Description Usage Arguments Details Value Note Author(s) See Also Examples
The function fits environmental vectors or factors onto an ordination. The projections of points onto vectors have maximum correlation with corresponding environmental variables, and the factors show the averages of factor levels.
1 2 3 4 5 6 7 8 9 10 11 12  ## Default S3 method:
envfit(ord, env, permutations = 999, strata = NULL,
choices=c(1,2), display = "sites", w = weights(ord), na.rm = FALSE, ...)
## S3 method for class 'formula'
envfit(formula, data, ...)
## S3 method for class 'envfit'
plot(x, choices = c(1,2), labels, arrow.mul, at = c(0,0),
axis = FALSE, p.max = NULL, col = "blue", bg, add = TRUE, ...)
## S3 method for class 'envfit'
scores(x, display, choices, ...)
vectorfit(X, P, permutations = 0, strata = NULL, w, ...)
factorfit(X, P, permutations = 0, strata = NULL, w, ...)

ord 
An ordination object or other structure from which the
ordination 
env 
Data frame, matrix or vector of environmental variables. The variables can be of mixed type (factors, continuous variables) in data frames. 
X 
Matrix or data frame of ordination scores. 
P 
Data frame, matrix or vector of environmental
variable(s). These must be continuous for 
permutations 
a list of control values for the permutations
as returned by the function 
formula, data 
Model 
na.rm 
Remove points with missing values in ordination scores
or environmental variables. The operation is casewise: the whole
row of data is removed if there is a missing value and

x 
A result object from 
choices 
Axes to plotted. 
labels 
Change plotting labels. The argument should be a list
with elements 
arrow.mul 
Multiplier for vector lengths. The arrows are
automatically scaled similarly as in 
at 
The origin of fitted arrows in the plot. If you plot arrows
in other places then origin, you probably have to specify

axis 
Plot axis showing the scaling of fitted arrows. 
p.max 
Maximum estimated P value for displayed
variables. You must calculate P values with setting

col 
Colour in plotting. 
bg 
Background colour for labels. If 
add 
Results added to an existing ordination plot. 
strata 
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. 
display 
In fitting functions these are ordinary site scores or
linear combination scores
( 
w 
Weights used in fitting (concerns mainly 
... 
Parameters passed to 
Function envfit
finds vectors or factor averages of
environmental variables. Function plot.envfit
adds these in an
ordination diagram. If X
is a data.frame
,
envfit
uses factorfit
for factor
variables and
vectorfit
for other variables. If X
is a matrix or a
vector, envfit
uses only vectorfit
. Alternatively, the
model can be defined a simplified model formula
, where
the left hand side must be an ordination result object or a matrix of
ordination scores, and right hand
side lists the environmental variables. The formula interface can be
used for easier selection and/or transformation of environmental
variables. Only the main effects will be analysed even if interaction
terms were defined in the formula.
The printed output of continuous variables (vectors) gives the
direction cosines which are the coordinates of the heads of unit
length vectors. In plot
these are scaled by their
correlation (square root of the column r2
) so that
“weak” predictors have shorter arrows than “strong”
predictors. You can see the scaled relative lengths using command
scores
. The plot
ted (and scaled) arrows are further
adjusted to the current graph using a constant multiplier: this will
keep the relative r2
scaled lengths of the arrows but tries
to fill the current plot. You can see the multiplier using
ordiArrowMul(result_of_envfit)
, and set it with the
argument arrow.mul
.
Functions vectorfit
and factorfit
can be called directly.
Function vectorfit
finds directions in the ordination space
towards which the environmental vectors change most rapidly and to
which they have maximal correlations with the ordination
configuration. Function factorfit
finds averages of ordination
scores for factor levels. Function factorfit
treats ordered
and unordered factors similarly.
If permutations
> 0, the ‘significance’ of fitted vectors
or factors is assessed using permutation of environmental variables.
The goodness of fit statistic is squared correlation coefficient
(r^2).
For factors this is defined as r^2 = 1  ss_w/ss_t, where
ss_w and ss_t are withingroup and total sums of
squares. See permutations
for additional details on
permutation tests in Vegan.
User can supply a vector of prior weights w
. If the ordination
object has weights, these will be used. In practise this means that
the row totals are used as weights with
cca
or decorana
results. If you do not
like this, but want to give
equal weights to all sites, you should set w = NULL
.
The weighted fitting gives similar results to biplot
arrows and class centroids in cca
.
For complete
similarity between fitted vectors and biplot arrows, you should set
display = "lc"
(and possibly scaling = 2
).
The lengths of arrows for fitted vectors are automatically adjusted
for the physical size of the plot, and the arrow lengths cannot be
compared across plots. For similar scaling of arrows, you must
explicitly set the arrow.mul
argument in the plot
command; see ordiArrowMul
and
ordiArrowTextXY
.
The results can be accessed with scores.envfit
function which
returns either the fitted vectors scaled by correlation coefficient or
the centroids of the fitted environmental variables.
Functions vectorfit
and factorfit
return lists of
classes vectorfit
and factorfit
which have a
print
method. The result object have the following items:
arrows 
Arrow endpoints from 
centroids 
Class centroids from 
r 
Goodness of fit statistic: Squared correlation coefficient 
permutations 
Number of permutations. 
control 
A list of control values for the permutations
as returned by the function 
pvals 
Empirical Pvalues for each variable. 
Function envfit
returns a list of class envfit
with
results of vectorfit
and envfit
as items.
Function plot.envfit
scales the vectors by correlation.
Fitted vectors have become the method of choice in displaying
environmental variables in ordination. Indeed, they are the optimal
way of presenting environmental variables in Constrained
Correspondence Analysis cca
, since there they are the
linear constraints.
In unconstrained ordination the relation between external variables
and ordination configuration may be less linear, and therefore other
methods than arrows may be more useful. The simplest is to adjust the
plotting symbol sizes (cex
, symbols
) by
environmental variables.
Fancier methods involve smoothing and regression methods that
abound in R, and ordisurf
provides a wrapper for some.
Jari Oksanen. The permutation test derives from the code suggested by Michael Scroggie.
A better alternative to vectors may be ordisurf
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  data(varespec)
data(varechem)
library(MASS)
ord < metaMDS(varespec)
(fit < envfit(ord, varechem, perm = 999))
scores(fit, "vectors")
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 = 999, display = "lc")
plot(fit, p.max = 0.05, col = "red")
## Class variables, formula interface, and displaying the
## interclass variability with `ordispider', and semitransparent
## white background for labels (semitransparent colours are not
## supported by all graphics devices)
data(dune)
data(dune.env)
attach(dune.env)
ord < cca(dune)
fit < envfit(ord ~ Moisture + A1, dune.env, perm = 0)
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, bg = rgb(1, 1, 1, 0.5))
## Use shorter labels for factor centroids
labels(fit)
plot(ord)
plot(fit, labels=list(factors = paste("M", c(1,2,4,5), sep = "")),
bg = rgb(1,1,0,0.5))
detach(dune.env)

