dune ~ Condition(Management) + Manure + A1, dune.env,
+              dist = "bray")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mancap <- capscale(dune ~ Condition(Management) + Manure + A1, dune.env,
+           dist = "manhattan")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mandb <- dbrda(dune ~ Condition(Management) + Manure + A1, dune.env,
+                dist = "manhattan")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> ## 0-rank constraints
> m0cca <- cca(dune ~ Condition(Management) + Management, dune.env)
> ## univariate model, rank-1 constraint
> H <- diversity(dune)
> m1rda <- rda(H ~  A1, dune.env)
> 
> ## general appearance
> mcca
Call: cca(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)

-- Model Summary --

              Inertia Proportion Rank
Total           2.115      1.000     
Conditional     0.604      0.285    3
Constrained     0.450      0.213    4
Unconstrained   1.062      0.502   12

Inertia is scaled Chi-square

-- Note --

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
  CCA1   CCA2   CCA3   CCA4 
0.2226 0.1226 0.0639 0.0406 

Eigenvalues for unconstrained axes:
  CA1   CA2   CA3   CA4   CA5   CA6   CA7   CA8   CA9  CA10  CA11  CA12 
0.318 0.159 0.140 0.116 0.079 0.075 0.045 0.040 0.038 0.028 0.013 0.012 

> mrda
Call: rda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)

-- Model Summary --

              Inertia Proportion Rank
Total          84.124      1.000     
Conditional    29.231      0.347    3
Constrained    16.791      0.200    4
Unconstrained  38.102      0.453   12

Inertia is variance

-- Note --

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
RDA1 RDA2 RDA3 RDA4 
8.54 4.33 2.21 1.72 

Eigenvalues for unconstrained axes:
  PC1   PC2   PC3   PC4   PC5   PC6   PC7   PC8   PC9  PC10  PC11  PC12 
10.25  8.21  4.95  3.36  3.12  2.49  1.87  1.26  1.02  0.74  0.48  0.35 

> mcap
Call: capscale(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, distance = "bray")

-- Model Summary --

              Inertia Proportion Rank
Total           4.299                
RealTotal       4.594      1.000     
Conditional     1.500      0.327    3
Constrained     1.073      0.233    4
Unconstrained   2.021      0.440   12
Imaginary      -0.295                

Inertia is squared Bray distance

-- Note --

Species scores projected from 'dune'

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
 CAP1  CAP2  CAP3  CAP4 
0.674 0.243 0.105 0.051 

Eigenvalues for unconstrained axes:
 MDS1  MDS2  MDS3  MDS4  MDS5  MDS6  MDS7  MDS8  MDS9 MDS10 MDS11 MDS12 
0.749 0.338 0.308 0.213 0.137 0.136 0.062 0.039 0.017 0.011 0.006 0.004 

> mdb
Call: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, distance = "bray")

-- Model Summary --

              Inertia Proportion Rank RealDims
Total           4.299      1.000              
Conditional     1.469      0.342    3         
Constrained     1.035      0.241    4        4
Unconstrained   1.796      0.418   12        9

Inertia is squared Bray distance

-- Note --

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
dbRDA1 dbRDA2 dbRDA3 dbRDA4 
 0.667  0.238  0.091  0.038 

Eigenvalues for unconstrained axes:
  MDS1   MDS2   MDS3   MDS4   MDS5   MDS6   MDS7   MDS8   MDS9  iMDS1  iMDS2 
 0.742  0.337  0.307  0.206  0.133  0.128  0.040  0.027  0.000 -0.020 -0.046 
 iMDS3 
-0.059 

> mancap
Call: capscale(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, distance = "manhattan")

-- Model Summary --

               Inertia Proportion Rank
Total          994.092                
RealTotal     1077.648      1.000     
Conditional    412.304      0.383    3
Constrained    213.079      0.198    4
Unconstrained  452.264      0.420   12
Imaginary      -83.555                

Inertia is mean squared Manhattan distance

-- Note --

Species scores projected from 'dune'

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
 CAP1  CAP2  CAP3  CAP4 
125.7  49.3  24.2  13.9 

Eigenvalues for unconstrained axes:
 MDS1  MDS2  MDS3  MDS4  MDS5  MDS6  MDS7  MDS8  MDS9 MDS10 MDS11 MDS12 
163.7  97.1  59.0  40.2  34.9  24.9  12.7  10.9   4.7   1.9   1.5   0.8 

> mandb
Call: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, distance = "manhattan")

-- Model Summary --

              Inertia Proportion Rank RealDims
Total         994.092      1.000              
Conditional   404.069      0.406    3         
Constrained   202.576      0.204    4        4
Unconstrained 387.447      0.390   12        8

Inertia is mean squared Manhattan distance

-- Note --

Some constraints or conditions were aliased because they were redundant.
This can happen if terms are linearly dependent (collinear): 'Manure^4'

-- Eigenvalues --

Eigenvalues for constrained axes:
dbRDA1 dbRDA2 dbRDA3 dbRDA4 
 123.2   47.4   21.9   10.1 

Eigenvalues for unconstrained axes:
 MDS1  MDS2  MDS3  MDS4  MDS5  MDS6  MDS7  MDS8 iMDS1 iMDS2 iMDS3 iMDS4 
161.5  96.1  58.8  38.5  33.4  24.6   9.6   6.0  -0.6  -6.3 -13.3 -20.8 

> m0cca
Call: cca(formula = dune ~ Condition(Management) + Management, data =
dune.env)

-- Model Summary --

              Inertia Proportion Rank
Total           2.115      1.000     
Conditional     0.604      0.285    3
Unconstrained   1.511      0.715   16

Inertia is scaled Chi-square

-- Eigenvalues --

Eigenvalues for unconstrained axes:
  CA1   CA2   CA3   CA4   CA5   CA6   CA7   CA8   CA9  CA10  CA11  CA12  CA13 
0.447 0.203 0.163 0.135 0.129 0.095 0.079 0.065 0.050 0.043 0.039 0.024 0.018 
 CA14  CA15  CA16 
0.009 0.008 0.004 

> m1rda
Call: rda(formula = H ~ A1, data = dune.env)

-- Model Summary --

              Inertia Proportion Rank
Total         0.07321    1.00000     
Constrained   0.00294    0.04020    1
Unconstrained 0.07027    0.95980    1

