adipart {vegan}R Documentation

Additive Diversity Partitioning and Hierarchical Null Model Testing


In additive diversity partitioning, mean values of alpha diversity at lower levels of a sampling hierarchy are compared to the total diversity in the entire data set (gamma diversity). In hierarchical null model testing, a statistic returned by a function is evaluated according to a nested hierarchical sampling design (hiersimu).


adipart(formula, data, index=c("richness", "shannon", "simpson"),
    weights=c("unif", "prop"), relative = FALSE, nsimul=99, ...)
hiersimu(formula, data, FUN, location = c("mean", "median"),
    relative = FALSE, drop.highest = FALSE, nsimul=99, ...)
## S3 method for class 'adipart':
print(x, ...)
## S3 method for class 'hiersimu':
print(x, ...)


formula A two sided model formula in the form y ~ x, where y is the community data matrix with samples as rows and species as column. Right hand side (x) must contain factors referring to levels of sampling hierarchy, terms from right to left will be treated as nested (first column is the lowest, last is the highest level). These variables must be factors in order to unambiguous handling. Interaction terms are not allowed.
data A data frame where to look for variables defined in the right hand side of formula. If missing, variables are looked in the global environment.
index Character, the diversity index to be calculated (see Details).
weights Character, "unif" for uniform weights, "prop" for weighting proportional to sample abundances to use in weighted averaging of individual alpha values within strata of a given level of the sampling hierarchy.
relative Logical, if TRUE then alpha and beta diversity values are given relative to the value of gamma for function adipart.
nsimul Number of permutation to use if matr is not of class 'permat'. If nsimul = 0, only the FUN argument is evaluated. It is thus possible to reuse the statistic values without using a null model.
FUN A function to be used by hiersimu. This must be fully specified, because currently other arguments cannot be passed to this function via ....
location Character, identifies which function (mean or median) is to be used to calculate location of the samples.
drop.highest Logical, to drop the highest level or not. When FUN evaluates only arrays with at least 2 dimensions, highest level should be dropped, or not selected at all.
x An object to print.
... Other arguments passed to functions, e.g. base of logarithm for Shannon diversity, or method, thin or burnin arguments for oecosimu.


Additive diversity partitioning means that mean alpha and beta diversity adds up to gamma diversity, thus beta diversity is measured in the same dimensions as alpha and gamma (Lande 1996). This additive procedure is than extended across multiple scales in a hierarchical sampling design with i = 1, 2, 3, ..., m levels of sampling (Crist et al. 2003). Samples in lower hierarchical levels are nested within higher level units, thus from i=1 to i=m grain size is increasing under constant survey extent. At each level i, α_i denotes average diversity found within samples.

At the highest sampling level, the diversity components are calculated as

beta_m = gamma - alpha_m

For each lower sampling level as

beta_i = alpha_i+1 - alpha_i

Then, the additive partition of diversity is

gamma = alpha_1 + sum(beta_i)

Average alpha components can be weighted uniformly (weight="unif") to calculate it as simple average, or proportionally to sample abundances (weight="prop") to calculate it as weighted average as follows

alpha_i = sum(D_ij*w_ij)

where D_{ij} is the diversity index and w_{ij} is the weight calculated for the jth sample at the ith sampling level.

The implementation of additive diversity partitioning in adipart follows Crist et al. 2003. It is based on species richness (S, not S-1), Shannon's and Simpson's diversity indices stated as the index argument.

The expected diversity components are calculated nsimul times by individual based randomisation of the community data matrix. This is done by the "r2dtable" method in oecosimu by default.

hiersimu works almost the same as adipart, but without comparing the actual statistic values returned by FUN to the highest possible value (cf. gamma diversity). This is so, because in most of the cases, it is difficult to ensure additive properties of the mean statistic values along the hierarchy.


An object of class 'adipart' or 'hiersimu' with same structure as 'oecosimu' objects.


P'eter S'olymos,


Crist, T.O., Veech, J.A., Gering, J.C. and Summerville, K.S. (2003). Partitioning species diversity across landscapes and regions: a hierarchical analysis of α, β, and gamma-diversity. Am. Nat., 162, 734–743.

Lande, R. (1996). Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos, 76, 5–13.

See Also

See oecosimu for permutation settings and calculating p-values.


## Function to get equal area partitions of the mite data
cutter <- function (x, cut = seq(0, 10, by = 2.5)) {
    out <- rep(1, length(x))
    for (i in 2:(length(cut) - 1))
        out[which(x > cut[i] & x <= cut[(i + 1)])] <- i
## The hierarchy of sample aggregation
levsm <- data.frame(
    l2=cutter(mite.xy$y, cut = seq(0, 10, by = 2.5)),
    l3=cutter(mite.xy$y, cut = seq(0, 10, by = 5)),
    l4=cutter(mite.xy$y, cut = seq(0, 10, by = 10)))
## Let's see in a map
plot(mite.xy, main="l1", col=as.numeric(levsm$l1)+1)
plot(mite.xy, main="l2", col=as.numeric(levsm$l2)+1)
plot(mite.xy, main="l3", col=as.numeric(levsm$l3)+1)
## Additive diversity partitioning
adipart(mite ~., levsm, index="richness", nsimul=20)
## Hierarchical null model testing
## diversity analysis (similar to adipart)
hiersimu(mite ~., levsm, diversity, relative=TRUE, nsimul=25)
## Hierarchical testing with the Morisita index
morfun <- function(x) dispindmorisita(x)$imst
hiersimu(mite ~., levsm, morfun, drop.highest=TRUE, nsimul=25)

[Package vegan version 1.16-32 Index]