R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("vegan-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('vegan')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "BCI"
> 
> ### * BCI
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: BCI
> ### Title: Barro Colorado Island Tree Counts
> ### Aliases: BCI
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(BCI)
> 
> 
> 
> cleanEx(); ..nameEx <- "anosim"
> 
> ### * anosim
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: anosim
> ### Title: Analysis of Similarities
> ### Aliases: anosim print.anosim summary.anosim plot.anosim
> ### Keywords: multivariate nonparametric htest
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> dune.dist <- vegdist(dune)
> attach(dune.env)
> dune.ano <- anosim(dune.dist, Management)
> summary(dune.ano)

Call:
anosim(dis = dune.dist, grouping = Management) 
Dissimilarity: bray 

ANOSIM statistic R: 0.2579 
      Significance: 0.005 

Based on  1000  permutations

Empirical upper confidence limits of R:
  90%   95% 97.5%   99% 
0.116 0.160 0.203 0.233 

Dissimilarity ranks between and within classes:
        0%   25%    50%     75%  100%   N
Between  4 58.50 104.00 145.500 188.0 147
BF       5 15.25  25.50  41.250  57.0   3
HF       1  7.25  46.25  68.125  89.5  10
NM       6 64.75 124.50 156.250 181.0  15
SF       3 32.75  53.50  99.250 184.0  15

> plot(dune.ano)
> 
> 
> 
> cleanEx(); ..nameEx <- "anova.cca"
> 
> ### * anova.cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: anova.cca
> ### Title: Permutation Test for Constrained Correspondence Analysis,
> ###   Redundancy Analysis and Constrained Analysis of Principal Coordinates
> ### Aliases: anova.cca permutest.cca print.permutest.cca print.anova.cca
> ### Keywords: multivariate htest
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> vare.cca <- cca(varespec ~ Al + P + K, varechem)
> anova(vare.cca)
Permutation test for cca under reduced model

Model: cca(formula = varespec ~ Al + P + K, data = varechem)
         Df  Chisq      F N.Perm  Pr(>F)    
Model     3 0.6441 2.9840    200 < 0.005 ***
Residual 20 1.4391                          
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> permutest.cca(vare.cca)

Permutation test for cca 
Call:
cca(formula = varespec ~ Al + P + K, data = varechem) 

Test for significance of all constrained eigenvalues
Pseudo-F:	 2.984036 
Significance:	 < 0.01 
Based on 100 permutations under reduced model.

> ## Test for adding variable N to the previous model:
> anova(cca(varespec ~ N + Condition(Al + P + K), varechem), step=40)
Permutation test for cca under reduced model

Model: cca(formula = varespec ~ N + Condition(Al + P + K), data = varechem)
         Df  Chisq      F N.Perm Pr(>F)
Model     1 0.1063 1.5148     40    0.2
Residual 19 1.3328                     
> 
> 
> 
> cleanEx(); ..nameEx <- "bioenv"
> 
> ### * bioenv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bioenv
> ### Title: Best Subset of Environmental Variables with Maximum (Rank)
> ###   Correlation with Community Dissimilarities
> ### Aliases: bioenv bioenv.default bioenv.formula print.bioenv
> ###   summary.bioenv print.summary.bioenv ripley.subsets ripley.subs
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> # The method is very slow for large number of possible subsets.
> # Therefore only 6 variables in this example.
> data(varespec)
> data(varechem)
> sol <- bioenv(wisconsin(varespec) ~ log(N) + P + K + Ca + pH + Al, varechem)
> sol

Call:
bioenv(formula = wisconsin(varespec) ~ log(N) + P + K + Ca +      pH + Al, data = varechem) 

Subset of environmental variables with best correlation to community data.

Correlations:      spearman 
Dissimilarities:   bray 

Best model has 3 parameters (max. 6 allowed):
P Ca Al
with correlation  0.4004806 

> summary(sol)
                    size correlation
P                      1      0.2516
P Al                   2      0.4004
P Ca Al                3      0.4005
P Ca pH Al             4      0.3619
log(N) P Ca pH Al      5      0.3216
log(N) P K Ca pH Al    6      0.2822
> 
> 
> 
> cleanEx(); ..nameEx <- "capscale"
> 
> ### * capscale
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: capscale
> ### Title: [Partial] Constrained Analysis of Principal Coordinates
> ### Aliases: capscale
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> vare.cap <- capscale(varespec ~ N + P + K + Condition(Al), varechem, dist="bray")
Warning in cmdscale(X, k = k, eig = TRUE, add = add) : 
	 some of the first 23 eigenvalues are < 0
Warning in sqrt(ev) : NaNs produced
> vare.cap

Call:
capscale(formula = varespec ~ N + P + K + Condition(Al), data = varechem,      distance = "bray") 

              Inertia Rank
Total          110.48     
Conditional     22.48    1
Constrained     22.93    3
Unconstrained   65.07   15
Inertia is squared Bray distance 

Eigenvalues for constrained axes:
  CAP1   CAP2   CAP3 
12.451  7.510  2.974 

Eigenvalues for unconstrained axes:
     PC1      PC2      PC3      PC4      PC5      PC6      PC7      PC8 
20.84991 11.79310  7.77204  6.03974  4.67406  3.72053  2.85601  1.96810 
     PC9     PC10     PC11     PC12     PC13     PC14     PC15 
 1.58427  1.34196  1.15191  0.63797  0.47930  0.16803  0.03093 

> plot(vare.cap)
> anova(vare.cap)
Permutation test for capscale under reduced model

Model: capscale(formula = varespec ~ N + P + K + Condition(Al), data = varechem, distance = "bray")
         Df     Var      F  N.Perm  Pr(>F)    
Model     3  22.935 1.7624 200.000 < 0.005 ***
Residual 15  65.068                           
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> 
> 
> cleanEx(); ..nameEx <- "cca"
> 
> ### * cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cca
> ### Title: [Partial] [Constrained] Correspondence Analysis and Redundancy
> ###   Analysis
> ### Aliases: cca cca.default cca.formula print.cca summary.cca
> ###   print.summary.cca rda rda.default rda.formula summary.rda
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> ## Common but bad way: use all variables you happen to have in your
> ## environmental data matrix
> vare.cca <- cca(varespec, varechem)
> vare.cca

Call:
cca(X = varespec, Y = varechem) 

              Inertia Rank
Total          2.0832     
Constrained    1.4415   14
Unconstrained  0.6417    9
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
    CCA1     CCA2     CCA3     CCA4     CCA5     CCA6     CCA7     CCA8 
0.438870 0.291775 0.162847 0.142130 0.117952 0.089029 0.070295 0.058359 
    CCA9    CCA10    CCA11    CCA12    CCA13    CCA14 
0.031141 0.013294 0.008364 0.006538 0.006156 0.004733 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8 
0.197765 0.141926 0.101174 0.070787 0.053303 0.033299 0.018868 0.015104 
     CA9 
0.009488 

> plot(vare.cca)
> ## Formula interface and a better model
> vare.cca <- cca(varespec ~ Al + P*(K + Baresoil), data=varechem)
> vare.cca

Call:
cca(formula = varespec ~ Al + P * (K + Baresoil), data = varechem) 

              Inertia Rank
Total           2.083     
Constrained     1.046    6
Unconstrained   1.038   17
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
   CCA1    CCA2    CCA3    CCA4    CCA5    CCA6 
0.37563 0.23419 0.14067 0.13229 0.10675 0.05614 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4     CA5     CA6     CA7     CA8 
0.27577 0.15411 0.13536 0.11803 0.08887 0.05511 0.04919 0.03781 
(Showed only 8 of all 17 unconstrained eigenvalues)

> plot(vare.cca)
> ## `Partialling out' and `negative components of variance'
> cca(varespec ~ Ca, varechem)

Call:
cca(formula = varespec ~ Ca, data = varechem) 

              Inertia Rank
Total          2.0832     
Constrained    0.1572    1
Unconstrained  1.9260   22
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
  CCA1 
0.1572 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4     CA5     CA6     CA7     CA8 
0.47455 0.29389 0.21403 0.19541 0.17482 0.11711 0.11207 0.08797 
(Showed only 8 of all 22 unconstrained eigenvalues)

> cca(varespec ~ Ca + Condition(pH), varechem)

Call:
cca(formula = varespec ~ Ca + Condition(pH), data = varechem) 

              Inertia Rank
Total          2.0832     
Conditional    0.1458    1
Constrained    0.1827    1
Unconstrained  1.7547   21
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
  CCA1 
0.1827 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4     CA5     CA6     CA7     CA8 
0.38343 0.27487 0.21233 0.17599 0.17013 0.11613 0.10892 0.08797 
(Showed only 8 of all 21 unconstrained eigenvalues)

> ## RDA
> data(dune)
> data(dune.env)
> dune.Manure <- rda(dune ~ Manure, dune.env)
> plot(dune.Manure) 
> 
> 
> 
> cleanEx(); ..nameEx <- "decorana"
> 
> ### * decorana
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: decorana
> ### Title: Detrended Correspondence Analysis and Basic Reciprocal Averaging
> ### Aliases: decorana print.decorana summary.decorana
> ###   print.summary.decorana plot.decorana downweight scores.decorana
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> vare.dca <- decorana(varespec)
> vare.dca

Call:
decorana(veg = varespec) 

Detrended correspondence analysis with 26 segments.
Rescaling of axes with 4 iterations.

                  DCA1   DCA2   DCA3    DCA4
Eigenvalues     0.5235 0.3253 0.2001 0.19176
Decorana values 0.5249 0.1572 0.0967 0.06075
Axis lengths    2.8161 2.2054 1.5465 1.64864

> summary(vare.dca)

Call:
decorana(veg = varespec) 

Detrended correspondence analysis with 26 segments.
Rescaling of axes with 4 iterations.

                  DCA1   DCA2   DCA3    DCA4
Eigenvalues     0.5235 0.3253 0.2001 0.19176
Decorana values 0.5249 0.1572 0.0967 0.06075
Axis lengths    2.8161 2.2054 1.5465 1.64864

Species scores:

            DCA1     DCA2     DCA3     DCA4 Totals
Cal.vul  0.04119 -1.53268 -2.55101  1.32277  45.07
Emp.nig  0.09019  0.82274  0.20569  0.30631 151.99
Led.pal  1.34533  2.47141 -0.34970 -1.13823   8.39
Vac.myr  1.86298  1.71424 -0.60535 -0.40205  50.71
Vac.vit  0.16641  0.71095  0.00313 -0.55801 275.03
Pin.syl -0.73490  1.62050 -1.60275 -2.10199   4.11
Des.fle  1.97061  1.81651  1.74896 -0.91463   5.60
Bet.pub  0.79745  3.36374 -0.94546 -1.01741   0.29
Vac.uli -0.08912 -1.17478  2.86624  0.87025  15.22
Dip.mon -0.82669 -0.44195  2.58579 -0.38459   3.24
Dic.sp   2.37743 -0.27373 -0.47099 -1.89036  40.50
Dic.fus  1.58267 -1.33770 -1.33563  1.47417 113.52
Dic.pol  0.86689  2.39519 -0.82064 -3.41534   6.06
Hyl.spl  2.66242  1.19669  1.48288 -0.69978  18.04
Ple.sch  1.64098  0.15607  0.30044 -0.26717 377.97
Pol.pil -0.56213  0.14009  0.25198  0.49177   0.61
Pol.jun  1.22244 -0.89173  0.61287  3.60066  13.85
Pol.com  1.01545  2.08388  0.06402  0.84199   0.71
Poh.nut -0.00712  1.09704 -0.82126 -1.59862   2.62
Pti.cil  0.48093  2.86420 -0.71801 -1.02698  14.01
Bar.lyc  0.58303  3.71792 -0.84212 -1.88837   3.19
Cla.arb -0.18554 -1.18973  0.68113  0.55399 255.05
Cla.ran -0.83427 -0.78085  0.90603  0.70057 388.71
Cla.ste -1.67768  0.98907 -0.83789 -0.60206 486.71
Cla.unc  0.97686 -1.70859 -1.68281 -2.26756  56.28
Cla.coc -0.27221 -0.76713 -0.63836  0.66927   2.79
Cla.cor  0.29068 -0.97039  0.50414  0.95738   6.22
Cla.gra  0.21778 -0.41879  0.06530 -0.31472   5.14
Cla.fim  0.00889 -0.23922 -0.26505  0.33123   3.96
Cla.cri  0.37774 -1.09161 -0.55627  0.23868   7.47
Cla.chl -0.91983  1.54955 -0.58109 -1.48643   1.16
Cla.bot  0.66438  2.19584 -0.90331 -0.91391   0.47
Cla.ama -0.96418 -0.98992  2.71458  0.52352   0.14
Cla.sp  -1.12318 -0.15330 -0.69833  0.44040   0.52
Cet.eri  0.27163 -1.28867 -0.81682 -1.93935   3.60
Cet.isl -0.50158  2.22098 -1.16461 -1.89349   2.03
Cet.niv -1.67937 -3.67985  4.15644  3.18919  11.85
Nep.arc  2.18561 -0.82837  0.71958  5.81930   5.26
Ste.sp  -0.78699 -2.01214  2.31212  2.03946  17.52
Pel.aph  0.45763 -0.34395  0.09916  1.34695   0.76
Ich.eri  0.04950 -1.97605  1.41509  2.10154   0.22
Cla.cer -1.21585 -2.30519  2.55186  3.41532   0.10
Cla.def  0.60517 -1.19771 -0.33388  0.22585  10.23
Cla.phy -1.53959  1.48574 -1.43209 -1.52387   0.80