Inertia is variance

-- Eigenvalues --

Eigenvalues for constrained axes:
    RDA1 
0.002943 

Eigenvalues for unconstrained axes:
   PC1 
0.0703 

> ## names
> sort(names(mcca))
 [1] "CA"          "CCA"         "Ybar"        "call"        "call"       
 [6] "colsum"      "grand.total" "inertia"     "method"      "pCCA"       
[11] "rowsum"      "terminfo"    "terms"       "tot.chi"    
> sort(names(mrda))
 [1] "CA"             "CCA"            "Ybar"           "call"          
 [5] "colsum"         "inertia"        "method"         "pCCA"          
 [9] "regularization" "terminfo"       "terms"          "tot.chi"       
> sort(names(mcap))
 [1] "CA"        "CCA"       "Ybar"      "adjust"    "call"      "colsum"   
 [7] "inertia"   "method"    "pCCA"      "sqrt.dist" "terminfo"  "terms"    
[13] "tot.chi"   "vdata"    
> sort(names(mdb))
 [1] "CA"        "CCA"       "Ybar"      "adjust"    "call"      "colsum"   
 [7] "inertia"   "method"    "pCCA"      "sqrt.dist" "terminfo"  "terms"    
[13] "tot.chi"  
> 
> ## diagnostics
> hatvalues(mcca)
      1       2       3       4       5       6       7       8       9      10 
0.38964 0.66464 0.39824 0.48282 0.43153 0.42904 0.57721 0.85494 0.66464 0.47319 
     11      12      13      14      15      16      17      18      19      20 
0.35412 0.62534 0.39046 0.32811 0.58922 0.38621 0.13392 0.20951 0.29994 0.31726 
> hatvalues(mrda)
 [1] 0.53471 0.65751 0.33777 0.40784 0.40677 0.37400 0.56067 0.84957 0.65751
[10] 0.42120 0.42260 0.64583 0.40092 0.33039 0.62433 0.39796 0.23669 0.20371
[19] 0.25735 0.27267
> hatvalues(mandb)
 [1] 0.53471 0.65751 0.33777 0.40784 0.40677 0.37400 0.56067 0.84957 0.65751
[10] 0.42120 0.42260 0.64583 0.40092 0.33039 0.62433 0.39796 0.23669 0.20371
[19] 0.25735 0.27267
> hatvalues(m1rda)
 [1] 0.096575 0.070198 0.053353 0.054682 0.073302 0.053353 0.096575 0.054682
 [9] 0.064657 0.076626 0.070198 0.060002 0.064657 0.269467 0.540109 0.058007
[17] 0.058007 0.050693 0.064657 0.070198
> 
> zapsmall(head(cooks.distance(mcca)))
  Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
1   0.2015   0.3909   0.0100   0.3198   0.0036   0.3208   0.1238   0.0004
2   0.1249   0.5641   0.0138   0.5688   0.9650   0.2343   0.0899   0.0372
3   0.0202   0.0466   0.0015   0.7564   0.0005   0.0621   0.3002   0.0001
4   0.0404   0.6089   0.0013   0.3372   0.0005   0.0288   0.9104   0.0001
5   0.0670   0.1356   0.0482   0.1869   0.3149   0.3882   0.2014   0.0265
6   0.0017   0.0004   0.0060   0.1985   0.0043   0.3420   0.3112   0.0546
  Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
1   0.4134   0.2264   0.0216   0.5968   0.0064   0.0085   0.0017   0.0017
2   0.0001   0.3117   0.0656   3.3013   0.0089   0.1618   0.8448   1.2765
3   1.0040   0.0347   0.0033   0.0338   0.0010   0.0013   0.0003   0.0003
4   3.0432   0.0290   0.0028   0.1762   0.0008   0.0011   0.0002   0.0002
5   0.0005   1.0857   0.0478   0.1519   0.0308   0.0660   0.0687   0.2020
6   0.0001   0.1346   0.0490   0.7247   0.0038   0.0002   0.0218   0.3566
  Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
1   1.5527   0.0010  0.7923  0.0079   0.0073   0.0001   0.1837   0.0485
2   0.6645   2.4053  0.0603  1.1534   0.0331   2.1543   0.0002   0.0667
3   0.0436   0.0002  0.0001  0.0555   0.0011   0.0000   0.3373   0.0074
4   0.6133   0.0001  0.5616  0.0444   0.0009   0.0000   1.1185   0.0062
5   0.0608   0.2669  0.0101  0.0460   0.0075   0.0783   0.0292   0.2324
6   0.2028   0.0874  0.0005  0.1772   0.0294   0.2935   0.0888   0.0288
  Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
1   0.1877   0.0003   0.0156   0.0001   0.0578   0.0018
2   0.0461   1.7937   0.0000   1.7194   0.8086   0.0164
3   0.0351   0.0000   0.0389   0.0000   0.0110   0.0003
4   0.0179   0.0000   0.0181   0.0000   0.0053   0.0002
5   0.0184   0.1001   0.3751   0.0695   0.0640   0.0000
6   0.0343   1.6066   0.1480   0.0601   0.2804   0.0179
> zapsmall(head(cooks.distance(mrda)))
  Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
1   0.1761   1.5406   0.0313   1.1176   0.0094   1.1835   0.3910   0.0006
2   0.1158   0.3965   0.0116   0.5059   1.4020   0.2724   0.1134   0.0392
3   0.0133   0.0020   0.0030   0.6281   0.0009   0.0920   0.1284   0.0001
4   0.0214   0.8231   0.0030   0.0617   0.0009   0.1397   0.7559   0.0001
5   0.0498   0.0658   0.0365   0.1882   0.3664   0.3256   0.1322   0.0324
6   0.0145   0.0020   0.0029   0.1431   0.0244   0.2416   0.1994   0.0384
  Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
1   1.1927   0.6321   0.0316   0.0002   0.0127   0.0207   0.0019   0.0026
2   0.0002   0.2331   0.0341   4.2057   0.0047   0.1666   0.9432   1.3977
3   0.3951   0.0600   0.0030   0.0000   0.0012   0.0020   0.0002   0.0002
4   2.3160   0.0598   0.0030   0.0000   0.0012   0.0020   0.0002   0.0002
5   0.0005   0.7370   0.0110   0.1449   0.0149   0.0456   0.0628   0.2543
6   0.0000   0.0588   0.0178   0.6361   0.0012   0.0001   0.0295   0.2742
  Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
1   0.2819   0.0021  0.1434  0.6899   0.0089   0.0000   0.6367   0.0748
2   1.5095   2.7465  0.3092  1.0935   0.0173   1.9478   0.0005   0.0276
3   0.0006   0.0002  0.1187  0.1113   0.0008   0.0000   0.1676   0.0071
4   0.1564   0.0002  0.0268  0.0256   0.0008   0.0000   1.1039   0.0071
5   0.3844   0.2391  0.1254  0.0186   0.0003   0.0398   0.0449   0.0873
6   0.7320   0.1480  0.0063  0.0894   0.0111   0.5069   0.0606   0.0070
  Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
1   0.7907   0.0003   0.1297   0.0005   0.2576   0.0023
2   0.0160   1.5145   0.0015   2.1843   0.9008   0.0144
3   0.0632   0.0000   0.0515   0.0000   0.0203   0.0002
4   0.0908   0.0000   0.0010   0.0000   0.0300   0.0002
5   0.0022   0.0881   0.3779   0.0844   0.0838   0.0026
6   0.0092   1.3701   0.1927   0.0551   0.3486   0.0118
> zapsmall(head(cooks.distance(mrda1)))
  Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
1   0.1761   1.5406   0.0313   1.1176   0.0094   1.1835   0.3910   0.0006
2   0.1158   0.3965   0.0116   0.5059   1.4020   0.2724   0.1134   0.0392
3   0.0133   0.0020   0.0030   0.6281   0.0009   0.0920   0.1284   0.0001
4   0.0214   0.8231   0.0030   0.0617   0.0009   0.1397   0.7559   0.0001
5   0.0498   0.0658   0.0365   0.1882   0.3664   0.3256   0.1322   0.0324
6   0.0145   0.0020   0.0029   0.1431   0.0244   0.2416   0.1994   0.0384
  Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
1   1.1927   0.6321   0.0316   0.0002   0.0127   0.0207   0.0019   0.0026
2   0.0002   0.2331   0.0341   4.2057   0.0047   0.1666   0.9432   1.3977
3   0.3951   0.0600   0.0030   0.0000   0.0012   0.0020   0.0002   0.0002
4   2.3160   0.0598   0.0030   0.0000   0.0012   0.0020   0.0002   0.0002
5   0.0005   0.7370   0.0110   0.1449   0.0149   0.0456   0.0628   0.2543
6   0.0000   0.0588   0.0178   0.6361   0.0012   0.0001   0.0295   0.2742
  Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
1   0.2819   0.0021  0.1434  0.6899   0.0089   0.0000   0.6367   0.0748
2   1.5095   2.7465  0.3092  1.0935   0.0173   1.9478   0.0005   0.0276
3   0.0006   0.0002  0.1187  0.1113   0.0008   0.0000   0.1676   0.0071
4   0.1564   0.0002  0.0268  0.0256   0.0008   0.0000   1.1039   0.0071
5   0.3844   0.2391  0.1254  0.0186   0.0003   0.0398   0.0449   0.0873
6   0.7320   0.1480  0.0063  0.0894   0.0111   0.5069   0.0606   0.0070
  Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
1   0.7907   0.0003   0.1297   0.0005   0.2576   0.0023
2   0.0160   1.5145   0.0015   2.1843   0.9008   0.0144
3   0.0632   0.0000   0.0515   0.0000   0.0203   0.0002
4   0.0908   0.0000   0.0010   0.0000   0.0300   0.0002
5   0.0022   0.0881   0.3779   0.0844   0.0838   0.0026
6   0.0092   1.3701   0.1927   0.0551   0.3486   0.0118
> zapsmall(head(cooks.distance(mcap, "canoco")))
     CAP1    CAP2    CAP3    CAP4
1 0.42135 0.71383 0.52485 0.00003
2 0.35667 0.91934 0.00051 0.34825
3 0.04306 0.05516 0.09142 0.00035
4 0.03627 0.08478 0.01578 0.00073
5 0.23671 0.09188 0.00653 0.26523
6 0.00064 0.00000 0.00033 0.07231
> zapsmall(head(cooks.distance(mdb, "canoco")))
   dbRDA1  dbRDA2  dbRDA3  dbRDA4
1 0.45656 0.82736 0.95105 0.09224
2 0.38438 0.83291 0.00814 0.35065
3 0.04581 0.06482 0.16066 0.00937
4 0.04026 0.09692 0.03121 0.00801
5 0.26263 0.06530 0.00010 0.22079
6 0.00141 0.00135 0.00737 0.12833
> zapsmall(head(cooks.distance(mancap, "canoco")))
     CAP1    CAP2    CAP3    CAP4
1 0.00378 0.00009 0.18185 0.45549
2 0.32121 1.64122 0.11530 2.20497
3 0.00679 0.01562 0.11032 0.01045
4 0.00349 0.02163 0.01335 0.11390
5 0.20285 0.07583 0.00167 0.29463
6 0.00344 0.03919 0.01336 0.27877
> zapsmall(head(cooks.distance(mandb, "canoco")))
   dbRDA1  dbRDA2  dbRDA3  dbRDA4
1 0.00914 0.00480 0.50784 0.16442
2 0.34821 1.48377 0.23249 1.60030
3 0.00735 0.01721 0.17781 0.00061
4 0.00158 0.01292 0.00085 0.06147
5 0.23684 0.04827 0.04109 0.20639
6 0.00207 0.05014 0.04443 0.36650
> zapsmall(head(cooks.distance(m1rda)))
     col1
1 0.47753
2 0.00170
3 0.00011
4 0.02525
5 0.10022
6 0.01147
> 
> head(goodness(mcca, display = "sites"))
      CCA1     CCA2    CCA3    CCA4
1 0.185250 0.224787 0.23190 0.23203
2 0.044206 0.054137 0.13403 0.24479
3 0.168758 0.475105 0.48459 0.48764
4 0.116243 0.295806 0.30207 0.30380
5 0.014540 0.057912 0.19448 0.19467
6 0.067333 0.067749 0.13876 0.13929
> head(goodness(mrda, display = "sites"))
        RDA1     RDA2    RDA3    RDA4
1 0.42239542 0.432516 0.43329 0.43348
2 0.01888621 0.044210 0.11461 0.17317
3 0.26198074 0.298577 0.30272 0.30748
4 0.23011480 0.259364 0.26228 0.26592
5 0.00027964 0.036798 0.11025 0.11469
6 0.01492482 0.083895 0.09990 0.09993
> head(goodness(mrda1, display = "sites"))
       RDA1     RDA2    RDA3    RDA4
1 0.4207789 0.451576 0.48069 0.48189
2 0.0552381 0.058798 0.14704 0.22767
3 0.2344181 0.381112 0.39558 0.40051
4 0.0988545 0.153807 0.15997 0.16183
5 0.0049954 0.029302 0.16899 0.17120
6 0.0391326 0.042622 0.10319 0.10322
> head(goodness(m1rda, display = "sites"))
       RDA1
1 0.0049860
2 0.1415108
3 0.2006191
4 0.0037679
5 0.0089639
6 0.0056118
> goodness(m1rda)       # fails in 2.5-3
         RDA1
col1 0.040196
> ## head(goodness(mcap, display = "sites")) # currently disabled
> ## head(goodness(mdb, display="sites"))  # not implemented for partial dbrda
> ## head(goodness(mancap, display="sites")) # currently disabled
> ## head(goodness(mandb, display="sites")) # not implemneted for partial dbrda
> ## head(goodness(m0cca)) # now an error: no goodness without constraints
> 
> head(inertcomp(mcca))
              pCCA       CCA       CA
Achimill 0.0153429 0.0048302 0.030529
Agrostol 0.0381018 0.0161939 0.027816
Airaprae 0.0258133 0.0134079 0.064877
Alopgeni 0.0487892 0.0092962 0.037121
Anthodor 0.0141466 0.0069150 0.072781
Bellpere 0.0069739 0.0106965 0.020072
> head(inertcomp(mrda))
            pCCA     CCA      CA
Achimill 0.60877 0.18696 0.74111
Agrostol 2.81228 1.14782 3.23990
Airaprae 0.15351 0.10549 0.35942
Alopgeni 3.26316 0.57391 3.06819
Anthodor 0.53421 0.27983 2.07806
Bellpere 0.21140 0.29749 0.57268
> head(inertcomp(mrda1))
            pCCA      CCA      CA
Achimill 0.39612 0.121651 0.48223
Agrostol 0.39059 0.159420 0.44999
Airaprae 0.24823 0.170578 0.58120
Alopgeni 0.47256 0.083113 0.44433
Anthodor 0.18471 0.096757 0.71853
Bellpere 0.19546 0.275055 0.52949
> head(inertcomp(mcap, display="sites"))
      pCCA      CCA       CA
1 0.058628 0.105577 0.104294
2 0.100405 0.035067 0.077139
3 0.058628 0.070870 0.039223
4 0.058628 0.072386 0.056966
5 0.043474 0.018994 0.080773
6 0.043474 0.028915 0.066973
> head(inertcomp(mdb, display = "sites"))
      pCCA      CCA       CA
1 0.058383 0.103846 0.080795
2 0.093318 0.028218 0.073292
3 0.058383 0.069481 0.024416
4 0.058383 0.070979 0.052324
5 0.042268 0.016687 0.063247
6 0.042268 0.026426 0.051382
> head(inertcomp(mancap, display = "sites"))
    pCCA     CCA     CA
1 14.310 19.2048 21.046
2 31.248 11.5984 26.506
3 14.310 15.4320  9.898
4 14.310 15.5966 15.754
5 17.177  5.8883 21.460
6 17.177  8.8555 27.470
> head(inertcomp(mandb, display = "sites"))
    pCCA     CCA      CA
1 14.211 18.6264 15.3043
2 29.512  9.8634 25.4006
3 14.211 14.9565  6.8683
4 14.211 15.1159 14.6604
5 16.995  5.4240 16.8238
6 16.995  8.3251 22.2002
> zapsmall(head(inertcomp(m0cca)))
             pCCA       CA
Achimill 0.015343 0.035359
Agrostol 0.038102 0.044009
Airaprae 0.025813 0.078285
Alopgeni 0.048789 0.046417
Anthodor 0.014147 0.079696
Bellpere 0.006974 0.030769
> inertcomp(m1rda)
           CCA       CA
col1 0.0029428 0.070268
> 
> abs(zapsmall(intersetcor(mcca)))
            CCA1    CCA2    CCA3    CCA4
Manure.L 0.16256 0.52974 0.27392 0.47312
Manure.Q 0.31167 0.59055 0.43511 0.14091
Manure.C 0.33679 0.23680 0.08339 0.60440
Manure^4 0.27194 0.16138 0.68107 0.13507
A1       0.64369 0.26617 0.35227 0.08656
> abs(zapsmall(intersetcor(mrda)))
            RDA1    RDA2    RDA3    RDA4
Manure.L 0.44970 0.45430 0.17052 0.41752
Manure.Q 0.64906 0.44643 0.11403 0.14879
Manure.C 0.47200 0.13567 0.08333 0.60716
Manure^4 0.27404 0.47959 0.51866 0.03987
A1       0.48811 0.17985 0.50083 0.29462
> abs(zapsmall(intersetcor(mrda1)))
            RDA1    RDA2    RDA3    RDA4
Manure.L 0.35700 0.44353 0.26187 0.50157
Manure.Q 0.47776 0.41663 0.48816 0.13407
Manure.C 0.40999 0.08092 0.01974 0.67542
Manure^4 0.39647 0.04685 0.69440 0.04289
A1       0.53789 0.47469 0.36590 0.13184
> abs(zapsmall(intersetcor(mcap)))
            CAP1    CAP2    CAP3    CAP4
Manure.L 0.34428 0.46883 0.08077 0.33049
Manure.Q 0.46742 0.48537 0.22608 0.13137
Manure.C 0.35114 0.05579 0.08638 0.48645
Manure^4 0.26818 0.13779 0.62087 0.05599
A1       0.57349 0.28004 0.35091 0.07576
> abs(zapsmall(intersetcor(mdb)))
          dbRDA1  dbRDA2  dbRDA3  dbRDA4
Manure.L 0.33636 0.46901 0.14552 0.19669
Manure.Q 0.46084 0.46800 0.19559 0.10617
Manure.C 0.35058 0.05075 0.15478 0.29989
Manure^4 0.26690 0.10088 0.53857 0.08724
A1       0.56939 0.29083 0.30919 0.02422
> abs(zapsmall(intersetcor(mancap)))
            CAP1    CAP2    CAP3    CAP4
Manure.L 0.38584 0.48506 0.00005 0.26424
Manure.Q 0.45373 0.44871 0.24500 0.15056
Manure.C 0.35825 0.09885 0.10252 0.45075
Manure^4 0.41554 0.33601 0.44684 0.03505
A1       0.36136 0.17672 0.51779 0.16025
> abs(zapsmall(intersetcor(mandb)))
          dbRDA1  dbRDA2  dbRDA3  dbRDA4
Manure.L 0.37496 0.48082 0.08018 0.15731
Manure.Q 0.44695 0.41430 0.22423 0.11920
Manure.C 0.35996 0.11590 0.00423 0.28532
Manure^4 0.41300 0.28868 0.42071 0.06480
A1       0.35511 0.20385 0.49290 0.06262
> abs(zapsmall(intersetcor(m1rda)))
      RDA1
A1 0.20049
> 
> tolerance(mcca)

