adonis  R Documentation 
Analysis of variance using distance matrices — for
partitioning distance matrices among sources of variation and fitting
linear models (e.g., factors, polynomial regression) to distance
matrices; uses a permutation test with pseudoF
ratios.
adonis2(formula, data, permutations = 999, method = "bray",
sqrt.dist = FALSE, add = FALSE, by = NULL,
parallel = getOption("mc.cores"), na.action = na.fail,
strata = NULL, ...)
formula 
Model formula. The lefthand side (LHS) of the formula
must be either a community data matrix or a dissimilarity matrix,
e.g., from 
data 
the data frame for the independent variables, with rows
in the same order as the community data matrix or dissimilarity
matrix named on the LHS of 
permutations 
a list of control values for the permutations
as returned by the function 
method 
the name of any method used in 
sqrt.dist 
Take square root of dissimilarities. This often euclidifies dissimilarities. 
add 
Add a constant to the nondiagonal dissimilarities such
that all eigenvalues are nonnegative in the underlying Principal
Coordinates Analysis (see 
by 

parallel 
Number of parallel processes or a predefined socket
cluster. With 
na.action 
Handling of missing values on the righthandside
of the formula (see 
strata 
Groups within which to constrain permutations. The traditional nonmovable strata are set as Blocks in the permute package, but some more flexible alternatives may be more appropriate. 
... 
Other arguments passed to 
adonis2
is a function for the analysis and partitioning sums of
squares using dissimilarities. The function is based on the principles
of McArdle & Anderson (2001) and can perform sequential, marginal and
overall tests. The function also allows using additive constants or
squareroot of dissimilarities to avoid negative eigenvalues, but can
also handle semimetric indices (such as BrayCurtis) that produce
negative eigenvalues. The adonis2
tests are identical to
anova.cca
of dbrda
. With Euclidean
distances, the tests are also identical to anova.cca
of
rda
.
The function partitions sums of squares of a multivariate data set,
and they are directly analogous to MANOVA (multivariate analysis of
variance). McArdle and Anderson (2001) and Anderson (2001) refer to
the method as “permutational MANOVA” (formerly
“nonparametric MANOVA”). Further, as the inputs are linear
predictors, and a response matrix of an arbitrary number of columns,
they are a robust alternative to both parametric MANOVA and to
ordination methods for describing how variation is attributed to
different experimental treatments or uncontrolled covariates. The
method is also analogous to distancebased redundancy analysis and
algorithmically similar to dbrda
(Legendre and Anderson
1999), and provides an alternative to AMOVA (nested analysis of
molecular variance, Excoffier, Smouse, and Quattro, 1992; amova
in the ade4 package) for both crossed and nested factors.
The function returns an anova.cca
result object with a
new column for partial R^2
: This is the proportion
of sum of squares from the total, and in marginal models
(by = "margin"
) the R^2
terms do not add up to
1.
Anderson (2001, Fig. 4) warns that the method may confound
location and dispersion effects: significant differences may be caused
by different withingroup variation (dispersion) instead of different
mean values of the groups (see Warton et al. 2012 for a general
analysis). However, it seems that adonis2
is less sensitive to
dispersion effects than some of its alternatives (anosim
,
mrpp
). Function betadisper
is a sister
function to adonis2
to study the differences in dispersion
within the same geometric framework.
Martin Henry H. Stevens and Jari Oksanen.
Anderson, M.J. 2001. A new method for nonparametric multivariate analysis of variance. Austral Ecology, 26: 32–46.
Excoffier, L., P.E. Smouse, and J.M. Quattro. 1992. Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data. Genetics, 131:479–491.
Legendre, P. and M.J. Anderson. 1999. Distancebased redundancy analysis: Testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69:1–24.
McArdle, B.H. and M.J. Anderson. 2001. Fitting multivariate models to community data: A comment on distancebased redundancy analysis. Ecology, 82: 290–297.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distancebased multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89–101.
mrpp
, anosim
,
mantel
, varpart
.
data(dune)
data(dune.env)
## default is overall (omnibus) test
adonis2(dune ~ Management*A1, data = dune.env)
## sequential tests
adonis2(dune ~ Management*A1, data = dune.env, by = "terms")
### Example of use with strata, for nested (e.g., block) designs.
dat < expand.grid(rep=gl(2,1), NO3=factor(c(0,10)),field=gl(3,1) )
dat
Agropyron < with(dat, as.numeric(field) + as.numeric(NO3)+2) +rnorm(12)/2
Schizachyrium < with(dat, as.numeric(field)  as.numeric(NO3)+2) +rnorm(12)/2
total < Agropyron + Schizachyrium
dotplot(total ~ NO3, dat, jitter.x=TRUE, groups=field,
type=c('p','a'), xlab="NO3", auto.key=list(columns=3, lines=TRUE) )
Y < data.frame(Agropyron, Schizachyrium)
mod < metaMDS(Y, trace = FALSE)
plot(mod)
### Ellipsoid hulls show treatment
with(dat, ordiellipse(mod, NO3, kind = "ehull", label = TRUE))
### Spider shows fields
with(dat, ordispider(mod, field, lty=3, col="red", label = TRUE))
### Incorrect (no strata)
adonis2(Y ~ NO3, data = dat, permutations = 199)
## Correct with strata
with(dat, adonis2(Y ~ NO3, data = dat, permutations = 199, strata = field))
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