Site scores:

      DCA1    DCA2    DCA3    DCA4 Totals
18 -0.1729 -0.2841  0.4775  0.2521   89.2
15  0.8539 -0.3360  0.0708  0.0924   89.8
24  1.2467 -0.1183 -0.1211 -0.8718   94.2
27  1.0675  0.4169  0.2897 -0.1758  125.6
23  0.4234  0.0112  0.2179  0.1265   90.5
19  0.0252  0.3600 -0.0263 -0.1168   81.3
22  1.0695 -0.3707 -0.4285  0.4145  109.8
16  0.7724 -0.5325 -0.2856  0.5269   88.5
28  1.6189  0.5482  0.2342 -0.3333  110.7
13 -0.2642 -0.6851 -0.3777  0.5003  101.9
14  0.6431 -0.9604 -0.6000 -0.2885   81.7
20  0.4504 -0.1666  0.1850 -0.1291   64.1
25  1.2501 -0.2248  0.0244  0.3741   94.1
7  -0.3910 -0.7618  0.8640  0.5557  103.4
5  -0.6407 -0.9427  0.9465  0.7769   94.8
6  -0.4523 -0.5529  0.3988  0.2781  110.9
3  -1.1043  0.2106 -0.0653 -0.0539  106.7
4  -0.9454 -0.5974  0.4639  0.4889   84.8
2  -1.1971  0.5691 -0.3246 -0.2522  119.1
9  -1.0983  0.7850 -0.5274 -0.4848  122.6
12 -0.8673  0.5621 -0.3254 -0.3217  119.8
10 -1.1842  0.7442 -0.4995 -0.3917  122.4
11 -0.4134  0.0260  0.0107 -0.0682  112.8
21  0.3210  1.2450 -0.2541 -0.5253   99.2

> plot(vare.dca)
> ### the detrending rationale:
> gaussresp <- function(x,u) exp(-(x-u)^2/2)
> x <- seq(0,6,length=15) ## The gradient
> u <- seq(-2,8,len=23)   ## The optima
> pack <- outer(x,u,gaussresp)
> matplot(x, pack, type="l", main="Species packing")
> opar <- par(mfrow=c(2,2))
> plot(scores(prcomp(pack)), asp=1, type="b", main="PCA")
> plot(scores(decorana(pack, ira=1)), asp=1, type="b", main="CA")
> plot(scores(decorana(pack)), asp=1, type="b", main="DCA")
> plot(scores(cca(pack ~ x), dis="sites"), asp=1, type="b", main="CCA")
> ### Let's add some noise:
> noisy <- (0.5 + runif(length(pack)))*pack
> par(mfrow=c(2,1))
> matplot(x, pack, type="l", main="Ideal model")
> matplot(x, noisy, type="l", main="Noisy model")
> par(mfrow=c(2,2))
> plot(scores(prcomp(noisy)), type="b", main="PCA", asp=1)
> plot(scores(decorana(noisy, ira=1)), type="b", main="CA", asp=1)
> plot(scores(decorana(noisy)), type="b", main="DCA", asp=1)
> plot(scores(cca(noisy ~ x), dis="sites"), asp=1, type="b", main="CCA")
> par(opar)
>   
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "decostand"
> 
> ### * decostand
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: decostand
> ### Title: Standardizaton Methods for Community Ecology
> ### Aliases: decostand wisconsin
> ### Keywords: multivariate manip
> 
> ### ** Examples
> 
> data(varespec)
> sptrans <- decostand(varespec, "max")
> apply(sptrans, 2, max)
Cal.vul Emp.nig Led.pal Vac.myr Vac.vit Pin.syl Des.fle Bet.pub Vac.uli Dip.mon 
      1       1       1       1       1       1       1       1       1       1 
 Dic.sp Dic.fus Dic.pol Hyl.spl Ple.sch Pol.pil Pol.jun Pol.com Poh.nut Pti.cil 
      1       1       1       1       1       1       1       1       1       1 
Bar.lyc Cla.arb Cla.ran Cla.ste Cla.unc Cla.coc Cla.cor Cla.gra Cla.fim Cla.cri 
      1       1       1       1       1       1       1       1       1       1 
Cla.chl Cla.bot Cla.ama  Cla.sp Cet.eri Cet.isl Cet.niv Nep.arc  Ste.sp Pel.aph 
      1       1       1       1       1       1       1       1       1       1 
Ich.eri Cla.cer Cla.def Cla.phy 
      1       1       1       1 
> sptrans <- wisconsin(varespec)
> # Chi-square: Similar but not identical to Correspondence Analysis.
> sptrans <- decostand(varespec, "chi.square")
> plot(procrustes(rda(sptrans), cca(varespec)))
> # Hellinger transformation (Legendre & Callagher 2001):
> sptrans <- sqrt(decostand(varespec, "total"))
> 
> 
> 
> cleanEx(); ..nameEx <- "deviance.cca"
> 
> ### * deviance.cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: deviance.cca
> ### Title: Statistics Resembling Deviance and AIC for Constrained
> ###   Ordination
> ### Aliases: deviance.cca deviance.rda deviance.capscale extractAIC.cca
> ### Keywords: multivariate models
> 
> ### ** Examples
> 
> # The deviance of correspondence analysis equals Chi-square
> data(dune)
> data(dune.env)
> chisq.test(dune)
Warning in chisq.test(dune) : Chi-squared approximation may be incorrect

	Pearson's Chi-squared test

data:  dune 
X-squared = 1448.956, df = 551, p-value < 2.2e-16

> deviance(cca(dune))
[1] 1448.956
> # Backward elimination from a complete model "dune ~ ."
> ord <- cca(dune ~ ., dune.env)
> ord

Call:
cca(formula = dune ~ A1 + Moisture + Management + Use + Manure,      data = dune.env) 

              Inertia Rank
Total          2.1153     
Constrained    1.5032   12
Unconstrained  0.6121    7
Inertia is mean squared contingency coefficient 
Some constraints were aliased because they were collinear (redundant)

Eigenvalues for constrained axes:
   CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7    CCA8    CCA9   CCA10 
0.46713 0.34102 0.17606 0.15317 0.09528 0.07027 0.05887 0.04993 0.03183 0.02596 
  CCA11   CCA12 
0.02282 0.01082 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4     CA5     CA6     CA7 
0.27237 0.10876 0.08975 0.06305 0.03489 0.02529 0.01798 

> step(ord)
Start:  AIC= 86.86 
 dune ~ A1 + Moisture + Management + Use + Manure 

             Df    AIC
- Use         2 86.711
<none>          86.857
- Management  2 87.470
- Manure      3 87.819
- A1          1 88.181
- Moisture    3 89.179

Step:  AIC= 86.71 
 dune ~ A1 + Moisture + Management + Manure 

             Df    AIC
- Manure      3 86.190
- Management  2 86.446
<none>          86.711
- Moisture    3 87.873
- A1          1 88.430

Step:  AIC= 86.19 
 dune ~ A1 + Moisture + Management 

             Df    AIC
<none>          86.190
- Moisture    3 86.460
- A1          1 86.813
- Management  3 86.992

Call:
cca(formula = dune ~ A1 + Moisture + Management, data = dune.env) 

              Inertia Rank
Total          2.1153     
Constrained    1.1392    7
Unconstrained  0.9761   12
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
   CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7 
0.44826 0.30014 0.14995 0.10733 0.05668 0.04335 0.03345 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8 
0.306366 0.131911 0.115157 0.109469 0.077242 0.075754 0.048714 0.037582 
     CA9     CA10     CA11     CA12 
0.031058 0.021024 0.012542 0.009277 

> # Stepwise selection (forward from an empty model "dune ~ 1")
> step(cca(dune ~ 1, dune.env), scope = formula(ord))
Start:  AIC= 87.66 
 dune ~ 1 

             Df    AIC
+ Moisture    3 86.608
+ Management  3 86.935
+ A1          1 87.411
<none>          87.657
+ Manure      4 88.832
+ Use         2 89.134

Step:  AIC= 86.61 
 dune ~ Moisture 

             Df    AIC
<none>          86.608
+ Management  3 86.813
+ A1          1 86.992
+ Use         2 87.259
+ Manure      4 87.342
- Moisture    3 87.657

Call:
cca(formula = dune ~ Moisture, data = dune.env) 

              Inertia Rank
Total          2.1153     
Constrained    0.6283    3
Unconstrained  1.4870   16
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
  CCA1   CCA2   CCA3 
0.4187 0.1330 0.0766 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8 
0.409782 0.225913 0.176062 0.123389 0.108171 0.090751 0.085878 0.060894 
     CA9     CA10     CA11     CA12     CA13     CA14     CA15     CA16 
0.056606 0.046688 0.041926 0.020103 0.014335 0.009917 0.008505 0.008033 

> # ANOVA for the added variable
> anova(cca(dune ~ Moisture, dune.env))
Permutation test for cca under reduced model

Model: cca(formula = dune ~ Moisture, data = dune.env)
         Df  Chisq      F N.Perm  Pr(>F)    
Model     3 0.6283 2.2536    200 < 0.005 ***
Residual 16 1.4870                          
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> # ANOVA for the next candidate variable that was not added
> anova(cca(dune ~ Condition(Moisture) + Management, dune.env), perm.max=1000)
Permutation test for cca under reduced model