Species Tolerance

Scaling: 2

            CCA1     CCA2
Achimill 0.61007 0.503578
Agrostol 1.35694 1.449646
Airaprae 0.10516 0.078256
Alopgeni 0.98368 1.398741
Anthodor 0.64966 0.568219
Bellpere 0.50902 0.824771
Bromhord 0.51376 0.715512
Chenalbu 0.00000 0.000000
Cirsarve 0.00000 0.000000
Comapalu 0.77116 0.573877
Eleopalu 1.38967 1.527094
Elymrepe 0.63733 0.927844
Empenigr 0.00000 0.000000
Hyporadi 0.75384 0.361128
Juncarti 1.49080 1.279732
Juncbufo 0.83160 0.650590
Lolipere 0.70897 0.735395
Planlanc 0.51563 0.436023
Poaprat  0.77305 0.833332
Poatriv  0.91211 1.060493
Ranuflam 1.55143 1.374797
Rumeacet 0.46610 0.821992
Sagiproc 0.91313 1.312686
Salirepe 0.28643 0.213149
Scorautu 0.97673 0.906578
Trifprat 0.56768 0.419267
Trifrepe 0.95609 0.941391
Vicilath 0.52385 0.187524
Bracruta 1.14404 1.091019
Callcusp 1.57627 1.446282

> tolerance(m0cca)

Species Tolerance

Scaling: 2

              CA1     CA2
Achimill 0.930813 0.67460
Agrostol 0.949483 0.83992
Airaprae 0.249010 1.16549
Alopgeni 0.726918 0.86630
Anthodor 1.160427 1.20647
Bellpere 0.321717 0.58968
Bromhord 0.304392 0.25205
Chenalbu 0.000000 0.00000
Cirsarve 0.000000 0.00000
Comapalu 0.041889 0.39785
Eleopalu 0.278432 0.81396
Elymrepe 0.482478 1.09766
Empenigr 0.000000 0.00000
Hyporadi 1.243512 1.04260
Juncarti 0.551515 0.67321
Juncbufo 0.346137 0.67554
Lolipere 0.472723 1.00637
Planlanc 0.685082 0.75194
Poaprat  0.622322 1.05260
Poatriv  0.539912 0.92947
Ranuflam 0.641115 0.77679
Rumeacet 0.311899 0.85299
Sagiproc 1.005528 1.03234
Salirepe 1.981465 1.87444
Scorautu 1.153131 1.16089
Trifprat 0.063055 0.11141
Trifrepe 0.938071 0.96335
Vicilath 0.266341 1.28007
Bracruta 1.095827 1.12812
Callcusp 0.152449 0.82496

> 
> vif.cca(mcca)
ManagementHF ManagementNM ManagementSF     Manure.L     Manure.Q     Manure.C 
      2.6392      59.4353       4.6922      29.4621      20.0580       7.0095 
    Manure^4           A1 
          NA       1.4324 
> vif.cca(mrda)
ManagementHF ManagementNM ManagementSF     Manure.L     Manure.Q     Manure.C 
      2.7608      82.0791       5.0631      38.4808      24.0685       7.4689 
    Manure^4           A1 
          NA       1.3916 
> vif.cca(mcap)
ManagementHF ManagementNM ManagementSF     Manure.L     Manure.Q     Manure.C 
      2.7608      82.0791       5.0631      38.4808      24.0685       7.4689 
    Manure^4           A1 
          NA       1.3916 
> vif.cca(mdb)
ManagementHF ManagementNM ManagementSF     Manure.L     Manure.Q     Manure.C 
      2.7608      82.0791       5.0631      38.4808      24.0685       7.4689 
    Manure^4           A1 
          NA       1.3916 
> 
> alias(mcca)
Model :
dune ~ Condition(Management) + Manure + A1

Complete :
         ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C A1
Manure^4               8.3666                    5.2915  -4.4721   2.6458    

> alias(mrda)
Model :
dune ~ Condition(Management) + Manure + A1

Complete :
         ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C A1
Manure^4               8.3666                    5.2915  -4.4721   2.6458    

> alias(mcap)
Model :
dune ~ Condition(Management) + Manure + A1

Complete :
         ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C A1
Manure^4               8.3666                    5.2915  -4.4721   2.6458    

> alias(mdb)
Model :
dune ~ Condition(Management) + Manure + A1

Complete :
         ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C A1
Manure^4               8.3666                    5.2915  -4.4721   2.6458    

