Permutational Multivariate Analysis of Variance Using Distance Matrices
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 pseudo-F ratios.
adonis2(formula, data, permutations = 999, method = "bray",
sqrt.dist = FALSE, add = FALSE, by = "terms",
parallel = getOption("mc.cores"), strata, ...)
adonis(formula, data, permutations = 999, method = "bray",
strata = NULL, contr.unordered = "contr.sum",
contr.ordered = "contr.poly", parallel = getOption("mc.cores"), ...)formula |
Model formula. The LHS must be either a community
data matrix or a dissimilarity matrix, e.g., from
|
data |
the data frame for the independent variables. |
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. Implemented in |
add |
Add a constant to the non-diagonal dissimilarities such
that all eigenvalues are non-negative in the underlying Principal
Co-ordinates Analysis (see |
by |
|
strata |
groups (strata) within which to constrain permutations.
NB. argument |
contr.unordered, contr.ordered |
contrasts used for the design
matrix (default in R is dummy or treatment contrasts for unordered
factors). Ignored in |
parallel |
Number of parallel processes or a predefined socket
cluster. With |
... |
Other arguments passed to |
adonis2 and adonis are functions for the analysis and
partitioning sums of squares using dissimilarities. Function
adonis is directly based on the algorithm of Anderson (2001) and
performs a sequential test of terms. Function adonis2 is based on
the principles of McArdle & Anderson (2001) and can perform sequential,
marginal and overall tests. Function adonis2 also allows using
additive constants or squareroot of dissimilarities to avoid negative
eigenvalues. but both functions can handle semimetric indices (such as
Bray-Curtis) that produce negative eigenvalues. Function adonis2
can be much slower than adonis, in particular with several
terms. With the same random permutation, tests are identical in both
functions, and the results are also identical to anova.cca
of dbrda and capscale. With Euclidean
distances, the tests are also identical to anova.cca of
rda.
The functions partition 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. Functions are also analogous to distance-based
redundancy analysis in functions dbrda and
capscale (Legendre and Anderson 1999). Functions provide
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.
Function adonis2 returns an anova.cca result
object with a new column for partial R-squared: This is the
proportion of sum of squares from the total, and in marginal models
(by = "margin") the R-squared terms do not add up to
1.
Function adonis returns an object of class "adonis" with
following components:
aov.tab |
Typical AOV table showing sources of variation, degrees of freedom, sequential sums of squares, mean squares, F statistics, partial R-squared and P values, based on N permutations. |
coefficients |
matrix of coefficients of the linear model, with rows representing sources of variation and columns representing species; each column represents a fit of a species abundance to the linear model. These are what you get when you fit one species to your predictors. These are NOT available if you supply the distance matrix in the formula, rather than the site x species matrix |
coef.sites |
matrix of coefficients of the linear model, with rows representing sources of variation and columns representing sites; each column represents a fit of a sites distances (from all other sites) to the linear model. These are what you get when you fit distances of one site to your predictors. |
f.perms |
an N by m matrix of the null F
statistics for each source of variation based on N
permutations of the data. The permutations can be inspected with
|
model.matrix |
The |
terms |
The |
Anderson (2001, Fig. 4) warns that the method may confound
location and dispersion effects: significant differences may be caused
by different within-group variation (dispersion) instead of different
mean values of the groups (see Warton et al. 2012 for a general
analysis). However, it seems that adonis is less sensitive to
dispersion effects than some of its alternatives (anosim,
mrpp). Function betadisper is a sister
function to adonis to study the differences in dispersion
within the same geometric framework.
adonis and adonis2 are different implementations and
they do not share all arguments. If you use arguments of the
wrong function, they may be silently ignored.
Martin Henry H. Stevens (adonis) and Jari Oksanen
(adonis2).
Anderson, M.J. 2001. A new method for non-parametric 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. Distance-based 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 distance-based redundancy analysis. Ecology, 82: 290–297.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89–101.
data(dune)
data(dune.env)
## default test by terms
adonis2(dune ~ Management*A1, data = dune.env)
## overall tests
adonis2(dune ~ Management*A1, data = dune.env, by = NULL)
### 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, field, kind = "ehull", label = TRUE))
### Spider shows fields
with(dat, ordispider(mod, field, lty=3, col="red"))
### Incorrect (no strata)
perm <- how(nperm = 199)
adonis2 (Y ~ NO3, data = dat, permutations = perm)
## Correct with strata
setBlocks(perm) <- with(dat, field)
adonis2(Y ~ NO3, data = dat, permutations = perm)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.