Model: cca(formula = dune ~ Condition(Moisture) + Management, data = dune.env)
         Df  Chisq      F N.Perm Pr(>F)  
Model     3 0.3741 1.4565   1000  0.051 .
Residual 13 1.1129                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> 
> 
> cleanEx(); ..nameEx <- "distconnected"
> 
> ### * distconnected
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: distconnected
> ### Title: Connectedness and Minimum Spanning Tree for Dissimilarities
> ### Aliases: distconnected no.shared spantree
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> ## There are no disconnected data in vegan, and the following uses an
> ## extremely low threshold limit for connectedness. This is for
> ## illustration only, and not a recommended practice.
> data(dune)
> dis <- vegdist(dune)
> ord <- cmdscale(dis) ## metric MDS
> gr <- distconnected(dis, toolong=0.4)
Connectivity of distance matrix with threshold dissimilarity 0.4 
Data are disconnected: 6 groups
Groups sizes
 1  2  3  4  5  6 
11  4  1  1  2  1 
> tr <- spantree(dis, toolong=0.4)
> ordiplot(ord, type="n")
Warning in ordiplot(ord, type = "n") : Species scores not available
> ordispantree(ord, tr, col="red", lwd=2)
> points(ord, cex=1.3, pch=21, col=1, bg = gr)
> # Make sites with no shared species as NA in Manhattan dissimilarities
> dis <- vegdist(dune, "manhattan")
> is.na(dis) <- no.shared(dune)
> 
> 
> 
> cleanEx(); ..nameEx <- "diversity"
> 
> ### * diversity
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: diversity
> ### Title: Ecological Diversity Indices and Rarefaction Species Richness
> ### Aliases: diversity rarefy renyi fisher.alpha specnumber
> ### Keywords: univar
> 
> ### ** Examples
> 
> data(BCI)
> H <- diversity(BCI)
> simp <- diversity(BCI, "simpson")
> invsimp <- diversity(BCI, "inv")
> r.2 <- rarefy(BCI, 2)
> alpha <- fisher.alpha(BCI)
> pairs(cbind(H, simp, invsimp, r.2, alpha), pch="+", col="blue")
> ## Species richness (S) and Pielou's evenness (J):
> S <- specnumber(BCI) ## rowSums(BCI > 0) does the same...
> J <- H/log(S)
> 
> 
> 
> cleanEx(); ..nameEx <- "dune"
> 
> ### * dune
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dune
> ### Title: Vegetation and Environment in Dutch Dune Meadows.
> ### Aliases: dune dune.env
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(dune)
> 
> 
> 
> cleanEx(); ..nameEx <- "envfit"
> 
> ### * envfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: envfit
> ### Title: Fits an Environmental Vector or Factor onto an Ordination
> ### Aliases: envfit envfit.default envfit.formula vectorfit factorfit
> ###   plot.envfit print.envfit print.factorfit print.vectorfit
> ###   scores.envfit
> ### Keywords: multivariate aplot htest
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> library(MASS)
> ord <- metaMDS(varespec)
Square root transformation
Wisconsin double standardization
Run 0 stress 18.44915 
Run 1 stress 18.45800 
... rmse 0.05246287   max residual 0.1748373 
Run 2 stress 24.19514 
Run 3 stress 19.69805 
Run 4 stress 19.74406 
Run 5 stress 18.43204 
... New best solution
... rmse 0.00448445   max residual 0.01722444 
Run 6 stress 19.48415 
Run 7 stress 19.48414 
Run 8 stress 20.57245 
Run 9 stress 21.00656 
Run 10 stress 20.06919 
Run 11 stress 18.52397 
Run 12 stress 21.37384 
Run 13 stress 19.5049 
Run 14 stress 21.67150 
Run 15 stress 22.65719 
Run 16 stress 21.0961 
Run 17 stress 18.25659 
... New best solution
... rmse 0.04191616   max residual 0.1532558 
Run 18 stress 19.48413 
Run 19 stress 21.77541 
Run 20 stress 22.24925 
> (fit <- envfit(ord, varechem, perm = 1000))

***VECTORS

             NMDS1     NMDS2     r2 Pr(>r)    
N        -0.057349 -0.998354 0.2537  0.045 *  
P         0.619854  0.784717 0.1938  0.102    
K         0.766510  0.642232 0.1810  0.142    
Ca        0.685179  0.728375 0.4119  0.007 ** 
Mg        0.632611  0.774470 0.4272  0.003 ** 
S         0.191631  0.981467 0.1752  0.139    
Al       -0.871518  0.490363 0.5269 <0.001 ***
Fe       -0.936058  0.351845 0.4451  0.001 ***
Mn        0.798539 -0.601944 0.5230 <0.001 ***
Zn        0.617746  0.786378 0.1879  0.124    
Mo       -0.902967  0.429710 0.0609  0.537    
Baresoil  0.924867 -0.380290 0.2508  0.039 *  
Humdepth  0.932733 -0.360568 0.5202  0.001 ***
pH       -0.647704  0.761892 0.2309  0.059 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
P values based on 1000 permutations.
> scores(fit, "vectors")
               NMDS1      NMDS2
N        -0.02888867 -0.5029042
P         0.27288032  0.3454586
K         0.32607474  0.2732065
Ca        0.43973962  0.4674626
Mg        0.41345930  0.5061752
S         0.08021282  0.4108214
Al       -0.63261567  0.3559438
Fe       -0.62449816  0.2347361
Mn        0.57751792 -0.4353369
Zn        0.26779998  0.3409037
Mo       -0.22279874  0.1060270
Baresoil  0.46316302 -0.1904451
Humdepth  0.67270911 -0.2600505
pH       -0.31126667  0.3661418
> plot(ord)
> plot(fit)
> plot(fit, p.max = 0.05, col = "red")
> ## Adding fitted arrows to CCA. We use "lc" scores, and hope
> ## that arrows are scaled similarly in cca and envfit plots
> ord <- cca(varespec ~ Al + P + K, varechem)
> plot(ord, type="p")
> fit <- envfit(ord, varechem, perm = 1000, display = "lc")
> plot(fit, p.max = 0.05, col = "red")
> ## Class variables, formula interface, and displaying the
> ## inter-class variability with `ordispider'
> data(dune)
> data(dune.env)
> attach(dune.env)
> ord <- cca(dune)
> fit <- envfit(ord ~ Moisture + A1, dune.env)
> plot(ord, type = "n")
> ordispider(ord, Moisture, col="skyblue")
> points(ord, display = "sites", col = as.numeric(Moisture), pch=16)
> plot(fit, cex=1.2, axis=TRUE)
> 
> 
> 
> cleanEx(); ..nameEx <- "fisherfit"
> 
> ### * fisherfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fisherfit
> ### Title: Fit Fisher's Logseries and Preston's Lognormal Model to
> ###   Abundance Data
> ### Aliases: fisherfit as.fisher plot.fisherfit print.fisherfit
> ###   profile.fisherfit confint.fisherfit plot.profile.fisherfit prestonfit
> ###   prestondistr as.preston plot.prestonfit lines.prestonfit
> ###   print.prestonfit veiledspec
> ### Keywords: univar distribution
> 
> ### ** Examples
> 
> data(BCI)
> mod <- fisherfit(BCI[5,])
> mod

Fisher log series model
No. of species: 101 

      Estimate Std. Error
alpha   37.964     4.6847

> plot(profile(mod))
> confint(mod)
Loading required package: MASS
   2.5 %   97.5 % 
29.65932 48.12558 
> # prestonfit seems to need large samples
> mod.oct <- prestonfit(colSums(BCI))
> mod.ll <- prestondistr(colSums(BCI))
> mod.oct

Preston lognormal model
Method: Poisson fit to octaves 
No. of species: 225 

     mode     width        S0 
 4.682037  3.232425 29.886591 

Frequencies by Octave
                0       1        2        3        4        5        6        7
Observed 19.00000 13.0000 14.00000 18.00000 30.00000 34.00000 31.00000 26.00000
Fitted   10.46872 15.6214 21.18270 26.10223 29.22866 29.74235 27.50278 23.11070
                8        9       10       11
Observed 18.00000 13.00000 7.000000 2.000000
Fitted   17.64755 12.24591 7.722047 4.424956

> mod.ll

Preston lognormal model
Method: maximized likelihood to log2 abundances 
No. of species: 225 

     mode     width        S0 
 4.365002  2.753531 33.458185 

Frequencies by Octave
                0        1        2        3        4        5        6
Observed 19.00000 13.00000 14.00000 18.00000 30.00000 34.00000 31.00000
Fitted    9.52392 15.85637 23.13724 29.58961 33.16552 32.58022 28.05054
                7        8         9       10       11
Observed 26.00000 18.00000 13.000000 7.000000 2.000000
Fitted   21.16645 13.99829  8.113746 4.121808 1.835160

> plot(mod.oct)  
> lines(mod.ll, line.col="blue3") # Different
> ## Smoothed density
> den <- density(log2(colSums(BCI)))
> lines(den$x, ncol(BCI)*den$y, lwd=2) # Fairly similar to mod.oct
> ## Extrapolated richness
> veiledspec(mod.oct)
Extrapolated     Observed       Veiled 
   242.15571    225.00000     17.15571 
> veiledspec(mod.ll)
Extrapolated     Observed       Veiled 
  230.931018   225.000000     5.931018 
> 
> 
> 
> cleanEx(); ..nameEx <- "goodness.cca"
> 
> ### * goodness.cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: goondess.cca
> ### Title: Diagnostic Tools for [Constrained] Ordination (CCA, RDA, DCA,
> ###   CA, PCA)
> ### Aliases: goodness goodness.rda goodness.cca inertcomp spenvcor vif.cca
> ###   alias.cca
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> mod <- cca(dune ~ A1 + Management + Condition(Moisture), data=dune.env)
> goodness(mod)
             CCA1      CCA2      CCA3      CCA4
Belper 0.41185412 0.4179432 0.4847618 0.4849622
Empnig 0.27089495 0.3132399 0.3153052 0.3154203
Junbuf 0.70439967 0.7226263 0.7228786 0.7257471
Junart 0.43923609 0.4492937 0.4871043 0.5224072
Airpra 0.36213737 0.3698100 0.3816619 0.3908018
Elepal 0.55132024 0.6099415 0.6193301 0.6259818
Rumace 0.44788204 0.5211145 0.7673956 0.7691199
Viclat 0.17824132 0.1784611 0.3762406 0.4279428
Brarut 0.15585567 0.1641095 0.1672797 0.2449864
Ranfla 0.68677962 0.6983001 0.7020461 0.7064850
Cirarv 0.29041563 0.3013655 0.3080671 0.3591280
Hyprad 0.31349648 0.3371809 0.3387669 0.3388716
Leoaut 0.54312496 0.5510319 0.6078931 0.6140593
Potpal 0.16338257 0.6836790 0.7390659 0.7963425
Poapra 0.40267189 0.4944813 0.5014516 0.5326546
Calcus 0.30771429 0.3143582 0.3308502 0.3518027
Tripra 0.37328840 0.4101104 0.6624199 0.6625703
Trirep 0.03048149 0.2115857 0.3300132 0.4207437
Antodo 0.24619147 0.2795001 0.3509172 0.3609709
Salrep 0.64788354 0.7264891 0.7276110 0.7639711
Achmil 0.36630013 0.3822685 0.3838616 0.4934158
Poatri 0.49694972 0.5409439 0.5468830 0.5594817
Chealb 0.23594716 0.2684323 0.2828928 0.2885321
Elyrep 0.25239595 0.2710266 0.2761491 0.2882666
Sagpro 0.27039747 0.3497634 0.3553109 0.3613746
Plalan 0.54969676 0.6084389 0.6802195 0.6826265
Agrsto 0.67247051 0.6724758 0.6779597 0.7773267
Lolper 0.48141171 0.5720410 0.5727299 0.6034007
Alogen 0.61547145 0.6966105 0.7042650 0.7212918
Brohor 0.33487622 0.3397416 0.3870032 0.5505037
> goodness(mod, summ = TRUE)
   Belper    Empnig    Junbuf    Junart    Airpra    Elepal    Rumace    Viclat 
0.4849622 0.3154203 0.7257471 0.5224072 0.3908018 0.6259818 0.7691199 0.4279428 
   Brarut    Ranfla    Cirarv    Hyprad    Leoaut    Potpal    Poapra    Calcus 
0.2449864 0.7064850 0.3591280 0.3388716 0.6140593 0.7963425 0.5326546 0.3518027 
   Tripra    Trirep    Antodo    Salrep    Achmil    Poatri    Chealb    Elyrep 
0.6625703 0.4207437 0.3609709 0.7639711 0.4934158 0.5594817 0.2885321 0.2882666 
   Sagpro    Plalan    Agrsto    Lolper    Alogen    Brohor 
0.3613746 0.6826265 0.7773267 0.6034007 0.7212918 0.5505037 
> # Inertia components
> inertcomp(mod, prop = TRUE)
             pCCA        CCA        CA
Belper 0.40972447 0.07523776 0.5150378
Empnig 0.10361994 0.21180040 0.6845797
Junbuf 0.66622672 0.05952038 0.2742529
Junart 0.43439190 0.08801527 0.4775928
Airpra 0.06404726 0.32675457 0.6091982
Elepal 0.53954819 0.08643366 0.3740182
Rumace 0.40125987 0.36786003 0.2308801
Viclat 0.12125433 0.30668844 0.5720572
Brarut 0.07222706 0.17275938 0.7550136
Ranfla 0.68509904 0.02138594 0.2935150
Cirarv 0.26649913 0.09262886 0.6408720
Hyprad 0.03889627 0.29997533 0.6611284
Leoaut 0.10895437 0.50510492 0.3859407
Potpal 0.16096277 0.63537969 0.2036575
Poapra 0.39408053 0.13857406 0.4673454
Calcus 0.29447422 0.05732850 0.6481973
Tripra 0.34544815 0.31712212 0.3374297
Trirep 0.02132183 0.39942191 0.5792563
Antodo 0.10259139 0.25837947 0.6390291
Salrep 0.12527838 0.63869277 0.2360289
Achmil 0.34271900 0.15069678 0.5065842
Poatri 0.05598349 0.50349824 0.4405183
Chealb 0.11064346 0.17788865 0.7114679
Elyrep 0.22234322 0.06592337 0.7117334
Sagpro 0.26050435 0.10087025 0.6386254
Plalan 0.51993753 0.16268893 0.3173735
Agrsto 0.55602406 0.22130269 0.2226733
Lolper 0.46273045 0.14067027 0.3965993
Alogen 0.34238968 0.37890210 0.2787082
Brohor 0.33046684 0.22003683 0.4494963
> inertcomp(mod, stat="d")
             pCCA        CCA         CA
Belper 0.81483759 0.14962874  1.0242789
Empnig 2.18604651 4.46830527 14.4424224
Junbuf 2.60346194 0.23259205  1.0717177
Junart 1.36667524 0.27691192  1.5025932
Airpra 0.91341031 4.66001211  8.6880830
Elepal 2.18604651 0.35019669  1.5153810
Rumace 1.09684464 1.00554611  0.6311112
Viclat 0.84063811 2.12622500  3.9659871
Brarut 0.04517898 0.10806328  0.4722710
Ranfla 2.18604651 0.06823926  0.9365617
Cirarv 3.79020979 1.31738817  9.1146243
Hyprad 0.35520990 2.73944513  6.0375798
Leoaut 0.03887246 0.18021004  0.1376949
Potpal 2.18604651 8.62913533  2.7658870
Poapra 0.20406096 0.07175578  0.2419987
Calcus 2.18604651 0.42558147  4.8119302
Tripra 1.74000000 1.59732360  1.6996117
Trirep 0.01215418 0.22768437  0.3301962
Antodo 0.31403667 0.79091068  1.9560957
Salrep 0.88898328 4.53220433  1.6748757
Achmil 0.74393575 0.32711556  1.0996359
Poatri 0.03136359 0.28207442  0.2467912
Chealb 2.18604651 3.51464840 14.0568809
Elyrep 0.51093664 0.15148951  1.6355375
Sagpro 0.51772816 0.20047024  1.2692085
Plalan 0.96463794 0.30183609  0.5888218
Agrsto 0.65154706 0.25932172  0.2609277
Lolper 0.43502729 0.13224850  0.3728553
Alogen 0.62026287 0.68640768  0.5048995
Brohor 0.82257902 0.54770300  1.1188603
> # vif.cca 
> vif.cca(mod)
  Moisture.L   Moisture.Q   Moisture.C           A1 ManagementHF ManagementNM 
    1.504327     1.284489     1.347660     1.367328     2.238653     2.570972 
ManagementSF 
    2.424444 
> # Aliased constraints
> mod <- cca(dune ~ ., dune.env)
> mod