> 
> ## basic statistic
> 
> abs(coef(mcca))
                 CCA1     CCA2      CCA3    CCA4
ManagementHF  0.62129 0.677568  0.035035 1.54946
ManagementNM 10.01217 2.637011 14.104915 5.41558
ManagementSF  0.61605 2.920127  0.607816 1.98726
Manure.L      5.75979 5.151196  8.203284 5.62141
Manure.Q      4.27478 0.010966  8.396272 3.23064
Manure.C      3.40803 1.878886  4.693036 0.25152
Manure^4           NA       NA        NA      NA
A1            0.49572 0.368902  0.137792 0.11238
> abs(coef(mrda))
                 RDA1     RDA2     RDA3     RDA4
ManagementHF 0.039701 0.196654 0.230283 0.331044
ManagementNM 1.885616 2.733188 2.661844 0.965079
ManagementSF 0.241056 0.566718 0.447380 0.355072
Manure.L     1.502678 1.057175 2.212531 0.972634
Manure.Q     0.627410 1.680780 1.472947 0.605660
Manure.C     0.776016 0.849770 0.855201 0.183062
Manure^4           NA       NA       NA       NA
A1           0.045186 0.061152 0.080351 0.056434
> abs(coef(mrda1))
                 RDA1     RDA2     RDA3     RDA4
ManagementHF 0.047647 0.200658 0.035428 0.398849
ManagementNM 2.609121 0.067114 3.393206 0.846634
ManagementSF 0.138903 0.649111 0.090944 0.506550
Manure.L     1.832076 0.744465 2.036043 1.077390
Manure.Q     1.090769 0.253091 2.052449 0.537289
Manure.C     0.942621 0.147407 1.065170 0.210566
Manure^4           NA       NA       NA       NA
A1           0.063521 0.099114 0.029881 0.025905
> abs(coef(mcap))
                 CAP1     CAP2     CAP3     CAP4
ManagementHF 0.054464 0.196369 0.064230 0.396506
ManagementNM 2.144319 0.975995 3.530608 1.013304
ManagementSF 0.118096 0.671018 0.100124 0.480901
Manure.L     1.510554 0.193391 2.360417 1.151619
Manure.Q     0.831594 0.804571 1.997158 0.653864
Manure.C     0.769068 0.163012 1.201823 0.163625
Manure^4           NA       NA       NA       NA
A1           0.074664 0.082683 0.048984 0.024736
> abs(coef(mdb))
               dbRDA1   dbRDA2    dbRDA3   dbRDA4
ManagementHF 0.057234 0.205998 0.0072718 0.396366
ManagementNM 2.148560 0.765167 3.3694004 1.577340
ManagementSF 0.112226 0.684272 0.0077129 0.473942
Manure.L     1.506447 0.341904 2.1389592 1.501846
Manure.Q     0.835134 0.685757 1.9060884 0.976819
Manure.C     0.771676 0.100214 1.2176754 0.030482
Manure^4           NA       NA        NA       NA
A1           0.074999 0.084173 0.0483834 0.019273
> abs(coef(m1rda))
      RDA1
A1 0.10527
> 
> eigenvals(mcca)
   CCA1    CCA2    CCA3    CCA4     CA1     CA2     CA3     CA4     CA5     CA6 
0.22257 0.12260 0.06390 0.04055 0.31761 0.15858 0.13966 0.11608 0.07907 0.07534 
    CA7     CA8     CA9    CA10    CA11    CA12 
0.04527 0.04018 0.03777 0.02799 0.01267 0.01158 
> eigenvals(mrda)
   RDA1    RDA2    RDA3    RDA4     PC1     PC2     PC3     PC4     PC5     PC6 
 8.5394  4.3297  2.2061  1.7162 10.2523  8.2069  4.9525  3.3577  3.1226  2.4941 
    PC7     PC8     PC9    PC10    PC11    PC12 
 1.8660  1.2579  1.0186  0.7428  0.4814  0.3488 
> eigenvals(mrda1)
  RDA1   RDA2   RDA3   RDA4    PC1    PC2    PC3    PC4    PC5    PC6    PC7 
2.6117 1.6991 1.1039 0.7261 3.4684 2.5471 2.1158 1.7223 1.4426 0.9611 0.8089 
   PC8    PC9   PC10   PC11   PC12 
0.7378 0.4903 0.3805 0.2472 0.1570 
> eigenvals(mcap)
   CAP1    CAP2    CAP3    CAP4    MDS1    MDS2    MDS3    MDS4    MDS5    MDS6 
0.67370 0.24300 0.10457 0.05136 0.74894 0.33796 0.30841 0.21316 0.13698 0.13604 
   MDS7    MDS8    MDS9   MDS10   MDS11   MDS12 
0.06196 0.03929 0.01687 0.01110 0.00646 0.00402 
> eigenvals(mdb)
  dbRDA1   dbRDA2   dbRDA3   dbRDA4     MDS1     MDS2     MDS3     MDS4 
 0.66660  0.23850  0.09102  0.03844  0.74204  0.33668  0.30662  0.20627 
    MDS5     MDS6     MDS7     MDS8     MDS9    iMDS1    iMDS2    iMDS3 
 0.13339  0.12829  0.03980  0.02745  0.00041 -0.01985 -0.04601 -0.05923 
> eigenvals(mancap)
   CAP1    CAP2    CAP3    CAP4    MDS1    MDS2    MDS3    MDS4    MDS5    MDS6 
125.658  49.308  24.239  13.875 163.684  97.079  59.006  40.210  34.854  24.943 
   MDS7    MDS8    MDS9   MDS10   MDS11   MDS12 
 12.724  10.918   4.686   1.896   1.506   0.758 
> eigenvals(mandb)
 dbRDA1  dbRDA2  dbRDA3  dbRDA4    MDS1    MDS2    MDS3    MDS4    MDS5    MDS6 
123.163  47.370  21.915  10.128 161.475  96.116  58.781  38.534  33.355  24.565 
   MDS7    MDS8   iMDS1   iMDS2   iMDS3   iMDS4 
  9.591   5.971  -0.590  -6.265 -13.300 -20.787 
> eigenvals(m0cca)
    CA1     CA2     CA3     CA4     CA5     CA6     CA7     CA8     CA9    CA10 
0.44737 0.20300 0.16301 0.13457 0.12940 0.09494 0.07904 0.06526 0.05004 0.04321 
   CA11    CA12    CA13    CA14    CA15    CA16 
0.03870 0.02385 0.01773 0.00917 0.00796 0.00416 
> eigenvals(m0cca, model = "constrained")
NULL
> eigenvals(m1rda)
    RDA1      PC1 
0.002943 0.070268 
> 
> nobs(mcca)
[1] 20
> nobs(mrda)
[1] 20
> nobs(mcap)
[1] 20
> nobs(mdb)
[1] 20
> nobs(m0cca)
[1] 20
> nobs(m1rda)
[1] 20
> 
> RsquareAdj(mcca)
$r.squared
[1] 0.21256

$adj.r.squared
[1] 0.054162

> RsquareAdj(mrda)
$r.squared
[1] 0.1996

$adj.r.squared
[1] 0.057747

> RsquareAdj(mrda1)
$r.squared
[1] 0.20469

$adj.r.squared
[1] 0.044112

> RsquareAdj(mcap)
$r.squared
[1] 0.23349

$adj.r.squared
[1] 0.11198

> RsquareAdj(mdb)
$r.squared
[1] 0.24065

$adj.r.squared
[1] 0.12042

> RsquareAdj(m1rda)
$r.squared
[1] 0.040196

$adj.r.squared
[1] -0.013127

> 
> head(model.frame(mcca))
  Management Manure  A1
1         SF      4 2.8
2         BF      2 3.5
3         SF      4 4.3
4         SF      4 4.2
5         HF      2 6.3
6         HF      2 4.3
> head(model.frame(mrda))
  Management Manure  A1
1         SF      4 2.8
2         BF      2 3.5
3         SF      4 4.3
4         SF      4 4.2
5         HF      2 6.3
6         HF      2 4.3
> head(model.frame(mrda1))
  Management Manure  A1
1         SF      4 2.8
2         BF      2 3.5
3         SF      4 4.3
4         SF      4 4.2
5         HF      2 6.3
6         HF      2 4.3
> head(model.frame(mcap))
  Management Manure  A1
1         SF      4 2.8
2         BF      2 3.5
3         SF      4 4.3
4         SF      4 4.2
5         HF      2 6.3
6         HF      2 4.3
> head(model.frame(mdb))
  Management Manure  A1
1         SF      4 2.8
2         BF      2 3.5
3         SF      4 4.3
4         SF      4 4.2
5         HF      2 6.3
6         HF      2 4.3
> head(model.frame(m0cca))
  Management
1         SF
2         BF
3         SF
4         SF
5         HF
6         HF
> head(model.frame(m1rda))
   A1
1 2.8
2 3.5
3 4.3
4 4.2
5 6.3
6 4.3
> 
> ## testing and model building -
> 
> deviance(mcca)
[1] 727.34
> deviance(mrda)
[1] 723.93
> deviance(mrda1)
[1] 286.5
> deviance(mcap)
[1] 38.402
> deviance(mdb)
[1] 34.121
> deviance(m0cca)
[1] 1035.3
> deviance(m1rda)
[1] 1.3351
> 
> per <- shuffleSet(nrow(dune), 49)
> permutest(mcca, per)

Permutation test for cca under reduced model 

Permutation: free
Number of permutations: 49
 
Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4    0.45 1.27   0.42
Residual 12    1.06            
> permutest(mrda, per)

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    16.8 1.32   0.08 .
Residual 12    38.1              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mrda1, per)

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, scale = TRUE)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4    6.14 1.22   0.16
Residual 12   15.08            
> permutest(mcap, per)

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 49
 
Model: capscale(formula = dune ~ Condition(Management) + Manure + A1,
data = dune.env, distance = "bray")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    1.07 1.59   0.08 .
Residual 12    2.02              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mdb, per)

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data
= dune.env, distance = "bray")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    1.03 1.73   0.08 .
Residual 12    1.80              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mancap, per)

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 49
 
Model: capscale(formula = dune ~ Condition(Management) + Manure + A1,
data = dune.env, distance = "manhattan")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4     213 1.41   0.12
Residual 12     452            
> permutest(mandb, per)

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data
= dune.env, distance = "manhattan")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4     203 1.57   0.08 .
Residual 12     387              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(m1rda, per)