Loading required package: permute
Loading required package: lattice
This is vegan 2.43
Square root transformation
Wisconsin double standardization
Run 0 stress 0.1843196
Run 1 stress 0.2386162
Run 2 stress 0.2140424
Run 3 stress 0.2141096
Run 4 stress 0.2335639
Run 5 stress 0.2265716
Run 6 stress 0.2094761
Run 7 stress 0.2254456
Run 8 stress 0.1974407
Run 9 stress 0.2325123
Run 10 stress 0.1843196
... New best solution
... Procrustes: rmse 1.758584e05 max resid 6.905317e05
... Similar to previous best
Run 11 stress 0.195049
Run 12 stress 0.2354621
Run 13 stress 0.2145795
Run 14 stress 0.2166094
Run 15 stress 0.2422932
Run 16 stress 0.2263597
Run 17 stress 0.1852397
Run 18 stress 0.2152708
Run 19 stress 0.2050707
Run 20 stress 0.267362
*** Solution reached
***VECTORS
NMDS1 NMDS2 r2 Pr(>r)
N 0.05039 0.99873 0.2080 0.101
P 0.68715 0.72652 0.1755 0.135
K 0.82741 0.56161 0.1657 0.154
Ca 0.75022 0.66118 0.2810 0.033 *
Mg 0.69688 0.71718 0.3493 0.008 **
S 0.27641 0.96104 0.1774 0.127
Al 0.83763 0.54625 0.5155 0.002 **
Fe 0.86176 0.50732 0.3999 0.005 **
Mn 0.80224 0.59700 0.5322 0.001 ***
Zn 0.66533 0.74655 0.1779 0.119
Mo 0.84871 0.52886 0.0517 0.564
Baresoil 0.87195 0.48960 0.2494 0.040 *
Humdepth 0.92627 0.37686 0.5591 0.001 ***
pH 0.79905 0.60127 0.2625 0.039 *

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Permutation: free
Number of permutations: 999
NMDS1 NMDS2
N 0.02298243 0.4555318
P 0.28786999 0.3043624
K 0.33677266 0.2285862
Ca 0.39766734 0.3504696
Mg 0.41185372 0.4238519
S 0.11640862 0.4047417
Al 0.60138592 0.3921850
Fe 0.54497790 0.3208271
Mn 0.58527476 0.4355458
Zn 0.28061460 0.3148670
Mo 0.19291014 0.1202102
Baresoil 0.43546052 0.2445131
Humdepth 0.69257033 0.2817812
pH 0.40937530 0.3080495
$vectors
[1] "A1"
$factors
[1] "Moisture1" "Moisture2" "Moisture4" "Moisture5"
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