Call:
cca(formula = dune ~ A1 + Moisture + Management + Use + Manure,      data = dune.env) 

              Inertia Rank
Total          2.1153     
Constrained    1.5032   12
Unconstrained  0.6121    7
Inertia is mean squared contingency coefficient 
Some constraints were aliased because they were collinear (redundant)

Eigenvalues for constrained axes:
   CCA1    CCA2    CCA3    CCA4    CCA5    CCA6    CCA7    CCA8    CCA9   CCA10 
0.46713 0.34102 0.17606 0.15317 0.09528 0.07027 0.05887 0.04993 0.03183 0.02596 
  CCA11   CCA12 
0.02282 0.01082 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4     CA5     CA6     CA7 
0.27237 0.10876 0.08975 0.06305 0.03489 0.02529 0.01798 

> vif.cca(mod)
          A1   Moisture.L   Moisture.Q   Moisture.C ManagementHF ManagementNM 
3.208249e+00 2.934142e+00 3.072715e+00 4.225058e+00 6.914185e+00 7.737385e+31 
ManagementSF        Use.L        Use.Q     Manure.L     Manure.Q     Manure.C 
1.337251e+01 2.667560e+00 3.089394e+00 3.345539e+31 2.600928e+31 8.476579e+30 
    Manure^4 
1.401215e+30 
> alias(mod)
Model :
dune ~ A1 + Moisture + Management + Use + Manure

Complete :
         A1 Moisture.L Moisture.Q Moisture.C ManagementHF ManagementNM
Manure^4                                                   8.366600   
         ManagementSF Use.L Use.Q Manure.L  Manure.Q  Manure.C 
Manure^4                           5.291503 -4.472136  2.645751

> with(dune.env, table(Management, Manure))
          Manure
Management 0 1 2 3 4
        BF 0 2 1 0 0
        HF 0 1 2 2 0
        NM 6 0 0 0 0
        SF 0 0 1 2 3
> 
> 
> 
> cleanEx(); ..nameEx <- "goodness.metaMDS"
> 
> ### * goodness.metaMDS
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: goodness.metaMDS
> ### Title: Goodness of Fit and Shepard Plot for Nonmetric Multidimensional
> ###   Scaling
> ### Aliases: goodness.metaMDS stressplot
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> mod <- metaMDS(varespec)
Square root transformation
Wisconsin double standardization
Loading required package: MASS
Run 0 stress 18.44915 
Run 1 stress 18.45800 
... rmse 0.05246287   max residual 0.1748373 
Run 2 stress 24.19514 
Run 3 stress 19.69805 
Run 4 stress 19.74406 
Run 5 stress 18.43204 
... New best solution
... rmse 0.00448445   max residual 0.01722444 
Run 6 stress 19.48415 
Run 7 stress 19.48414 
Run 8 stress 20.57245 
Run 9 stress 21.00656 
Run 10 stress 20.06919 
Run 11 stress 18.52397 
Run 12 stress 21.37384 
Run 13 stress 19.5049 
Run 14 stress 21.67150 
Run 15 stress 22.65719 
Run 16 stress 21.0961 
Run 17 stress 18.25659 
... New best solution
... rmse 0.04191616   max residual 0.1532558 
Run 18 stress 19.48413 
Run 19 stress 21.77541 
Run 20 stress 22.24925 
> stressplot(mod)
Square root transformation
Wisconsin double standardization
> gof <- goodness(mod)
Square root transformation
Wisconsin double standardization
> gof
      18       15       24       27       23       19       22       16 
2.984496 3.514129 4.188692 4.598210 4.002773 3.441293 3.294609 3.051738 
      28       13       14       20       25        7        5        6 
3.060659 2.993482 3.526967 2.621578 3.829350 2.982187 3.370348 2.226679 
       3        4        2        9       12       10       11       21 
3.561311 3.506032 6.577579 3.268019 3.502878 2.957059 5.167546 4.601390 
> plot(mod, display = "sites", type = "n")
> points(mod, display = "sites", cex = gof/2)
> 
> 
> 
> cleanEx(); ..nameEx <- "humpfit"
> 
> ### * humpfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: humpfit
> ### Title: No-interaction Model for Hump-backed Species Richness vs.
> ###   Biomass
> ### Aliases: humpfit print.humpfit summary.humpfit print.summary.humpfit
> ###   lines.humpfit plot.humpfit points.humpfit predict.humpfit
> ###   profile.humpfit
> ### Keywords: models regression nonlinear
> 
> ### ** Examples
> 
> ##
> ## Data approximated from Al-Mufti et al. (1977)
> ##
> mass <- c(140,230,310,310,400,510,610,670,860,900,1050,1160,1900,2480)
> spno <- c(1,  4,  3,  9, 18, 30, 20, 14,  3,  2,  3,  2,  5,  2)
> sol <- humpfit(mass, spno)
Warning in log(x) : NaNs produced
Warning in log(x) : NaNs produced
Warning in dpois(x, lambda, log) : NaNs produced
Warning: NA/Inf replaced by maximum positive value
Warning in log(x) : NaNs produced
Warning in log(x) : NaNs produced
Warning in dpois(x, lambda, log) : NaNs produced
Warning: NA/Inf replaced by maximum positive value
Warning in log(x) : NaNs produced
Warning in log(x) : NaNs produced
Warning in dpois(x, lambda, log) : NaNs produced
Warning: NA/Inf replaced by maximum positive value
> summary(sol) # Almost infinite alpha...

Hump-backed Null model of richness vs. productivity

Family: poisson 
Link function: Fisher diversity

Coefficients:

        Estimate Std. Error
hump  5.3766e+02 3.3547e+01
scale 1.8394e+01 1.7470e+00
alpha 4.3952e+06 1.2719e+07

Dispersion parameter for poisson family taken to be 1 

Deviance 41.44823 with 11 residual degrees of freedom
AIC: 96.37776    BIC: 98.29494 

Correlation of Coefficients:
      hump  scale
scale -0.21      
alpha  0.02 -0.05

Diagnostics from nlm:
Number of iterations: 75, code: 1
> plot(sol)
> # confint is in MASS, and impicitly calls profile.humpfit.
> # Parameter 3 (alpha) is too extreme for profile and confint, and we
> # must use only "hump" and "scale".
> library(MASS)
> plot(profile(sol, parm=1:2))
> confint(sol, parm=c(1,2))
Waiting for profiling to be done...
          2.5 %    97.5 %
hump  494.13821 607.26013
scale  15.17641  22.02865
> 
> 
> 
> cleanEx(); ..nameEx <- "make.cepnames"
> 
> ### * make.cepnames
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: make.cepnames
> ### Title: Abbreviates a Botanical or Zoological Latin Name into an
> ###   Eight-character Name
> ### Aliases: make.cepnames
> ### Keywords: character
> 
> ### ** Examples
> 
> make.cepnames(c("Aa maderoi", "Poa sp.", "Cladina rangiferina",
+ "Cladonia cornuta", "Cladonia cornuta var. groenlandica",
+ "Cladonia rangiformis", "Bryoerythrophyllum"))
[1] "Aamade"     "Poasp"      "Cladrang"   "Cladcorn"   "Cladgroe"  
[6] "Cladrang.1" "Bryrythr"  
> data(BCI)
> colnames(BCI) <- make.cepnames(colnames(BCI))
> 
> 
> 
> cleanEx(); ..nameEx <- "mantel"
> 
> ### * mantel
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mantel
> ### Title: Mantel and Partial Mantel Tests for Dissimilarity Matrices
> ### Aliases: mantel mantel.partial print.mantel
> ### Keywords: multivariate htest
> 
> ### ** Examples
> 
> ## Is vegetation related to environment?
> data(varespec)
> data(varechem)
> veg.dist <- vegdist(varespec) # Bray-Curtis
> env.dist <- vegdist(scale(varechem), "euclid")
> mantel(veg.dist, env.dist)

Mantel statistic based on Pearson's product-moment correlation 

Call:
mantel(xdis = veg.dist, ydis = env.dist) 

Mantel statistic r: 0.3047 
      Significance: < 0.001 

Empirical upper confidence limits of r:
  90%   95% 97.5%   99% 
0.107 0.145 0.169 0.200 

Based on 1000 permutations

> mantel(veg.dist, env.dist, method="spear")

Mantel statistic based on Spearman's rank correlation rho 

Call:
mantel(xdis = veg.dist, ydis = env.dist, method = "spear") 