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = H ~ A1, data = dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     1  0.0029 0.75   0.44
Residual 18  0.0703            
> 
> drop1(mcca,  test = "permutation", permutations = per)
                      Df  AIC    F Pr(>F)  
<none>                   87.9              
Condition(Management)  2 87.9              
Manure                 3 86.5 1.03   0.86  
A1                     1 89.0 2.00   0.04 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(mrda,  test = "permutation", permutations = per)
                      Df  AIC    F Pr(>F)
<none>                   87.8            
Condition(Management)  2 89.2            
Manure                 3 87.4 1.30   0.12
A1                     1 87.5 1.09   0.40
> drop1(mrda1, test = "permutation", permutations = per)
                      Df  AIC    F Pr(>F)
<none>                   69.2            
Condition(Management)  2 69.8            
Manure                 3 68.2 1.12   0.22
A1                     1 69.6 1.48   0.14
> drop1(mcap,  test = "permutation", permutations = per)
                      Df  AIC    F Pr(>F)  
<none>                   29.1              
Condition(Management)  2 29.4              
Manure                 3 28.4 1.24   0.22  
A1                     1 30.4 2.19   0.08 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(mdb,   test = "permutation", permutations = per)
                      Df  AIC    F Pr(>F)  
<none>                   26.7              
Condition(Management)  2 27.2              
Manure                 3 26.4 1.32   0.18  
A1                     1 28.4 2.46   0.08 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(m1rda, test = "permutation", permutations = per)
       Df   AIC    F Pr(>F)
<none>    -50.1            
A1      1 -51.3 0.75   0.44
> 
> anova(mcca, permutations = per)
Permutation test for cca under reduced model
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)
Model     4      0.45 1.27   0.42
Residual 12      1.06            
> anova(mrda, permutations = per)
Permutation test for rda under reduced model
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)  
Model     4     16.8 1.32   0.08 .
Residual 12     38.1              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda1, permutations = per)
Permutation test for rda under reduced model
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Model     4     6.14 1.22   0.16
Residual 12    15.08            
> anova(mcap, permutations = per)
Permutation test for capscale under reduced model
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Model     4     1.07 1.59   0.08 .
Residual 12     2.02              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb, permutations = per)
Permutation test for dbrda under reduced model
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Model     4     1.03 1.73   0.08 .
Residual 12     1.80              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per)
Permutation test for capscale under reduced model
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Model     4      213 1.41   0.12
Residual 12      452            
> anova(mandb, permutations = per)
Permutation test for dbrda under reduced model
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)  
Model     4      203 1.57   0.08 .
Residual 12      387              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(m0cca, permutations = per)
No constrained component

Model: cca(formula = dune ~ Condition(Management) + Management, data = dune.env)
         Df ChiSquare  F Pr(>F)
Model     0      0.00  0       
Residual 19      1.51          
> 
> anova(mcca, permutations = per, by="term")
Permutation test for cca under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)  
Manure    3     0.273 1.03   1.00  
A1        1     0.177 2.00   0.02 *
Residual 12     1.062              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda, permutations = per, by="term")
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
Manure    3     13.3 1.40    0.1
A1        1      3.5 1.09    0.4
Residual 12     38.1            
> anova(mrda1, permutations = per, by="term")
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Manure    3     4.28 1.14   0.20
A1        1     1.86 1.48   0.14
Residual 12    15.08            
> anova(mcap, permutations = per, by="term")
Permutation test for capscale under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.703 1.39   0.12  
A1        1    0.370 2.19   0.08 .
Residual 12    2.021              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb, permutations = per, by="term")
Permutation test for dbrda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.667 1.49   0.12  
A1        1    0.367 2.46   0.08 .
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by="term")
Permutation test for capscale under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      173 1.53   0.14
A1        1       40 1.07   0.34
Residual 12      452            
> anova(mandb, permutations = per, by="term")
Permutation test for dbrda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      163 1.68   0.14
A1        1       39 1.22   0.26
Residual 12      387            
> anova(m1rda, permutations = per, by="term")
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
A1        1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> anova(mcca, permutations = per, by="margin")
Permutation test for cca under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)  
Manure    3     0.274 1.03   0.86  
A1        1     0.177 2.00   0.04 *
Residual 12     1.062              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda, permutations = per, by="margin")
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
Manure    3     12.4 1.30   0.12
A1        1      3.5 1.09   0.40
Residual 12     38.1            
> anova(mrda1, permutations = per, by="margin")
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Manure    3     4.21 1.12   0.22
A1        1     1.86 1.48   0.14
Residual 12    15.08            
> anova(mcap, permutations = per, by="margin")
Permutation test for capscale under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.627 1.24   0.22  
A1        1    0.370 2.19   0.08 .
Residual 12    2.021              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb, permutations = per, by="margin")
Permutation test for dbrda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.594 1.32   0.18  
A1        1    0.367 2.46   0.08 .
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by="margin")
Permutation test for capscale under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      165 1.46   0.12
A1        1       40 1.07   0.34
Residual 12      452            
> anova(mandb, permutations = per, by="margin")
Permutation test for dbrda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      155 1.60   0.12
A1        1       39 1.22   0.26
Residual 12      387            
> anova(m1rda, permutations = per, by="margin")
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
A1        1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> anova(mcca, permutations = per, by="axis")
Permutation test for cca under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)
CCA1      1     0.223 2.52   0.26
CCA2      1     0.123 1.39   0.96
CCA3      1     0.064 0.72   1.00
CCA4      1     0.041 0.46       
Residual 12     1.062            
> anova(mrda, permutations = per, by="axis")
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
RDA1      1      8.5 2.69   0.10
RDA2      1      4.3 1.36   0.62
RDA3      1      2.2 0.69   0.98
RDA4      1      1.7 0.54   0.98
Residual 12     38.1            
> anova(mrda1, permutations = per, by="axis")
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
RDA1      1     2.61 2.08   0.22
RDA2      1     1.70 1.35   0.62
RDA3      1     1.10 0.88   0.94
RDA4      1     0.73 0.58   0.98
Residual 12    15.08            
> anova(mcap, permutations = per, by="axis")
Permutation test for capscale under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)
CAP1      1    0.674 4.00   0.12
CAP2      1    0.243 1.44   0.66
CAP3      1    0.105 0.62   0.98
CAP4      1    0.051 0.30   0.98
Residual 12    2.021            
> anova(mdb, permutations = per, by="axis")
Permutation test for dbrda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
dbRDA1    1    0.667 4.45   0.08 .
dbRDA2    1    0.238 1.59   0.58  
dbRDA3    1    0.091 0.61   0.98  
dbRDA4    1    0.038 0.26   0.98  
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by="axis")
Permutation test for capscale under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
CAP1      1      126 3.33   0.18
CAP2      1       49 1.31   0.74
CAP3      1       24 0.64   0.98
CAP4      1       14 0.37   0.98
Residual 12      452            
> anova(mandb, permutations = per, by="axis")
Permutation test for dbrda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
dbRDA1    1      123 3.81   0.18
dbRDA2    1       47 1.47   0.68
dbRDA3    1       22 0.68   0.98
dbRDA4    1       10 0.31   0.98
Residual 12      387            
> anova(m1rda, permutations = per, by="axis")
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
RDA1      1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> ## permutation tests in parallel
> clust <- makeCluster(2) # socket cluster: the only one that works in Windows
> 
> permutest(mcca,   per, parallel = clust) # use socket cluster

Permutation test for cca under reduced model 

Permutation: free
Number of permutations: 49
 
Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4    0.45 1.27   0.42
Residual 12    1.06            
> permutest(mrda,   per, parallel = clust) # use socket cluster

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    16.8 1.32   0.08 .
Residual 12    38.1              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mrda1,  per, parallel = clust) # use socket cluster

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data =
dune.env, scale = TRUE)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4    6.14 1.22   0.16
Residual 12   15.08            
> permutest(mcap,   per, parallel = clust) # use socket cluster

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 49
 
Model: capscale(formula = dune ~ Condition(Management) + Manure + A1,
data = dune.env, distance = "bray")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    1.07 1.59   0.08 .
Residual 12    2.02              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mdb,    per, parallel = clust) # use socket cluster

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data
= dune.env, distance = "bray")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4    1.03 1.73   0.08 .
Residual 12    1.80              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(mancap, per, parallel = clust) # use socket cluster

Permutation test for capscale under reduced model 

Permutation: free
Number of permutations: 49
 
Model: capscale(formula = dune ~ Condition(Management) + Manure + A1,
data = dune.env, distance = "manhattan")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     4     213 1.41   0.12
Residual 12     452            
> permutest(mandb,  per, parallel = clust) # use socket cluster

Permutation test for dbrda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data
= dune.env, distance = "manhattan")
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)  
Model     4     203 1.57   0.08 .
Residual 12     387              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> permutest(m1rda,  per, parallel = clust) # use socket cluster

