R: Additive Diversity Partitioning and Hierarchical Null Model...

adipart {vegan} | R Documentation

## Additive Diversity Partitioning and Hierarchical Null Model Testing

### Description

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`).

### Usage

    adipart(...)
    ## Default S3 method:
    adipart(y, x, index=c("richness", "shannon", "simpson"),
        weights=c("unif", "prop"), relative = FALSE, nsimul=99,
        method = "r2dtable", ...)
    ## S3 method for class 'formula'
    adipart(formula, data, index=c("richness", "shannon", "simpson"),
        weights=c("unif", "prop"), relative = FALSE, nsimul=99,
        method = "r2dtable", ...)

    hiersimu(...)
    ## Default S3 method:
    hiersimu(y, x, FUN, location = c("mean", "median"),
        relative = FALSE, drop.highest = FALSE, nsimul=99,
        method = "r2dtable", ...)
    ## S3 method for class 'formula'
    hiersimu(formula, data, FUN, location = c("mean", "median"),
        relative = FALSE, drop.highest = FALSE, nsimul=99,
        method = "r2dtable", ...)

### Arguments

`y` | A community matrix.
`x` | A matrix with same number of rows as in `y`, columns coding the levels of sampling hierarchy. The number of groups within the hierarchy must decrease from left to right. If `x` is missing, function performs an overall decomposition into alpha, beta and gamma diversities.
`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 be grouping variables 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, at least two levels specified). 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 permutations to use. If `nsimul = 0`, only the `FUN` argument is evaluated. It is thus possible to reuse the statistic values without a null model.
`method` | Null model method: either a name (character string) of a method defined in `make.commsim` or a `commsim` function. The default `"r2dtable"` keeps row sums and column sums fixed. See `oecosimu` for Details and Examples.
`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.
`...` | Other arguments passed to functions, e.g. base of logarithm for Shannon diversity, or `method`, `thin` or `burnin` arguments for `oecosimu`.

### Details

Additive diversity partitioning means that mean alpha and beta diversities add up to gamma diversity, thus beta diversity is measured in the same dimensions as alpha and gamma (Lande 1996). This additive procedure is then 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 in the same way 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.

### Value

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

### Author(s)

Péter Sólymos, solymos@ualberta.ca

### References

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 γ-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. `multipart` for multiplicative diversity partitioning.

### Examples

    ## NOTE: 'nsimul' argument usually needs to be >= 99
    ## here much lower value is used for demonstration

    data(mite)
    data(mite.xy)
    data(mite.env)
    ## 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
        return(out)}
    ## The hierarchy of sample aggregation
    levsm <- with(mite.xy, data.frame(
        l1=1:nrow(mite),
        l2=cutter(y, cut = seq(0, 10, by = 2.5)),
        l3=cutter(y, cut = seq(0, 10, by = 5)),
        l4=cutter(y, cut = seq(0, 10, by = 10))))
    ## Let's see in a map
    par(mfrow=c(1,3))
    plot(mite.xy, main="l1", col=as.numeric(levsm$l1)+1, asp = 1)
    plot(mite.xy, main="l2", col=as.numeric(levsm$l2)+1, asp = 1)
    plot(mite.xy, main="l3", col=as.numeric(levsm$l3)+1, asp = 1)
    par(mfrow=c(1,1))
    ## Additive diversity partitioning
    adipart(mite, index="richness", nsimul=19)
    adipart(mite ~ ., levsm, index="richness", nsimul=19)
    ## Hierarchical null model testing
    ## diversity analysis (similar to adipart)
    hiersimu(mite, FUN=diversity, relative=TRUE, nsimul=19)
    hiersimu(mite ~., levsm, FUN=diversity, relative=TRUE, nsimul=19)
    ## Hierarchical testing with the Morisita index
    morfun <- function(x) dispindmorisita(x)$imst
    hiersimu(mite ~., levsm, morfun, drop.highest=TRUE, nsimul=19)

[Package vegan version 2.4-3 Index]