Mantel statistic r: 0.2838 
      Significance: < 0.001 

Empirical upper confidence limits of r:
  90%   95% 97.5%   99% 
0.108 0.141 0.169 0.196 

Based on 1000 permutations

> 
> 
> 
> cleanEx(); ..nameEx <- "metaMDS"
> 
> ### * metaMDS
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: metaMDS
> ### Title: Nonmetric Multidimensional Scaling with Stable Solution from
> ###   Random Starts, Axis Scaling and Species Scores
> ### Aliases: metaMDS metaMDSdist metaMDSiter metaMDSredist initMDS postMDS
> ###   print.metaMDS plot.metaMDS points.metaMDS text.metaMDS scores.metaMDS
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> ## The recommended way of running NMDS (Minchin 1987)
> ##
> data(dune)
> library(MASS) ## isoMDS
> # NMDS
> sol <- metaMDS(dune)
Run 0 stress 12.05894 
Run 1 stress 18.21960 
Run 2 stress 18.97837 
Run 3 stress 18.57544 
Run 4 stress 19.42521 
Run 5 stress 12.04546 
... New best solution
... rmse 0.003139708   max residual 0.01078196 
Run 6 stress 18.91766 
Run 7 stress 12.04548 
... rmse 0.0001744095   max residual 0.0004460873 
*** Solution reached

> sol

Call:
metaMDS(comm = dune) 

Nonmetric Multidimensional Scaling using isoMDS (MASS package)

Data:     dune 
Distance: bray 

Dimensions: 2 
Stress:     12.04546 
Two convergent solutions found after 7 tries
Score scaling: centring, PC rotation, halfchange scaling 

> plot(sol, type="t")
> 
> 
> 
> cleanEx(); ..nameEx <- "ordihull"
> 
> ### * ordihull
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ordihull
> ### Title: Add Graphical Items to Ordination Diagrams
> ### Aliases: ordihull ordiarrows ordisegments ordigrid ordispider
> ###   ordiellipse ordicluster ordispantree weights.cca weights.rda
> ###   weights.decorana
> ### Keywords: aplot
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> mod <- cca(dune ~ Moisture, dune.env)
> attach(dune.env)
> plot(mod, type="n")
> ordihull(mod, Moisture)
> ordispider(mod, col="red")
> plot(mod, type = "p", display="sites")
> ordicluster(mod, hclust(vegdist(dune)), prune=3, col = "blue")
> # The following is not executed automatically because it needs
> # a non-standard library `ellipse'. 
> ## Not run: ordiellipse(mod, Moisture, kind="se", level=0.95, lwd=2, col="blue")
> 
> 
> 
> cleanEx(); ..nameEx <- "ordiplot"
> 
> ### * ordiplot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ordiplot
> ### Title: Alternative plot and identify Functions for Ordination
> ### Aliases: ordiplot identify.ordiplot scores.ordiplot points.ordiplot
> ###   text.ordiplot
> ### Keywords: hplot iplot aplot
> 
> ### ** Examples
> 
> # Draw a cute NMDS plot from a non-vegan ordinatin (isoMDS).
> # Function metaMDS would be an easier alternative.
> data(dune)
> dune.dis <- vegdist(wisconsin(dune))
> library(MASS)
> dune.mds <- isoMDS(dune.dis)
initial  value 17.440604 
iter   5 value 11.776556
iter  10 value 11.603233
iter  10 value 11.596516
final  value 11.562320 
converged
> dune.mds <- postMDS(dune.mds, dune.dis)
> dune.mds$species <- wascores(dune.mds$points, dune, expand = TRUE)
> fig <- ordiplot(dune.mds, type = "none")
> points(fig, "sites", pch=21, col="red", bg="yellow")
> text(fig, "species", col="blue", cex=0.9)
> # A quick plot of the previous.
> # identify is not run automatically because it needs user interaction:
> ## Not run: fig <- ordiplot(dune.mds)
> ## Not run: identify(fig, "spec")
> 
> 
> 
> cleanEx(); ..nameEx <- "ordiplot3d"
> 
> ### * ordiplot3d
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ordiplot3d
> ### Title: Three-Dimensional and Dynamic Ordination Graphics
> ### Aliases: ordiplot3d ordirgl orglpoints orgltext orglsegments orglspider
> ### Keywords: hplot dynamic
> 
> ### ** Examples
> 
> ## Examples are not run, because they need non-standard packages
> ## 'scatterplot3d' and 'rgl' (and the latter needs user interaction).
> #####
> #### Default 'ordiplot3d'
> ## Not run: data(dune)
> ## Not run: data(dune.env)
> ## Not run: ord <- cca(dune ~ A1 + Moisture, dune.env)
> ## Not run: ordiplot3d(ord)
> #### A boxed 'pin' version
> ## Not run: ordiplot3d(ord, type = "h")
> #### More user control
> ## Not run: pl <- ordiplot3d(ord, angle=15, type="n")
> ## Not run: points(pl, "points", pch=16, col="red", cex = 0.7)
> #### identify(pl, "arrows", col="blue") would put labels in better positions
> ## Not run: text(pl, "arrows", col="blue", pos=3)
> ## Not run: text(pl, "centroids", col="blue", pos=1, cex = 1.2)
> #### ordirgl
> ## Not run: ordirgl(ord, size=2)
> ## Not run: ordirgl(ord, display = "species", type = "t")
> ## Not run: rgl.quit() ## Safe with me, but may crash
> 
> 
> 
> cleanEx(); ..nameEx <- "ordisurf"
> 
> ### * ordisurf
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ordisurf
> ### Title: Smooths Variables and Plots Contours on Ordination.
> ### Aliases: ordisurf
> ### Keywords: multivariate aplot
> 
> ### ** Examples
> 
> ## The examples are not run by `example(ordisurf)' because they need
> ## libraries `mgcv' and `akima' which may not exist in every system.
> ## Not run: data(varespec)
> ## Not run: data(varechem)
> ## Not run: library(MASS)
> ## Not run: vare.dist <- vegdist(varespec)
> ## Not run: vare.mds <- isoMDS(vare.dist)
> ## Not run: attach(varespec)
> ## Not run: attach(varechem)
> ## Not run: ordisurf(vare.mds, Baresoil, xlab="Dim1", ylab="Dim2")
> ## Total cover of reindeer lichens
> ## Not run: ordisurf(vare.mds, Cla.ste+Cla.arb+Cla.ran, xlab="Dim1", ylab="Dim2") 
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.cca"
> 
> ### * plot.cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.cca
> ### Title: Plot or Extract Results of Constrained Correspondence Analysis
> ###   or Redundancy Analysis
> ### Aliases: plot.cca text.cca points.cca scores.cca
> ### Keywords: hplot aplot
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> mod <- cca(dune ~ A1 + Moisture + Management, dune.env)
> plot(mod, type="n")
> text(mod, dis="cn", arrow = 2)
> points(mod, pch=21, col="red", bg="yellow", cex=1.2)
> text(mod, "species", col="blue", cex=0.8)
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.cca"
> 
> ### * predict.cca
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.cca
> ### Title: Prediction Tools for [Constrained] Ordination (CCA, RDA, DCA,
> ###   CA, PCA)
> ### Aliases: fitted.cca fitted.rda residuals.cca residuals.rda predict.cca
> ###   predict.rda predict.decorana coef.cca coef.rda calibrate.cca
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> mod <- cca(dune ~ A1 + Management + Condition(Moisture), data=dune.env)
> # Definition of the concepts 'fitted' and 'residuals'
> mod

Call:
cca(formula = dune ~ A1 + Management + Condition(Moisture), data = dune.env) 

              Inertia Rank
Total          2.1153     
Conditional    0.6283    3
Constrained    0.5109    4
Unconstrained  0.9761   12
Inertia is mean squared contingency coefficient 

Eigenvalues for constrained axes:
   CCA1    CCA2    CCA3    CCA4 
0.24932 0.12090 0.08160 0.05904 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8 
0.306366 0.131911 0.115157 0.109469 0.077242 0.075754 0.048714 0.037582 
     CA9     CA10     CA11     CA12 
0.031058 0.021024 0.012542 0.009277 

> cca(fitted(mod))

Call:
cca(X = fitted(mod)) 

              Inertia Rank
Total          0.5109     
Unconstrained  0.5109    4
Inertia is mean squared contingency coefficient 

Eigenvalues for unconstrained axes:
    CA1     CA2     CA3     CA4 
0.24932 0.12090 0.08160 0.05904 

> cca(residuals(mod))

Call:
cca(X = residuals(mod)) 

              Inertia Rank
Total          0.9761     
Unconstrained  0.9761   12
Inertia is mean squared contingency coefficient 

Eigenvalues for unconstrained axes:
     CA1      CA2      CA3      CA4      CA5      CA6      CA7      CA8 
0.306366 0.131911 0.115157 0.109469 0.077242 0.075754 0.048714 0.037582 
     CA9     CA10     CA11     CA12 
0.031058 0.021024 0.012542 0.009277 

> # Remove rare species (freq==1) from 'cca' and find their scores
> # 'passively'.
> freq <- specnumber(dune, MARGIN=2)
> freq
Belper Empnig Junbuf Junart Airpra Elepal Rumace Viclat Brarut Ranfla Cirarv 
     6      1      4      5      2      5      5      3     15      6      1 
Hyprad Leoaut Potpal Poapra Calcus Tripra Trirep Antodo Salrep Achmil Poatri 
     3     18      2     14      3      3     16      6      3      7     13 
Chealb Elyrep Sagpro Plalan Agrsto Lolper Alogen Brohor 
     1      6      7      7     10     12      8      5 
> mod <- cca(dune[, freq>1] ~ A1 + Management + Condition(Moisture), dune.env)
> predict(mod, type="sp", newdata=dune[, freq==1], scaling=2)
             CCA1      CCA2       CCA3        CCA4
Empnig -1.8771953 0.9904299  0.2446222 -0.04858656
Cirarv  0.5945146 0.3714228  0.2862647 -0.88373727
Chealb  1.5737337 0.7842538 -0.5503660 -0.35108333
> # New sites
> predict(mod, type="lc", new=data.frame(A1 = 3, Management="NM", Moisture="2"), scal=2)
        CCA1     CCA2      CCA3     CCA4
1 -0.4015781 1.294107 0.2743152 1.313303
> # Calibration and residual plot
> mod <- cca(dune ~ A1 + Moisture, dune.env)
> pred <- calibrate.cca(mod)
> pred
           A1  Moisture.L  Moisture.Q   Moisture.C
2   4.0510042 -0.47341146 -0.36986691  0.474939409
13  4.9034218  0.47069541 -0.54378271 -0.118643453
4   4.5398659  0.03192745 -1.12417368  0.932223234
16  7.9892176  0.96421599  0.46793089  0.373647014
6   5.1962100 -0.91316862  1.11354235 -0.804453944
1   2.2630533 -0.62633470 -0.20456759  0.220761764
8   5.0208369  0.43886340  0.08169514  0.132995916
5   5.0409406 -0.84235946  0.43000738 -0.291599200
17  0.9218684 -0.15822891  0.14593271  1.189161582
15 10.7829689  0.69208513  0.82190786  0.237311062
10  4.0411356 -0.65472729  0.02832164  0.558402684
11  2.8280051 -0.45762457  0.63079135 -0.089977975
9   4.2663219  0.10720486 -0.34067849 -0.675151598
18  3.1680733 -0.41737900  1.03352732 -0.236938282
3   4.2752294 -0.07214500 -0.60797514  0.303213289
20  4.7876770  1.00324330  1.49898460  0.009202396
14 11.6455841  0.60920550  0.78341426  0.532852308
19 -1.2003506  0.57033354  0.72777285  0.509955590
12  5.1204137  0.36328912 -0.69118581 -0.665622948
7   4.2452549 -0.76452556  0.60464291 -0.484842066
> with(dune.env, plot(A1, pred[,"A1"] - A1, ylab="Prediction Error"))
> abline(h=0)
> 
> 
> 
> cleanEx(); ..nameEx <- "procrustes"
> 
> ### * procrustes
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: procrustes
> ### Title: Procrustes Rotation of Two Configurations
> ### Aliases: procrustes print.procrustes summary.procrustes
> ###   print.summary.procrustes plot.procrustes points.procrustes
> ###   lines.procrustes residuals.procrustes fitted.procrustes protest
> ###   print.protest
> ### Keywords: multivariate htest
> 
> ### ** Examples
> 
> data(varespec)
> vare.dist <- vegdist(wisconsin(varespec))
> library(MASS)  ## isoMDS
> mds.null <- isoMDS(vare.dist, tol=1e-7)
initial  value 27.004018 
iter   5 value 19.627798
iter  10 value 19.080657
iter  15 value 18.587495
iter  20 value 18.075166
iter  25 value 17.922314
iter  30 value 17.858977
iter  35 value 17.823041
iter  40 value 17.816456
iter  45 value 17.812079
iter  50 value 17.811040
final  value 17.811040 
stopped after 50 iterations
> mds.alt <- isoMDS(vare.dist, initMDS(vare.dist), maxit=200, tol=1e-7)
initial  value 40.946864 
iter   5 value 35.233817
iter  10 value 29.213576
iter  15 value 27.267129
iter  20 value 26.789268
iter  25 value 26.326361
iter  30 value 26.022929
iter  35 value 25.583087
iter  40 value 24.798014
iter  45 value 24.186366
iter  50 value 22.970805
iter  55 value 22.791064
iter  60 value 22.650504
iter  65 value 22.192285
iter  70 value 22.042446
iter  75 value 22.016123
iter  80 value 22.006493
iter  85 value 22.003260
iter  90 value 22.002696
iter  95 value 22.002568
final  value 22.002559 
converged
> vare.proc <- procrustes(mds.alt, mds.null)
> vare.proc