Permutation test for rda under reduced model 

Permutation: free
Number of permutations: 49
 
Model: rda(formula = H ~ A1, data = dune.env)
Permutation test for all constrained eigenvalues
         Df Inertia    F Pr(>F)
Model     1  0.0029 0.75   0.44
Residual 18  0.0703            
> 
> 
> drop1(mcca,  test = "permutation", permutations = per, parallel = clust)
                      Df  AIC    F Pr(>F)  
<none>                   87.9              
Condition(Management)  2 87.9              
Manure                 3 86.5 1.03   0.86  
A1                     1 89.0 2.00   0.04 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(mrda,  test = "permutation", permutations = per, parallel = clust)
                      Df  AIC    F Pr(>F)
<none>                   87.8            
Condition(Management)  2 89.2            
Manure                 3 87.4 1.30   0.12
A1                     1 87.5 1.09   0.40
> drop1(mrda1, test = "permutation", permutations = per, parallel = clust)
                      Df  AIC    F Pr(>F)
<none>                   69.2            
Condition(Management)  2 69.8            
Manure                 3 68.2 1.12   0.22
A1                     1 69.6 1.48   0.14
> drop1(mcap,  test = "permutation", permutations = per, parallel = clust)
                      Df  AIC    F Pr(>F)  
<none>                   29.1              
Condition(Management)  2 29.4              
Manure                 3 28.4 1.24   0.22  
A1                     1 30.4 2.19   0.08 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(mdb,   test = "permutation", permutations = per, parallel = clust)
                      Df  AIC    F Pr(>F)  
<none>                   26.7              
Condition(Management)  2 27.2              
Manure                 3 26.4 1.32   0.18  
A1                     1 28.4 2.46   0.08 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> drop1(m1rda, test = "permutation", permutations = per, parallel = clust)
       Df   AIC    F Pr(>F)
<none>    -50.1            
A1      1 -51.3 0.75   0.44
> 
> anova(mcca,   permutations = per, parallel = clust)
Permutation test for cca under reduced model
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)
Model     4      0.45 1.27   0.42
Residual 12      1.06            
> anova(mrda,   permutations = per, parallel = clust)
Permutation test for rda under reduced model
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)  
Model     4     16.8 1.32   0.08 .
Residual 12     38.1              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda1,  permutations = per, parallel = clust)
Permutation test for rda under reduced model
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Model     4     6.14 1.22   0.16
Residual 12    15.08            
> anova(mcap,   permutations = per, parallel = clust)
Permutation test for capscale under reduced model
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Model     4     1.07 1.59   0.08 .
Residual 12     2.02              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb,    permutations = per, parallel = clust)
Permutation test for dbrda under reduced model
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Model     4     1.03 1.73   0.08 .
Residual 12     1.80              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, parallel = clust)
Permutation test for capscale under reduced model
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Model     4      213 1.41   0.12
Residual 12      452            
> anova(mandb,  permutations = per, parallel = clust)
Permutation test for dbrda under reduced model
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)  
Model     4      203 1.57   0.08 .
Residual 12      387              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(m0cca,  permutations = per, parallel = clust)
No constrained component

Model: cca(formula = dune ~ Condition(Management) + Management, data = dune.env)
         Df ChiSquare  F Pr(>F)
Model     0      0.00  0       
Residual 19      1.51          
> 
> anova(mcca,   permutations = per, by = "term", parallel = clust)
Permutation test for cca under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)  
Manure    3     0.273 1.03   1.00  
A1        1     0.177 2.00   0.02 *
Residual 12     1.062              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda,   permutations = per, by = "term", parallel = clust)
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
Manure    3     13.3 1.40    0.1
A1        1      3.5 1.09    0.4
Residual 12     38.1            
> anova(mrda1,  permutations = per, by = "term", parallel = clust)
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Manure    3     4.28 1.14   0.20
A1        1     1.86 1.48   0.14
Residual 12    15.08            
> anova(mcap,   permutations = per, by = "term", parallel = clust)
Permutation test for capscale under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.703 1.39   0.12  
A1        1    0.370 2.19   0.08 .
Residual 12    2.021              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb,    permutations = per, by = "term", parallel = clust)
Permutation test for dbrda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.667 1.49   0.12  
A1        1    0.367 2.46   0.08 .
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by = "term", parallel = clust)
Permutation test for capscale under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      173 1.53   0.14
A1        1       40 1.07   0.34
Residual 12      452            
> anova(mandb,  permutations = per, by = "term", parallel = clust)
Permutation test for dbrda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      163 1.68   0.14
A1        1       39 1.22   0.26
Residual 12      387            
> anova(m1rda,  permutations = per, by = "term", parallel = clust)
Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
A1        1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> anova(mcca,   permutations = per, by = "margin", parallel = clust)
Permutation test for cca under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)  
Manure    3     0.274 1.03   0.86  
A1        1     0.177 2.00   0.04 *
Residual 12     1.062              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mrda,   permutations = per, by = "margin", parallel = clust)
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
Manure    3     12.4 1.30   0.12
A1        1      3.5 1.09   0.40
Residual 12     38.1            
> anova(mrda1,  permutations = per, by = "margin", parallel = clust)
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
Manure    3     4.21 1.12   0.22
A1        1     1.86 1.48   0.14
Residual 12    15.08            
> anova(mcap,   permutations = per, by = "margin", parallel = clust)
Permutation test for capscale under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.627 1.24   0.22  
A1        1    0.370 2.19   0.08 .
Residual 12    2.021              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mdb,    permutations = per, by = "margin", parallel = clust)
Permutation test for dbrda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
Manure    3    0.594 1.32   0.18  
A1        1    0.367 2.46   0.08 .
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by = "margin", parallel = clust)
Permutation test for capscale under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      165 1.46   0.12
A1        1       40 1.07   0.34
Residual 12      452            
> anova(mandb,  permutations = per, by = "margin", parallel = clust)
Permutation test for dbrda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
Manure    3      155 1.60   0.12
A1        1       39 1.22   0.26
Residual 12      387            
> anova(m1rda,  permutations = per, by = "margin", parallel = clust)
Permutation test for rda under reduced model
Marginal effects of terms
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
A1        1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> anova(mcca,   permutations = per, by = "axis", parallel = clust)
Permutation test for cca under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: cca(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df ChiSquare    F Pr(>F)
CCA1      1     0.223 2.52   0.26
CCA2      1     0.123 1.39   0.96
CCA3      1     0.064 0.72   1.00
CCA4      1     0.041 0.46       
Residual 12     1.062            
> anova(mrda,   permutations = per, by = "axis", parallel = clust)
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env)
         Df Variance    F Pr(>F)
RDA1      1      8.5 2.69   0.10
RDA2      1      4.3 1.36   0.62
RDA3      1      2.2 0.69   0.98
RDA4      1      1.7 0.54   0.98
Residual 12     38.1            
> anova(mrda1,  permutations = per, by = "axis", parallel = clust)
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, scale = TRUE)
         Df Variance    F Pr(>F)
RDA1      1     2.61 2.08   0.22
RDA2      1     1.70 1.35   0.62
RDA3      1     1.10 0.88   0.94
RDA4      1     0.73 0.58   0.98
Residual 12    15.08            
> anova(mcap,   permutations = per, by = "axis", parallel = clust)
Permutation test for capscale under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)
CAP1      1    0.674 4.00   0.12
CAP2      1    0.243 1.44   0.66
CAP3      1    0.105 0.62   0.98
CAP4      1    0.051 0.30   0.98
Residual 12    2.021            
> anova(mdb,    permutations = per, by = "axis", parallel = clust)
Permutation test for dbrda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "bray")
         Df SumOfSqs    F Pr(>F)  
dbRDA1    1    0.667 4.45   0.08 .
dbRDA2    1    0.238 1.59   0.58  
dbRDA3    1    0.091 0.61   0.98  
dbRDA4    1    0.038 0.26   0.98  
Residual 12    1.796              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(mancap, permutations = per, by = "axis", parallel = clust)
Permutation test for capscale under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: capscale(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
CAP1      1      126 3.33   0.18
CAP2      1       49 1.31   0.74
CAP3      1       24 0.64   0.98
CAP4      1       14 0.37   0.98
Residual 12      452            
> anova(mandb,  permutations = per, by = "axis", parallel = clust)
Permutation test for dbrda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: dbrda(formula = dune ~ Condition(Management) + Manure + A1, data = dune.env, distance = "manhattan")
         Df Variance    F Pr(>F)
dbRDA1    1      123 3.81   0.18
dbRDA2    1       47 1.47   0.68
dbRDA3    1       22 0.68   0.98
dbRDA4    1       10 0.31   0.98
Residual 12      387            
> anova(m1rda,  permutations = per, by = "axis", parallel = clust)
Permutation test for rda under reduced model
Forward tests for axes
Permutation: free
Number of permutations: 49

Model: rda(formula = H ~ A1, data = dune.env)
         Df Variance    F Pr(>F)
RDA1      1   0.0029 0.75   0.44
Residual 18   0.0703            
> 
> # stop the cluster as we are finished
> stopCluster(clust)
> 
> ## the following do not all work with partial models
> 
> mcca <- cca(dune ~ Management + Manure + A1, dune.env)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mrda <- rda(dune ~ Management + Manure + A1, dune.env)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mrda1 <- rda(dune ~ Management + Manure + A1, dune.env, scale = TRUE)

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mcap <- capscale(dune ~ Management + Manure + A1, dune.env, dist = "bray")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mdb <- dbrda(dune ~ Management + Manure + A1, dune.env, dist = "bray")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mancap <- capscale(dune ~ Management + Manure + A1, dune.env, dist = "man")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> mandb <- dbrda(dune ~ Management + Manure + A1, dune.env, dist = "man")

