varpart {vegan}  R Documentation 
The function partitions the variation of response table Y with respect to two, three, or four explanatory tables, using redundancy analysis ordination (RDA). If Y contains a single vector, partitioning is by partial regression. Collinear variables in the explanatory tables do NOT have to be removed prior to partitioning.
varpart(Y, X, ..., data, transfo, scale = FALSE) showvarparts(parts, labels, ...) ## S3 method for class 'varpart234': plot(x, cutoff = 0, digits = 1, ...)
Y 
Data frame or matrix containing the response data table. In community ecology, that table is often a sitebyspecies table. 
X 
Two to four explanatory models, variables or tables. These can
be defined in three alternative ways: (1) onesided model formulae
beginning with ~ and then defining the model, (2) name of a
single numeric variable, or (3) name of data frame or matrix with
numeric variables. The model formulae can have factors,
interaction terms and transformations of variables. The names of the
variables in the model formula are found in data frame given in
data argument, and if not found there, in the user
environment. Single numeric variables, data frames or matrices are
found in the user environment. All entries till the next argument
(data or transfo ) are interpreted as explanatory
models, and the names of these arguments cannot be abbreviated nor
omitted.

data 
The data frame with the variables used in the formulae in
X . 
transfo 
Transformation for Y (community data) using
decostand . All alternatives in decostand can be
used, and those preserving Euclidean metric include
"hellinger" , "chi.square" , "total" , "norm" . 
scale 
Should the columns of Y be standardized to unit variance 
parts 
Number of explanatory tables (circles) displayed. 
labels 
Labels used for displayed fractions. Default is to use the same letters as in the printed output. 
x 
The varpart result. 
cutoff 
The values below cutoff will not be displayed. 
digits 
The number of significant digits; the number of decimal places is at least one higher. 
... 
Other parameters passed to functions. 
The functions partition the variation in Y
into components
accounted for by two to four explanatory tables and their combined
effects. If Y
is a multicolumn data frame or
matrix, the partitioning is based on redundancy analysis (RDA, see
rda
), and if Y
is a single variable, the
partitioning is based on linear regression. A simplified, fast
version of RDA is used (function simpleRDA2
). The actual
calculations are done in functions varpart2
to varpart4
,
but these are not intended to be called directly by the user.
The function primarily uses adjusted R squares to assess the partitions explained by the explanatory tables and their combinations, because this is the only unbiased method (PeresNeto et al., 2006). The raw R squares for basic fractions are also displayed, but these are biased estimates of variation explained by the explanatory table.
The identifiable fractions are designated by lower case alphabets. The
meaning of the symbols can be found in the separate document
"partitioning.pdf" (which can be read using vegandocs
),
or can be displayed graphically using function
showvarparts
.
A fraction is testable if it can be directly
expressed as an RDA model. In these cases the printed output also
displays the corresponding RDA model using notation where explanatory
tables after 
are conditions (partialled out; see
rda
for details). Although single fractions can be
testable, this does not mean that all fractions simultaneously can be
tested, since there number of testable fractions is higher than
the number of estimated models.
An abridged explanation of the alphabetic symbols for the individual
fractions follows, but computational details should be checked in
"partitioning.pdf" (readable with vegandocs
) or in the
source code.
With two explanatory tables, the fractions explained
uniquely by each of the two tables are [a]
and
[c]
, and their joint effect
is [b]
following Borcard et al. (1992).
With three explanatory tables, the fractions explained uniquely
by each of the three tables are
[a]
to [c]
, joint fractions between two tables are
[d]
to [f]
, and the joint fraction between all three
tables is [g]
.
With four explanatory tables, the fractions explained uniquely by each
of the four tables are [a]
to [d]
, joint fractions between two tables are [e]
to
[j]
, joint fractions between three variables are [k]
to
[n]
, and the joint fraction between all four tables is
[o]
.
There is a plot
function that displays the Venn
diagram and labels each intersection (individual fraction) with the
adjusted R squared if this is higher than cutoff
. A helper
function showvarpart
displays the fraction labels.
Function varpart
returns an
object of class "varpart"
with items scale
and
transfo
(can be missing) which hold information on
standardizations, tables
which contains names of explanatory
tables, and call
with the function call
. The
function varpart
calls function varpart2
,
varpart3
or varpart4
which return an object of class
"varpart234"
and saves its result in the item part
.