Call:
procrustes(X = mds.alt, Y = mds.null) 

Procrustes sum of squares:
476.9 

> summary(vare.proc)

Call:
procrustes(X = mds.alt, Y = mds.null) 

Number of objects: 24    Number of dimensions: 2 

Procrustes sum of squares:  
 476.9 
Procrustes root mean squared error: 
 4.458 
Quantiles of Procrustes errors:
       Min         1Q     Median         3Q        Max 
 0.4414805  1.4921114  2.0623186  4.1475454 13.2852587 

> plot(vare.proc)
> plot(vare.proc, kind=2)
> residuals(vare.proc)
        18         15         24         27         23         19         22 
 1.9188822  0.7545389  7.8149973  3.8711767  2.3330069  0.8367255  1.9704564 
        16         28         13         14         20         25          7 
 1.3378486  7.4734078  1.9821648  1.2580153  0.4414805  2.3028258  3.4903312 
         5          6          3          4          2          9         12 
 5.6982274  1.5244639  1.9559438  4.9766513 13.2852587  1.8906924  1.3950539 
        10         11         21 
 2.1424725  3.4187558  6.6343849 
> 
> 
> 
> cleanEx(); ..nameEx <- "radfit"
> 
> ### * radfit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: radfit
> ### Title: Rank - Abundance or Dominance / Diversity Models
> ### Aliases: radfit radfit.default radfit.data.frame AIC.radfit as.rad
> ###   coef.radfit fitted.radfit lines.radline plot.radfit.frame plot.radfit
> ###   plot.radline plot.rad points.radline print.radfit.frame print.radfit
> ###   print.radline rad.preempt rad.lognormal rad.veil rad.zipf
> ###   rad.zipfbrot
> ### Keywords: univar distribution
> 
> ### ** Examples
> 
> data(BCI)
> mod <- rad.veil(BCI[1,])
> mod

RAD model: Veil Log-Normal 
Family: poisson 
No. of species:  93 
Total abundance: 448 

     log.mu   log.sigma        veil    Deviance         AIC         BIC 
  0.9603092   1.0678903   0.9387607  23.0642419 304.9744085 312.5722070 
> plot(mod)
> mod <- radfit(BCI[1,])
> plot(mod)
> # Take a subset of BCI to save time and nerves
> mod <- radfit(BCI[2:5,])
> mod

Deviance for RAD models:

                 2       3       4       5
Preemption 29.5066 58.9295 39.7817 76.3108
Lognormal  18.8511 29.2719 16.6588 17.0775
Veiled.LN  15.8990 22.9190 13.3208  8.3445
Zipf       48.4277 50.1262 47.9108 30.9358
Mandelbrot  4.7586  5.7342  5.5665 10.5733
> plot(mod, pch=".")
Loading required package: lattice
> 
> 
> 
> cleanEx(); ..nameEx <- "rankindex"
> 
> ### * rankindex
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rankindex
> ### Title: Compares Dissimilarity Indices for Gradient Detection
> ### Aliases: rankindex
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> ## The next scales all environmental variables to unit variance.
> ## Some would use PCA transformation.
> rankindex(scale(varechem), varespec)
      euc       man       gow       bra       kul 
0.2396330 0.2735087 0.2288358 0.2837910 0.2839834 
> rankindex(scale(varechem), wisconsin(varespec))
      euc       man       gow       bra       kul 
0.4200990 0.4215642 0.3708606 0.4215642 0.4215642 
> 
> 
> 
> cleanEx(); ..nameEx <- "read.cep"
> 
> ### * read.cep
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: read.cep
> ### Title: Reads a CEP (Canoco) data file
> ### Aliases: read.cep
> ### Keywords: IO file
> 
> ### ** Examples
> 
> ## Provided that you have the file `dune.spe'
> ## Not run: theclassic <- read.cep("dune.spe", force=T)
> 
> 
> 
> cleanEx(); ..nameEx <- "scores"
> 
> ### * scores
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: scores
> ### Title: Get Species or Site Scores from an Ordination
> ### Aliases: scores scores.default
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> vare.pca <- prcomp(varespec)
> scores(vare.pca, choices=c(1,2))
           PC1         PC2
18 -10.7847878  18.7094315
15 -27.8036826 -11.7414745
24 -25.6919559 -14.5399684
27 -31.7820166 -31.2216800
23 -19.6315869  -2.5541193
19  -0.2413294 -11.4974077
22 -26.6771373 -12.3140897
16 -21.9230366   0.4449159
28 -39.6083051 -41.8877392
13  -4.0664328  20.4191153
14 -18.4416245   5.4406988
20 -17.3999191   2.3653380
25 -25.1673547 -13.2508067
7  -11.4065430  41.7356300
5   -8.4243752  45.3805255
6   -2.0759474  36.9311222
3   39.8617580   8.0590041
4   13.1065901  12.8377217
2   57.6827011  -4.8983565
9   63.3138332 -22.4481549
12  44.1073111 -10.1653935
10  64.9418975 -16.7633564
11  11.5313633   3.9720890
21  -3.4194194  -3.0130455
> 
> 
> 
> cleanEx(); ..nameEx <- "specaccum"
> 
> ### * specaccum
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: specaccum
> ### Title: Species Accumulation Curves
> ### Aliases: specaccum print.specaccum summary.specaccum plot.specaccum
> ###   boxplot.specaccum
> ### Keywords: univar
> 
> ### ** Examples
> 
> data(BCI)
> sp1 <- specaccum(BCI)
Warning in cor(x, y, na.method, method == "kendall") : 
	 the standard deviation is zero
> sp2 <- specaccum(BCI, "random")
> sp2
Species Accumulation Curve
Accumulation method: random, with 100 permutations
Call: specaccum(comm = BCI, method = "random") 

                                                                        
Sites     1.00000   2.000000   3.000000   4.000000   5.000000   6.000000
Richness 91.34000 121.010000 138.720000 150.540000 159.540000 166.500000
sd        7.21001   6.928925   6.748109   6.509387   6.125654   5.934831
                                                                          
Sites      7.000000   8.000000   9.000000  10.000000  11.000000  12.000000
Richness 171.820000 176.180000 179.790000 182.730000 185.950000 188.590000
sd         5.603714   5.182293   5.129229   5.175418   4.719131   4.521766
                                                                          
Sites     13.000000  14.000000  15.000000  16.000000  17.000000  18.000000
Richness 191.080000 193.100000 194.920000 196.870000 198.270000 199.670000
sd         4.421435   4.372781   4.527536   4.421378   4.287296   4.032832
                                                                          
Sites     19.000000  20.000000  21.000000  22.000000  23.000000  24.000000
Richness 201.000000 202.470000 203.950000 205.180000 206.210000 207.230000
sd         4.005047   3.968194   3.952687   3.774931   3.682596   3.700546
                                                                          
Sites     25.000000  26.000000  27.000000  28.000000  29.000000  30.000000
Richness 208.380000 209.390000 210.540000 211.430000 212.290000 213.230000
sd         3.323561   3.323911   3.316381   3.156699   3.098696   2.957118
                                                                          
Sites     31.000000  32.000000  33.000000  34.000000  35.000000  36.000000
Richness 214.100000 214.880000 215.620000 216.370000 217.000000 217.550000
sd         2.761569   2.575251   2.529742   2.588455   2.486326   2.371442
                                                                          
Sites     37.000000  38.000000  39.000000  40.000000  41.000000  42.000000
Richness 218.160000 218.770000 219.340000 219.970000 220.600000 221.210000
sd         2.364382   2.210421   2.041093   2.071719   1.964328   1.945183
                                                                           
Sites     43.000000  44.000000  45.000000  46.000000  47.000000  48.0000000
Richness 221.850000 222.360000 222.890000 223.320000 223.710000 224.1700000
sd         1.771691   1.586050   1.490000   1.476277   1.208514   0.9749903
                        