Some constraints or conditions were aliased because they were redundant. This
can happen if terms are linearly dependent (collinear): 'Manure^4'
> 
> head(calibrate(mcca))
  ManagementHF ManagementNM ManagementSF   Manure.L Manure.Q Manure.C     A1
1     0.883602    -0.178091      0.36500  0.7922315  0.78355  0.57312 1.3024
2    -0.257595    -0.069182      0.46841  0.2174342 -0.27084  0.18996 4.2482
3    -0.055206    -0.068419      1.04034  0.6060948  0.21723  0.09595 4.2281
4    -0.304369     0.132054      1.21814  0.5919769  0.71695  0.40928 4.8630
5     0.961520     0.091569     -0.12497 -0.0029732 -0.49357 -0.11564 4.9642
6     1.449919     0.075602     -0.42298 -0.0535267 -0.68574 -0.40418 4.7055
> head(calibrate(mrda))
  ManagementHF ManagementNM ManagementSF Manure.L  Manure.Q Manure.C     A1
1      0.29401     0.408403     0.440828  0.34294  0.960228  0.25907 3.1367
2     -0.32193    -0.210940     0.525258  0.25761 -0.426433  0.32086 4.7427
3     -0.06329    -0.382552     1.295568  0.88816  0.051051  0.20844 3.0244
4     -0.23072    -0.025851     1.263604  0.66627  0.592289  0.48117 5.1389
5      1.09411     0.333615    -0.086119  0.10122 -0.218722 -0.47284 5.6906
6      1.54974     0.128610    -0.647474 -0.24172 -0.688913 -0.24163 4.9992
> head(calibrate(mrda1))
  ManagementHF ManagementNM ManagementSF  Manure.L Manure.Q  Manure.C     A1
1    0.4195172     0.195602     0.489930  0.408945  0.63673  0.144131 3.2457
2   -0.2555697    -0.159948     0.512425  0.339689 -0.36751  0.098438 4.1415
3    0.0088535    -0.149923     1.023768  0.659460  0.19479  0.184543 3.8499
4   -0.4283707    -0.045680     1.486302  0.828962  0.77205  0.620009 4.2044
5    0.8791230     0.132390    -0.061982  0.027179 -0.43322 -0.200905 4.8834
6    1.5945412     0.099612    -0.601114 -0.217085 -0.77311 -0.325635 4.9080
> head(calibrate(mcap))
  ManagementHF ManagementNM ManagementSF Manure.L  Manure.Q Manure.C     A1
1      0.35351    0.1299840      0.73772  0.83346  1.150928  0.34051 1.5819
2     -0.27328   -0.1807926      0.57688  0.36108 -0.389540  0.11337 4.5618
3     -0.11521   -0.1378795      1.07627  0.50500  0.078248  0.33544 5.1742
4     -0.23830    0.0078955      1.18601  0.55891  0.374392  0.27273 4.5439
5      1.06102    0.4254412      0.13710  0.28460  0.040009 -0.59962 4.9298
6      1.21797    0.1198752     -0.54117 -0.26797 -0.686710 -0.18564 4.7785
> head(calibrate(mdb))
  ManagementHF ManagementNM ManagementSF Manure.L  Manure.Q Manure.C      A1
1      1.05945      0.29233      0.45310  0.87163  1.686742  0.39091 0.84665
2     -0.34870     -0.23103      0.57147  0.27070 -0.480259  0.28872 4.72537
3     -0.47320     -0.16902      1.26895  0.52349 -0.119173  0.25712 5.74253
4     -0.58626     -0.12331      1.27795  0.50225  0.035999  0.30065 4.71082
5      1.33269      0.79710      0.31597  0.70260  0.684932 -1.30598 5.00807
6      1.02170      0.04279     -0.45446 -0.19833 -0.946468 -0.41926 4.83736
> head(calibrate(mancap))
  ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C     A1
1    0.1281240      0.49145      0.55983  0.38470  1.01262  0.05207 2.9860
2   -0.2879151     -0.26123      0.60310  0.35832 -0.34121  0.38002 4.7783
3    0.0069596     -0.30212      1.12067  0.67840 -0.01814  0.29692 5.0313
4   -0.1350836     -0.18933      1.31950  0.83427  0.60909  0.59970 3.2827
5    1.0725483      0.45851      0.19538  0.40446  0.19234 -0.66824 4.1253
6    1.2857657      0.17740     -0.75589 -0.46798 -0.90859 -0.30014 5.4699
> head(calibrate(mandb))
  ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C     A1
1      0.66644      0.97505      0.47379  0.66422  2.09891 -0.22874 1.9653
2     -0.38822     -0.34825      0.53059  0.12940 -0.50764  0.77856 5.6362
3     -0.32924     -0.58837      1.19831  0.53616 -0.68211  0.41320 5.7036
4     -0.33720     -0.38668      1.32790  0.69699  0.18678  0.76423 3.6311
5      1.79594      1.19611      0.29836  1.11710  1.76562 -1.62223 2.1351
6      0.94598     -0.19327     -0.59457 -0.39197 -1.80062 -0.68601 5.2833
> 
> head(calibrate(mcca, newdata=dune[11:15,]))
   ManagementHF ManagementNM ManagementSF Manure.L Manure.Q Manure.C      A1
11     0.233858      0.13861     -0.32589 -0.67553 -0.10659  0.96310  2.3507
12    -0.260642     -0.13316      1.17152 -0.18386 -0.69386  0.46843  5.9871
13    -0.081594     -0.30854      1.18097  0.46491 -0.63881 -0.47286  4.3479
14    -0.502316      1.06326      0.16060 -0.79843  0.41515 -0.15379 12.3207
15     0.559981      0.90354     -0.15982 -0.50872  0.61926 -0.36272 10.2026
> head(calibrate(mrda, newdata=dune[11:15,]))
   ManagementHF ManagementNM ManagementSF Manure.L  Manure.Q   Manure.C      A1
11     0.201986      0.28140    -0.260060 -0.57309  0.052355  0.6582554  1.8489
12    -0.321917     -0.25129     1.208336 -0.11711 -0.804022  0.3936137  4.4676
13    -0.032546     -0.39458     1.249458  0.62224 -0.686520 -0.5422918  3.4391
14    -0.351860      0.97669    -0.021120 -0.83760  0.391761  0.0098888 12.3969
15     0.294308      1.01918    -0.072777 -0.57590  0.635282 -0.4504748  9.7828
> head(calibrate(mrda1, newdata=dune[11:15,]))
   ManagementHF ManagementNM ManagementSF Manure.L  Manure.Q Manure.C      A1
11     0.155890     0.255231    -0.302207 -0.73488 -0.013315  0.90939  2.6425
12    -0.218095    -0.072054     1.150670 -0.14978 -0.564254  0.42810  5.9670
13    -0.049615    -0.458412     1.292784  0.66760 -0.789885 -0.72793  4.0747
14    -0.234464     1.037849     0.029142 -0.75498  0.435175 -0.26652 11.9376
15     0.298221     1.006569    -0.102984 -0.60489  0.611461 -0.36576 10.3615
> ## head(calibrate(m1rda, newdata=dune[11:15,]))## fails
> 
> head(predict(mcca, newdata = dune.env))
  Achimill Agrostol  Airaprae Alopgeni  Anthodor Bellpere Bromhord   Chenalbu
1  0.24866  1.73029  0.136732  1.56567  0.176689  0.69298  0.51661 -0.0066751
2  3.38022 -1.33575  0.103100  0.65804  1.869170  2.61940  3.71719 -0.0403493
3  0.34629  4.86894 -0.077815  3.49921 -0.100555  1.55684  1.16941  0.0037988
4  0.40505  5.40077 -0.058917  3.93512 -0.076134  1.75018  1.31398  0.0028763
5  1.40721  1.39415 -0.409583  1.63738  1.727211  0.95730  1.09875 -0.0725665
6  1.90089 -0.08191  0.153453  1.79584  2.717164  1.04159  1.19230 -0.1108163
    Cirsarve Comapalu Eleopalu Elymrepe  Empenigr  Hyporadi  Juncarti  Juncbufo
1  0.3441739 -0.23208 -0.45345   2.1049  0.057806  0.185956 -0.099929  0.061638
2 -0.0040270 -0.17500 -0.50790   1.1357  0.043588  0.520382 -1.422491 -1.092553
3  0.7797384  0.13208  0.25806   4.6558 -0.032898 -0.105828  0.056870 -0.035078
4  0.8760877  0.10000  0.19539   5.2394 -0.024908 -0.080127  0.043059 -0.026559
5  0.0159981  0.69521  0.92329   2.6923 -0.173160 -0.707302  0.863780  0.925259
6 -0.0059938 -0.26047 -0.99453   3.0401  0.064876  0.040954  0.517926  1.308129
  Lolipere  Planlanc Poaprat Poatriv Ranuflam   Rumeacet Sagiproc Salirepe
1   3.3037  0.084120  2.3947  2.2427 -0.13537  0.0087837 0.960535  0.29588
2   6.5539  2.660088  3.7155  5.1158 -0.18507  0.9898833 0.020732  0.22310
3   6.9004 -0.047873  4.9787  5.0651  0.07704 -0.0049989 1.892379 -0.16839
4   7.7960 -0.036247  5.6267  5.6922  0.05833 -0.0037848 2.147087 -0.12749
5   3.0005  3.113739  2.2475  5.1987  0.18798  4.5983853 0.523997 -0.88631
6   4.0551  3.851490  3.0574  5.6731 -0.39474  5.1723104 0.972355  0.33206
  Scorautu   Trifprat Trifrepe   Vicilath Bracruta  Callcusp
1  0.82391  0.0197135  0.31089  0.0069474  0.74251 -0.088855
2  5.26245  0.9904728  4.99741  0.5754882  1.78447 -0.172948
3  1.48233 -0.0112191  1.28649 -0.0039538  1.52865  0.050568
4  1.69376 -0.0084944  1.40263 -0.0029936  1.72884  0.038287
5  2.64699  2.4979708  4.08460 -0.2462139  3.06843 -0.011518
6  3.51252  2.8764755  3.60655 -0.2438153  3.61943 -0.409696
> predict(mrda, newdata = dune.env[1:4,])
  Achimill Agrostol  Airaprae Alopgeni Anthodor Bellpere Bromhord   Chenalbu
1  0.42151   3.5776  0.169954  2.96527  0.22365   1.3183  0.98345 -0.0071714
2  3.31141  -1.2047  0.068507  0.67566  1.81429   2.5802  3.64850 -0.0373735
3  0.28468   4.2330 -0.093768  3.01916 -0.12339   1.3416  1.00913  0.0039566
4  0.29380   4.1893 -0.076186  3.01557 -0.10026   1.3401  1.00742  0.0032148