The items in this object are:
SS.Y 
Sum of squares of matrix Y . 
n 
Number of observations (rows). 
nsets 
Number of explanatory tables 
bigwarning 
Warnings on collinearity. 
fract 
Basic fractions from all estimated constrained models. 
indfract 
Individual fractions or all possible subsections in
the Venn diagram (see showvarparts ). 
contr1 
Fractions that can be found after conditioning on single explanatory table in models with three or four explanatory tables. 
contr2 
Fractions that can be found after conditioning on two explanatory tables in models with four explanatory tables. 
Items fract
,
indfract
, contr1
and contr2
are all data frames with
items:
fract
and this is NA
in other items.Testable
, and this field is
TRUE
. In that case the fraction label also gives the
specification of the testable RDA model.
You can use command vegandocs
to display document
"partitioning.pdf" which presents
Venn diagrams showing the fraction names in partitioning the variation of
Y with respect to 2, 3, and 4 tables of explanatory variables, as well
as the equations used in variation partitioning.
The functions frequently give negative estimates of variation. Adjusted Rsquares can be negative for any fraction; unadjusted R squares of testable fractions always will be nonnegative. Nontestable fractions cannot be found directly, but by subtracting different models, and these subtraction results can be negative. The fractions are orthogonal, or linearly independent, but more complicated or nonlinear dependencies can cause negative nontestable fractions.
The current function will only use RDA in multivariate partitioning. It is much more complicated to estimate the adjusted Rsquares for CCA, and unbiased analysis of CCA is not currently implemented.
Pierre Legendre, Departement de Sciences Biologiques, Universite de Montreal, Canada. Adapted to vegan by Jari Oksanen.
(a) References on variation partitioning
Borcard, D., P. Legendre & P. Drapeau. 1992. Partialling out the spatial component of ecological variation. Ecology 73: 1045–1055.
Legendre, P. & L. Legendre. 1998. Numerical ecology, 2nd English edition. Elsevier Science BV, Amsterdam.
(b) Reference on transformations for species data
Legendre, P. and E. D. Gallagher. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129: 271–280.
(c) Reference on adjustment of the bimultivariate redundancy statistic
PeresNeto, P., P. Legendre, S. Dray and D. Borcard. 2006. Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87: 2614–2625.
For analysing testable fractions, see rda
and
anova.cca
. For data transformation, see
decostand
. Function inertcomp
gives
(unadjusted) components of variation for each species or site
separately.
data(mite) data(mite.env) data(mite.pcnm) ## See detailed documentation: ## Not run: vegandocs("partition") ## End(Not run) # Two explanatory matrices  Hellingertransform Y # Formula shortcut "~ ." means: use all variables in 'data'. mod < varpart(mite, ~ ., mite.pcnm, data=mite.env, transfo="hel") mod showvarparts(2) plot(mod) # Alternative way of to conduct this partitioning # Change the data frame with factors into numeric model matrix mm < model.matrix(~ SubsDens + WatrCont + Substrate + Shrub + Topo, mite.env)[,1] mod < varpart(decostand(mite, "hel"), mm, mite.pcnm) # Test fraction [a] using RDA: rda.result < rda(decostand(mite, "hell"), mm, mite.pcnm) anova(rda.result, step=200, perm.max=200) # Three explanatory matrices mod < varpart(mite, ~ SubsDens + WatrCont, ~ Substrate + Shrub + Topo, mite.pcnm, data=mite.env, transfo="hel") mod showvarparts(3) plot(mod) # An alternative formulation of the previous model using # matrices mm1 amd mm2 and Hellinger transformed species data mm1 < model.matrix(~ SubsDens + WatrCont, mite.env)[,1] mm2 < model.matrix(~ Substrate + Shrub + Topo, mite.env)[, 1] mite.hel < decostand(mite, "hel") mod < varpart(mite.hel, mm1, mm2, mite.pcnm) # Use RDA to test fraction [a] # Matrix can be an argument in formula rda.result < rda(mite.hel ~ mm1 + Condition(mm2) + Condition(as.matrix(mite.pcnm))) anova(rda.result, step=200, perm.max=200) # Four explanatory tables mod < varpart(mite, ~ SubsDens + WatrCont, ~Substrate + Shrub + Topo, mite.pcnm[,1:11], mite.pcnm[,12:22], data=mite.env, transfo="hel") mod plot(mod) # Show values for all partitions by putting 'cutoff' low enough: plot(mod, cutoff = Inf, cex = 0.7)