Sites     49.0000000  50
Richness 224.6500000 225
sd         0.6092718   0
> summary(sp2)
 1 sites          2 sites         3 sites         4 sites        
 Min.   : 77.00   Min.   :105.0   Min.   :123.0   Min.   :135.0  
 1st Qu.: 86.00   1st Qu.:116.0   1st Qu.:133.8   1st Qu.:145.8  
 Median : 91.00   Median :120.5   Median :140.0   Median :150.5  
 Mean   : 91.34   Mean   :121.0   Mean   :138.7   Mean   :150.5  
 3rd Qu.: 97.00   3rd Qu.:127.0   3rd Qu.:144.0   3rd Qu.:155.0  
 Max.   :109.00   Max.   :136.0   Max.   :158.0   Max.   :162.0  
 5 sites         6 sites         7 sites         8 sites        
 Min.   :144.0   Min.   :152.0   Min.   :156.0   Min.   :160.0  
 1st Qu.:155.0   1st Qu.:162.0   1st Qu.:168.0   1st Qu.:173.0  
 Median :159.5   Median :167.0   Median :173.0   Median :177.0  
 Mean   :159.5   Mean   :166.5   Mean   :171.8   Mean   :176.2  
 3rd Qu.:164.0   3rd Qu.:171.0   3rd Qu.:175.2   3rd Qu.:179.0  
 Max.   :174.0   Max.   :180.0   Max.   :183.0   Max.   :187.0  
 9 sites         10 sites        11 sites        12 sites       
 Min.   :161.0   Min.   :164.0   Min.   :174.0   Min.   :178.0  
 1st Qu.:177.0   1st Qu.:179.0   1st Qu.:182.8   1st Qu.:186.0  
 Median :180.0   Median :184.0   Median :187.0   Median :189.0  
 Mean   :179.8   Mean   :182.7   Mean   :185.9   Mean   :188.6  
 3rd Qu.:183.0   3rd Qu.:186.0   3rd Qu.:188.0   3rd Qu.:191.0  
 Max.   :194.0   Max.   :196.0   Max.   :198.0   Max.   :199.0  
 13 sites        14 sites        15 sites        16 sites       
 Min.   :179.0   Min.   :181.0   Min.   :185.0   Min.   :186.0  
 1st Qu.:188.0   1st Qu.:191.0   1st Qu.:192.0   1st Qu.:194.0  
 Median :191.0   Median :193.0   Median :195.0   Median :197.0  
 Mean   :191.1   Mean   :193.1   Mean   :194.9   Mean   :196.9  
 3rd Qu.:194.0   3rd Qu.:196.0   3rd Qu.:198.0   3rd Qu.:200.0  
 Max.   :201.0   Max.   :203.0   Max.   :205.0   Max.   :207.0  
 17 sites        18 sites        19 sites      20 sites        21 sites       
 Min.   :187.0   Min.   :189.0   Min.   :189   Min.   :189.0   Min.   :189.0  
 1st Qu.:195.8   1st Qu.:197.0   1st Qu.:199   1st Qu.:200.0   1st Qu.:202.0  
 Median :198.0   Median :200.0   Median :201   Median :202.5   Median :204.0  
 Mean   :198.3   Mean   :199.7   Mean   :201   Mean   :202.5   Mean   :203.9  
 3rd Qu.:201.0   3rd Qu.:202.2   3rd Qu.:204   3rd Qu.:205.0   3rd Qu.:207.0  
 Max.   :208.0   Max.   :209.0   Max.   :211   Max.   :212.0   Max.   :213.0  
 22 sites        23 sites        24 sites        25 sites       
 Min.   :194.0   Min.   :195.0   Min.   :197.0   Min.   :198.0  
 1st Qu.:203.0   1st Qu.:204.0   1st Qu.:205.0   1st Qu.:206.0  
 Median :205.0   Median :206.5   Median :207.0   Median :209.0  
 Mean   :205.2   Mean   :206.2   Mean   :207.2   Mean   :208.4  
 3rd Qu.:207.2   3rd Qu.:209.0   3rd Qu.:210.0   3rd Qu.:211.0  
 Max.   :213.0   Max.   :215.0   Max.   :216.0   Max.   :216.0  
 26 sites        27 sites        28 sites        29 sites       
 Min.   :199.0   Min.   :201.0   Min.   :202.0   Min.   :203.0  
 1st Qu.:207.0   1st Qu.:208.8   1st Qu.:210.0   1st Qu.:211.0  
 Median :209.0   Median :211.0   Median :211.0   Median :212.0  
 Mean   :209.4   Mean   :210.5   Mean   :211.4   Mean   :212.3  
 3rd Qu.:212.0   3rd Qu.:213.0   3rd Qu.:214.0   3rd Qu.:214.0  
 Max.   :218.0   Max.   :218.0   Max.   :218.0   Max.   :219.0  
 30 sites        31 sites        32 sites        33 sites       
 Min.   :203.0   Min.   :204.0   Min.   :206.0   Min.   :206.0  
 1st Qu.:211.0   1st Qu.:212.0   1st Qu.:213.0   1st Qu.:214.0  
 Median :213.0   Median :214.0   Median :215.0   Median :216.0  
 Mean   :213.2   Mean   :214.1   Mean   :214.9   Mean   :215.6  
 3rd Qu.:215.0   3rd Qu.:216.0   3rd Qu.:217.0   3rd Qu.:218.0  
 Max.   :220.0   Max.   :220.0   Max.   :220.0   Max.   :220.0  
 34 sites        35 sites      36 sites        37 sites        38 sites       
 Min.   :208.0   Min.   :209   Min.   :209.0   Min.   :212.0   Min.   :214.0  
 1st Qu.:214.8   1st Qu.:216   1st Qu.:216.0   1st Qu.:217.0   1st Qu.:217.0  
 Median :216.0   Median :217   Median :218.0   Median :218.0   Median :219.0  
 Mean   :216.4   Mean   :217   Mean   :217.6   Mean   :218.2   Mean   :218.8  
 3rd Qu.:218.0   3rd Qu.:219   3rd Qu.:219.0   3rd Qu.:220.0   3rd Qu.:220.0  
 Max.   :222.0   Max.   :222   Max.   :223.0   Max.   :223.0   Max.   :224.0  
 39 sites        40 sites        41 sites        42 sites       
 Min.   :214.0   Min.   :214.0   Min.   :216.0   Min.   :216.0  
 1st Qu.:218.0   1st Qu.:219.0   1st Qu.:219.0   1st Qu.:220.0  
 Median :220.0   Median :220.0   Median :221.0   Median :221.0  
 Mean   :219.3   Mean   :220.0   Mean   :220.6   Mean   :221.2  
 3rd Qu.:221.0   3rd Qu.:222.0   3rd Qu.:222.0   3rd Qu.:223.0  
 Max.   :224.0   Max.   :224.0   Max.   :224.0   Max.   :225.0  
 43 sites        44 sites        45 sites        46 sites       
 Min.   :217.0   Min.   :217.0   Min.   :219.0   Min.   :219.0  
 1st Qu.:221.0   1st Qu.:221.8   1st Qu.:222.0   1st Qu.:223.0  
 Median :222.0   Median :223.0   Median :223.0   Median :224.0  
 Mean   :221.8   Mean   :222.4   Mean   :222.9   Mean   :223.3  
 3rd Qu.:223.0   3rd Qu.:223.0   3rd Qu.:224.0   3rd Qu.:224.0  
 Max.   :225.0   Max.   :225.0   Max.   :225.0   Max.   :225.0  
 47 sites        48 sites        49 sites        50 sites     
 Min.   :220.0   Min.   :221.0   Min.   :222.0   Min.   :225  
 1st Qu.:223.0   1st Qu.:224.0   1st Qu.:224.0   1st Qu.:225  
 Median :224.0   Median :224.0   Median :225.0   Median :225  
 Mean   :223.7   Mean   :224.2   Mean   :224.7   Mean   :225  
 3rd Qu.:225.0   3rd Qu.:225.0   3rd Qu.:225.0   3rd Qu.:225  
 Max.   :225.0   Max.   :225.0   Max.   :225.0   Max.   :225  
> plot(sp1, ci.type="poly", col="blue", lwd=2, ci.lty=0, ci.col="lightblue")
> boxplot(sp2, col="yellow", add=TRUE, pch="+")
> 
> 
> 
> cleanEx(); ..nameEx <- "specpool"
> 
> ### * specpool
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: specpool
> ### Title: Extrapolated Species Richness in a Species Pool
> ### Aliases: specpool specpool2vect estimateR estimateR.default
> ###   estimateR.matrix estimateR.data.frame
> ### Keywords: univar
> 
> ### ** Examples
> 
> data(dune)
> data(dune.env)
> attach(dune.env)
> pool <- specpool(dune, Management)
> pool
   Species     Chao   Chao.SE   Jack.1 Jack1.SE   Jack.2     Boot  Boot.SE n
BF      16 17.28906  2.189126 19.33333 2.211083 19.83333 17.74074 1.646379 3
HF      21 21.39844  1.119337 23.40000 1.876166 22.05000 22.56864 1.821518 5
NM      21 22.70370  2.501562 26.00000 3.291403 25.73333 23.77696 2.300982 6
SF      21 28.25000 10.270418 27.66667 3.496029 31.40000 23.99496 1.850288 6
> op <- par(mfrow=c(1,2))
> boxplot(specnumber(dune) ~ Management, col="hotpink", border="cyan3",
+  notch=TRUE)
> boxplot(specnumber(dune)/specpool2vect(pool) ~ Management, col="hotpink",
+  border="cyan3", notch=TRUE)
> par(op)
> data(BCI)
> estimateR(BCI[1:5,])
                  1          2          3          4          5
S.obs     93.000000  84.000000  90.000000  94.000000 101.000000
S.chao1  117.516620 117.293367 141.340237 111.583750 136.055556
se.chao1  12.578970  17.841763  26.075747   9.647692  16.882684
S.ACE    122.848959 117.317307 134.669844 118.729941 137.114088
se.ACE     5.736054   5.571998   6.191618   5.367571   5.848474
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "stepacross"
> 
> ### * stepacross
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: stepacross
> ### Title: Stepacross as Flexible Shortest Paths or Extended
> ###   Dissimilarities
> ### Aliases: stepacross
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> # There are no data sets with high beta diversity in vegan, but this
> # should give an idea.
> data(dune)
> dis <- vegdist(dune)
> edis <- stepacross(dis)
Too long or NA distances: 5 out of 190 (2.6%)
Stepping across 190 dissimilarities...
> plot(edis, dis, xlab = "Shortest path", ylab = "Original")
> ## Manhattan distance have no fixed upper limit.
> dis <- vegdist(dune, "manhattan")
> is.na(dis) <- no.shared(dune)
> dis <- stepacross(dis, toolong=0)
Too long or NA distances: 5 out of 190 (2.6%)
Stepping across 190 dissimilarities...
> 
> 
> 
> cleanEx(); ..nameEx <- "varechem"
> 
> ### * varechem
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: varespec
> ### Title: Vegetation and environment in lichen pastures
> ### Aliases: varechem varespec
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> 
> 
> 
> cleanEx(); ..nameEx <- "vegdist"
> 
> ### * vegdist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: vegdist
> ### Title: Dissimilarity Indices for Community Ecologists
> ### Aliases: vegdist
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(varespec)
> vare.dist <- vegdist(varespec)
> # Orlóci's Chord distance: range 0 .. sqrt(2)
> vare.dist <- vegdist(decostand(varespec, "norm"), "euclidean")
> 
> 
> 
> cleanEx(); ..nameEx <- "vegemite"
> 
> ### * vegemite
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: vegemite
> ### Title: Prints a Compact, Ordered Vegetation Table
> ### Aliases: vegemite coverscale
> ### Keywords: print manip
> 
> ### ** Examples
> 
> data(varespec)
> ## Print only more common species 
> freq <- apply(varespec > 0, 2, sum)
> vegemite(varespec, scale="Hult", sp.ind = freq > 10)
                                 
         1122212121122       1112
         854739268340575634292011
 Cal.vul 111...11.311...1111.111.
 Emp.nig 211332121112211111212213
 Vac.vit 323332212113221211233234
 Pin.syl 111.111111111.11.1111111
 Dic.fus 12.111441121211111111111
 Dic.pol .11.11.11..1.11....1.111
 Ple.sch 144533435123411111111131
 Pol.jun 111.11.111112111.111.111
 Poh.nut 111111111111.1..11.11111
 Pti.cil 1111111111..1..11.11..12
 Cla.arb 321122121332143423111121
 Cla.ran 321221131312145443313241
 Cla.ste 11111311.211.11254555542
 Cla.unc 112111111131111111111111
 Cla.coc 11..11111111111111.1.11.
 Cla.cor 111111111111111111111111
 Cla.gra 111111111111111111111.11
 Cla.fim 11.1111111111111111111.1
 Cla.cri 111111111111111111111111
 Cla.chl ..1.111..1...1.11.11.1.1
 Cet.eri 111...11.111111111.1.1..
 Cet.isl .11....1111.1....1.11111
 Ste.sp  111.11.1111.112111...11.
 Cla.def 1111111111111111111111.1
> ## Order by correspondence analysis, use Hill scaling and layout:
> dca <- decorana(varespec)
> vegemite(varespec, dca, "Hill", zero="-")
                                 