    Cirsarve Comapalu Eleopalu Elymrepe  Empenigr Hyporadi  Juncarti  Juncbufo
1  0.6537462 -0.25642 -0.48190   3.9671  0.071560  0.23272 -0.093331  0.071945
2 -0.0052081 -0.10336 -0.33218   1.0902  0.028845  0.43864 -1.382448 -1.108931
3  0.6737952  0.14147  0.26587   4.0182 -0.039481 -0.12840  0.051493 -0.039694
4  0.6724586  0.11495  0.21602   4.0147 -0.032078 -0.10432  0.041838 -0.032251
  Lolipere  Planlanc Poaprat Poatriv  Ranuflam   Rumeacet Sagiproc Salirepe
1   6.1341  0.110732  4.4479  4.2624 -0.132118  0.0061432  1.75867  0.36823
2   6.3299  2.630842  3.5634  5.1093 -0.122221  1.0714418 -0.03188  0.14843
3   5.9260 -0.061094  4.2701  4.3725  0.072893 -0.0033894  1.61591 -0.20316
4   5.9399 -0.049639  4.2820  4.3651  0.059225 -0.0027539  1.62542 -0.16507
  Scorautu   Trifprat Trifrepe   Vicilath Bracruta  Callcusp
1   1.5171  0.0205888  0.77684  0.0121579   1.4156 -0.082638
2   5.1431  1.0427819  4.94453  0.5221421   1.7573 -0.136759
3   1.2319 -0.0113594  1.12312 -0.0067078   1.2879  0.045593
4   1.2509 -0.0092295  1.10004 -0.0054501   1.2965  0.037045
> predict(mrda1, newdata = dune.env[1:4,])
  Achimill Agrostol  Airaprae Alopgeni Anthodor Bellpere Bromhord   Chenalbu
1  0.42151   3.5776  0.169954  2.96527  0.22365   1.3183  0.98345 -0.0071714
2  3.31141  -1.2047  0.068507  0.67566  1.81429   2.5802  3.64850 -0.0373735
3  0.28468   4.2330 -0.093768  3.01916 -0.12339   1.3416  1.00913  0.0039566
4  0.29380   4.1893 -0.076186  3.01557 -0.10026   1.3401  1.00742  0.0032148
    Cirsarve Comapalu Eleopalu Elymrepe  Empenigr Hyporadi  Juncarti  Juncbufo
1  0.6537462 -0.25642 -0.48190   3.9671  0.071560  0.23272 -0.093331  0.071945
2 -0.0052081 -0.10336 -0.33218   1.0902  0.028845  0.43864 -1.382448 -1.108931
3  0.6737952  0.14147  0.26587   4.0182 -0.039481 -0.12840  0.051493 -0.039694
4  0.6724586  0.11495  0.21602   4.0147 -0.032078 -0.10432  0.041838 -0.032251
  Lolipere  Planlanc Poaprat Poatriv  Ranuflam   Rumeacet Sagiproc Salirepe
1   6.1341  0.110732  4.4479  4.2624 -0.132118  0.0061432  1.75867  0.36823
2   6.3299  2.630842  3.5634  5.1093 -0.122221  1.0714418 -0.03188  0.14843
3   5.9260 -0.061094  4.2701  4.3725  0.072893 -0.0033894  1.61591 -0.20316
4   5.9399 -0.049639  4.2820  4.3651  0.059225 -0.0027539  1.62542 -0.16507
  Scorautu   Trifprat Trifrepe   Vicilath Bracruta  Callcusp
1   1.5171  0.0205888  0.77684  0.0121579   1.4156 -0.082638
2   5.1431  1.0427819  4.94453  0.5221421   1.7573 -0.136759
3   1.2319 -0.0113594  1.12312 -0.0067078   1.2879  0.045593
4   1.2509 -0.0092295  1.10004 -0.0054501   1.2965  0.037045
> predict(mcap, newdata = dune.env[1:4,])
          1         2         3
2 0.4410552                    
3 0.1132396 0.4889419          
4 0.1056903 0.4850746 0.0075493
> predict(mdb, newdata = dune.env[1:4,])
          1         2         3
2 0.4101123                    
3 0.1129160 0.4608659          
4 0.1053882 0.4567899 0.0075277
> predict(mancap, newdata = dune.env[1:4,])
         1        2        3
2 8.064421                  
3 1.182080 8.684763         
4 1.103275 8.639762 0.078805
> predict(mandb, newdata = dune.env[1:4,])
         1        2        3
2 7.600620                  
3 1.170623 8.248343         
4 1.092581 8.201556 0.078042
> predict(m1rda, newdata = dune.env[1:4,])
    col1
1 2.2142
2 2.1968
3 2.1769
4 2.1794
> 
> ## the sign is arbitrary
> abs(predict(mcca, newdata = dune[1:4,], type="wa"))
     CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7
1 1.62466 0.11383 1.78622 0.47896 2.12030 1.39557 3.08506
2 1.06133 0.20433 1.30825 0.37139 0.76061 1.33289 1.37522
3 0.71033 0.77748 0.81637 0.93095 0.66982 0.70982 0.35968
4 0.64819 0.72329 1.44737 1.14892 1.84672 0.30213 0.86769
> abs(predict(mrda, newdata = dune[1:4,], type="wa"))
     RDA1     RDA2    RDA3    RDA4     RDA5      RDA6    RDA7
1 0.18535 0.022419 0.40394 0.28201 0.401393 0.0089804 0.17894
2 0.34065 0.015217 0.15589 0.29898 0.481298 0.3110483 0.19056
3 0.20203 0.385177 0.21607 0.16160 0.166526 0.0095877 0.15736
4 0.11484 0.349445 0.34771 0.24737 0.051871 0.3004530 0.11508
> abs(predict(mrda1, newdata = dune[1:4,], type="wa"))
      RDA1     RDA2    RDA3    RDA4    RDA5     RDA6     RDA7
1 0.095172 0.104425 0.22637 0.17358 0.30374 0.152736 0.308891
2 0.365200 0.034168 0.28660 0.18871 0.10331 0.478363 0.288641
3 0.141907 0.261778 0.22356 0.14939 0.13501 0.111882 0.075503
4 0.147735 0.348054 0.43875 0.29730 0.40430 0.024991 0.312684
> 
> ## the sign is arbitrary
> abs(predict(mcca, newdata = dune[,1:4], type="sp"))
            CCA1   CCA2    CCA3    CCA4    CCA5    CCA6     CCA7
Achimill 0.84687 1.0701 0.23634 0.82289 1.50817 1.01313 0.550205
Agrostol 0.77155 1.3011 0.42471 0.53466 0.71397 0.13494 0.051337
Airaprae 2.15432 3.1226 0.52500 2.50252 1.15845 1.26403 0.033265
Alopgeni 0.14431 1.6487 0.42805 1.37756 0.61985 0.93554 0.806710
> abs(predict(mrda, newdata = dune[,1:4], type="sp"))
             RDA1     RDA2     RDA3     RDA4     RDA5     RDA6       RDA7
Achimill 0.156357 0.109758 0.051875 0.155370 0.192307 0.021201 0.05592900
Agrostol 0.245787 0.453963 0.162518 0.018188 0.172589 0.119162 0.01098465
Airaprae 0.052576 0.094503 0.014547 0.129765 0.049461 0.117122 0.08994751
Alopgeni 0.024101 0.516842 0.132875 0.087468 0.396101 0.104365 0.00093612
> abs(predict(mrda1, newdata = dune[,1:4], type="sp"))
             RDA1    RDA2     RDA3       RDA4     RDA5     RDA6     RDA7
Achimill 0.257242 0.15508 0.023807 0.12405544 0.167384 0.214501 0.028569
Agrostol 0.196652 0.30574 0.103167 0.00039545 0.045675 0.006216 0.010224
Airaprae 0.117004 0.25667 0.028025 0.25799706 0.066905 0.086901 0.012198
Alopgeni 0.031859 0.35291 0.051066 0.12889917 0.190337 0.197400 0.181314
> 
> abs(predict(mcca, newdata = dune.env[1:4,], type="lc"))
     CCA1    CCA2    CCA3    CCA4   CCA5    CCA6     CCA7
1 0.98522 0.18116 1.06369 1.50574 1.3173 0.28751 0.141532
2 1.13730 1.06013 0.82297 0.86803 1.2579 1.77285 1.123271
3 0.80654 0.70480 1.31221 0.80414 1.4683 0.13208 0.010662
4 0.81845 0.66990 1.29564 0.85092 1.4582 0.14245 0.000516
> abs(predict(mrda, newdata = dune.env[1:4,], type="lc"))
     RDA1    RDA2     RDA3    RDA4     RDA5     RDA6    RDA7
1 0.18523 0.20623 0.316247 0.30245 0.049422 0.025451 0.16224
2 0.36803 0.22424 0.027466 0.34105 0.454235 0.099307 0.29753
3 0.15757 0.25460 0.326062 0.19053 0.121045 0.141679 0.14397
4 0.15942 0.25137 0.325408 0.19799 0.116270 0.133930 0.14518
> abs(predict(mrda1, newdata = dune.env[1:4,], type="lc"))
     RDA1    RDA2    RDA3    RDA4    RDA5     RDA6     RDA7
1 0.14664 0.19636 0.27651 0.30865 0.25564 0.021393 0.012121
2 0.41723 0.24524 0.14249 0.22618 0.15529 0.482284 0.212404
3 0.11814 0.26110 0.30710 0.15053 0.29502 0.020007 0.034328
4 0.12004 0.25679 0.30507 0.16108 0.29239 0.017247 0.032847
> abs(predict(mcap, newdata = dune.env[1:4,], type="lc"))
     CAP1    CAP2    CAP3    CAP4     CAP5     CAP6     CAP7
1 0.27462 0.15007 0.21773 0.28034 0.099690 0.245828 0.058665
2 0.32370 0.22297 0.10532 0.25592 0.502586 0.084408 0.341630
3 0.21968 0.23163 0.27891 0.14326 0.097533 0.278465 0.020906
4 0.22334 0.22620 0.27483 0.15240 0.097677 0.276289 0.023424
> abs(predict(mdb, newdata = dune.env[1:4,], type="lc"))
   dbRDA1  dbRDA2  dbRDA3  dbRDA4  dbRDA5  dbRDA6   dbRDA7
1 0.27666 0.14786 0.21628 0.27463 0.10935 0.23099 0.108744
2 0.32039 0.21931 0.11598 0.22087 0.13951 0.50786 0.342277
3 0.22194 0.22991 0.27926 0.13863 0.14881 0.24437 0.080877
4 0.22559 0.22444 0.27506 0.14769 0.14618 0.24348 0.082735
> abs(predict(mancap, newdata = dune.env[1:4,], type="lc"))
     CAP1    CAP2    CAP3     CAP4     CAP5    CAP6     CAP7
1 0.15906 0.20999 0.26950 0.273591 0.085989 0.26571 0.053587
2 0.38906 0.25364 0.20949 0.094601 0.472958 0.21394 0.263674
3 0.13353 0.26897 0.28834 0.159016 0.012678 0.29389 0.050910
4 0.13523 0.26503 0.28708 0.166654 0.017565 0.29201 0.043944
> abs(predict(m1rda, newdata = dune.env[1:4,], type="lc"))
      RDA1
1 0.215813
2 0.142121
3 0.057901
4 0.068429
> abs(predict(mandb, newdata = dune.env[1:4,]))
         1        2        3
2 7.600620                  
3 1.170623 8.248343         
4 1.092581 8.201556 0.078042
> ## reset
> options(op)
> 
> proc.time()
   user  system elapsed 
  0.865   0.090   1.528 