          1   1  1 11122211122222
         203942561738913046572458
 Cet.niv -1114-11-1-11-1---------
 Cla.ste 5555551451425411111211--
 Cla.phy -1-1----1-------1-------
 Cla.cer 1---1-----------------1-
 Cla.sp  ---11--1--11---1-1-11-1-
 Cla.ama --1---1----1------------
 Cla.chl 1111---1-11-111-----11--
 Cla.ran 535254555555223414332321
 Dip.mon --11-----112----------1-
 Ste.sp  -11-1-4111111-1-111--111
 Pin.syl 11-111111-111111111-1111
 Pol.pil ------111--11-11--1-----
 Cet.isl -1-111--1-1--1--111--111
 Cla.coc -1111-1111111-11111-1-11
 Cla.arb 113142453555313343413231
 Vac.uli --1-1----3-1---1---12-11
 Poh.nut -11111--11111111111111-1
 Cla.fim 11111111-111111111111-11
 Cal.vul 111-21-12-51---1221-21--
 Ich.eri ------1--1------11------
 Emp.nig 342214131314344333143131
 Vac.vit 342514244334455432444443
 Cla.gra 1-1111111111111111111111
 Cet.eri -1111-11-111---1111-111-
 Cla.cor 111111111111111111111111
 Cla.cri 111111111111111111111111
 Pel.aph --------1-11--1----1--1-
 Pti.cil 1-11---11-11141--1111111
 Bar.lyc ----------1-121----1----
 Cla.def 11111111-111111111111111
 Cla.bot ----------1-1111---1-1-1
 Bet.pub -------------1------1-1-
 Dic.pol -1-1--1-11--1211-11--1-1
 Cla.unc 111111122111111251212311
 Pol.com ------------11--1--1--1-
 Pol.jun 11-11-1111111121111--131
 Led.pal ----------1--2-----21--1
 Dic.fus 111111111121112145425-41
 Ple.sch 111213114132524434555555
 Vac.myr ---1------1-24--12133--4
 Des.fle ----1----1--11-----21-11
 Nep.arc --1------1-1---1------2-
 Dic.sp  -----1----1--1-1-11-1541
 Hyl.spl ---------------1---3--13
> 
> 
> 
> cleanEx(); ..nameEx <- "wascores"
> 
> ### * wascores
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wascores
> ### Title: Weighted Averages Scores for Species
> ### Aliases: wascores eigengrad
> ### Keywords: multivariate univar
> 
> ### ** Examples
> 
> data(varespec)
> data(varechem)
> library(MASS)  ## isoMDS
> vare.dist <- vegdist(wisconsin(varespec))
> vare.mds <- isoMDS(vare.dist)
initial  value 27.004018 
iter   5 value 19.627798
iter  10 value 19.080657
iter  15 value 18.587495
iter  20 value 18.075166
iter  20 value 18.064314
final  value 17.850149 
converged
> vare.points <- postMDS(vare.mds$points, vare.dist)
> vare.wa <- wascores(vare.points, varespec)
> plot(scores(vare.points), pch="+", asp=1)
> text(vare.wa, rownames(vare.wa), cex=0.8, col="blue")
> ## Omit rare species (frequency <= 4)
> freq <- apply(varespec>0, 2, sum)
> plot(scores(vare.points), pch="+", asp=1)
> text(vare.wa[freq > 4,], rownames(vare.wa)[freq > 4],cex=0.8,col="blue")
> ## Works for environmental variables, too.
> wascores(varechem, varespec)
               N        P         K       Ca        Mg        S        Al
Cal.vul 25.12401 41.66188 246.92383 572.3431  99.40828 49.10552 245.15751
Emp.nig 21.61371 44.17350 158.92517 580.8403  89.20628 35.75327 107.05670
Led.pal 22.34553 40.35530 162.31108 643.8819  95.07712 30.84303  28.83159
Vac.myr 24.96352 49.80649 189.70177 656.4179  96.75529 34.55190  32.75705
Vac.vit 21.14028 45.86984 162.12372 613.2126  94.30084 37.26975 116.14656
Pin.syl 18.37299 44.24818 163.60195 670.9387  93.52214 37.02238 150.45523
Des.fle 22.24089 54.74804 212.20357 771.0159 114.15179 38.00000  24.64143
Bet.pub 21.51034 28.86552 112.28276 513.5586  75.15172 23.55172  33.12414
Vac.uli 28.00729 33.48758 114.90230 372.9653  70.89954 29.32378 202.89008
Dip.mon 22.34228 39.71049 127.44259 446.1565  80.16173 32.32963 122.31574
Dic.sp  21.33007 60.03758 185.04563 828.0544 148.67509 46.75427  90.42294
Dic.fus 23.45681 39.14575 162.91954 578.2309  77.81648 33.48086  60.66890
Dic.pol 20.65446 43.87409 150.51485 665.5845 115.22112 36.17079  90.16733
Hyl.spl 26.10599 67.88980 245.78681 779.6520 111.96685 42.27433  24.92738
Ple.sch 22.60476 54.22534 199.96241 712.6278 109.23425 40.01132  70.43900
Pol.pil 23.17377 43.75902 144.82623 724.9738  85.42623 30.58525 145.73115
Pol.jun 22.89480 47.98022 154.81906 643.3864  87.27819 33.63863  53.24888
Pol.com 21.73521 41.17042 154.91549 631.8704 101.84789 32.17324  46.80986
Poh.nut 19.99885 48.59198 169.68855 678.3813 104.31641 39.94427 132.05458
Pti.cil 21.27880 33.44211 127.08522 564.5652  85.96417 27.11720  56.60692
Bar.lyc 21.17461 27.93323 113.13542 497.9138  77.50564 23.72288  42.09749
Cla.arb 23.56127 38.04952 142.03073 454.9019  74.00779 33.81002 173.12698
Cla.ran 24.28421 38.60534 135.31177 463.2750  70.54209 32.53349 183.79979
Cla.ste 19.28049 46.71060 158.00576 540.4904  80.19153 40.29106 225.89526
Cla.unc 21.41240 45.49844 163.40402 621.9100  98.35538 40.00734 119.59481
Cla.coc 21.72473 42.80681 156.32330 557.9007  80.95448 36.25161 149.82616
Cla.cor 22.11640 47.06656 160.36881 623.5185  95.17781 36.75273 104.71463
Cla.gra 22.51887 44.06576 156.50214 583.1558  94.10292 36.93930 134.13424
Cla.fim 21.77980 41.82652 153.29444 512.4646  78.28232 35.62323 128.96061
Cla.cri 20.88795 44.12262 171.04016 574.5672  92.52169 38.24003 116.03507
Cla.chl 19.51207 45.39655 150.93190 571.0233  95.77586 39.50862 156.81983
Cla.bot 22.97660 38.89574 167.20000 590.8021  99.57234 34.79362  87.75957
Cla.ama 25.07143 35.84286 105.07857 395.2214  68.18571 27.11429  95.91429
Cla.sp  19.21923 47.37308 168.49231 526.7654  79.54423 45.15385 215.33846
Cet.eri 21.00944 47.76972 165.07972 579.6322  99.14944 42.25472 163.46000
Cet.isl 18.36552 42.73695 151.78374 626.2813  89.77833 35.33498 132.68227
Cet.niv 18.56110 61.18194 207.67705 502.9203  60.91755 50.22532 396.82405
Nep.arc 23.33099 49.10019 146.84715 618.1601  64.27319 29.95760  31.72300
Ste.sp  28.19743 32.84800  94.33459 389.5143  53.25377 24.22175  95.39326
Pel.aph 21.08553 54.45395 193.38816 886.5487 119.35132 37.92500 106.16447
Ich.eri 28.88636 27.00000  87.86818 307.0500  40.48182 22.17273  89.94091
Cla.cer 20.25000 56.79000 192.36000 519.2300  62.10000 45.18000 314.92000
Cla.def 22.19198 45.22981 167.73069 583.7983  92.01320 38.51369 100.46139
Cla.phy 15.73750 54.56875 180.39375 775.4500  99.65625 43.35000 208.55000
                Fe        Mn        Zn        Mo  Baresoil Humdepth       pH
Cal.vul  75.457843  52.38247  8.281074 0.4734635 27.241036 2.187819 2.845108
Emp.nig  38.146102  53.49357  7.159938 0.3289657 27.324317 2.367439 2.888078
Led.pal   5.560906  70.48260  7.444100 0.2251490 37.325030 2.689154 2.895352
Vac.myr   5.589213  75.17221  7.838533 0.2666732 31.404171 2.798935 2.855216
Vac.vit  37.586067  51.81515  7.617213 0.3680289 26.307701 2.307879 2.923128
Pin.syl  39.121898  35.22311  7.733333 0.3485401 17.762968 1.996350 3.049148
Des.fle   6.066429 110.87232  9.526607 0.2316071 22.740179 2.834821 2.822857
Bet.pub   5.417241  37.53448  5.637931 0.2068966 51.496552 2.527586 2.979310
Vac.uli  93.963929  37.73062  4.593824 0.3780552 21.410710 2.041196 3.006965
Dip.mon  73.281173  46.88025  4.593827 0.3725309 31.836574 2.103704 2.856790
Dic.sp   22.504617  65.35020 13.060765 0.5610370 23.182889 2.232247 2.954272
Dic.fus  13.922252  61.40958  6.922859 0.3218816 26.918674 2.484399 2.806431
Dic.pol  20.973927  33.28779  9.110561 0.3892739 37.304043 2.228713 3.015842
Hyl.spl   4.729157 115.14606  9.885976 0.2851996 20.956264 2.925000 2.807594
Ple.sch  19.113811  77.12277  9.007860 0.3405945 24.584979 2.596881 2.858446
Pol.pil  51.993443  36.74754  8.045902 0.2204918 17.368852 1.493443 3.227869
Pol.jun  12.885704  82.56274  7.945126 0.2760289 28.116303 2.615523 2.874729
Pol.com   7.895775  68.22535  7.843662 0.2591549 38.687324 2.926761 2.860563
Poh.nut  33.089313  42.02290  8.452290 0.3935115 24.709351 2.147328 2.985496
Pti.cil  14.036188  33.93547  5.906924 0.2303712 48.941884 2.502498 2.973376
Bar.lyc   8.199687  31.11379  5.550784 0.2084639 54.331975 2.514734 2.986834
Cla.arb  65.470394  38.28429  6.387500 0.4464046 22.592997 2.048540 2.937879
Cla.ran  76.612752  34.86010  6.616452 0.3903501 17.270158 1.799128 3.022346
Cla.ste  84.639467  33.27903  7.287216 0.4054879  9.854042 1.851973 3.052167
Cla.unc  27.463504  40.10322  9.108102 0.5120114 28.312376 2.362687 2.858564
Cla.coc  46.653763  43.53584  7.269176 0.3698925 19.972222 2.025090 2.974194
Cla.cor  32.916238  53.38441  7.518489 0.3639871 26.620868 2.399518 2.890997
Cla.gra  45.758366  44.63911  7.702724 0.4244163 25.546654 2.230350 2.933658
Cla.fim  41.710354  47.83687  6.815152 0.3887626 24.763889 2.239394 2.902778
Cla.cri  34.729585  44.75984  6.933735 0.3746988 29.711352 2.400000 2.841633
Cla.chl  42.089655  35.13276  7.908621 0.3814655 22.319655 2.075000 3.022414
Cla.bot  23.374468  46.54255  7.263830 0.3106383 45.725532 2.580851 2.904255
Cla.ama  68.971429  41.98571  4.928571 0.3214286 27.592857 1.857143 2.914286
Cla.sp   47.913462  49.61923  8.421154 0.6173077 16.864423 2.213462 2.921154
Cet.eri  42.614167  36.96694  9.516389 0.5687500 21.452639 2.058056 2.923889
Cet.isl  29.617734  33.24138  7.518227 0.3192118 26.417980 2.027586 3.065025
Cet.niv  94.339916  37.03232  9.116371 0.9987764 19.692312 1.799241 2.923629
Nep.arc  12.910837 115.15684  7.743536 0.2180608 23.135932 2.541065 2.918251
Ste.sp   30.226998  31.97061  7.635502 0.2828767 15.844007 1.477740 3.038756
Pel.aph  37.598684  56.64079  7.652632 0.2046053 28.321053 2.286842 3.026316
Ich.eri  24.236364  23.95909  6.618182 0.2863636 18.727273 1.568182 2.968182
Cla.cer 111.090000  52.04000  8.530000 0.6800000 15.393000 1.870000 2.900000
Cla.def  25.116325  48.81105  7.599609 0.4096285 33.814545 2.468133 2.823656
Cla.phy  50.475000  35.28125  8.568750 0.2812500  7.728125 1.575000 3.231250
> ## And the strengths of these variables are:
> eigengrad(varechem, varespec)
         N          P          K         Ca         Mg          S         Al 
0.13000842 0.18880078 0.16246365 0.15722067 0.16359171 0.13391967 0.29817406 
        Fe         Mn         Zn         Mo   Baresoil   Humdepth         pH 
0.20766831 0.27254480 0.16783834 0.09542514 0.20931501 0.25051326 0.14583161 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  35.2 0.94 36.39 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')