R: Multiplicative Diversity Partitioning

multipart {vegan} | R Documentation

## Multiplicative Diversity Partitioning

### Description

In multiplicative 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 or the pooled samples (gamma diversity).

### Usage

    multipart(...)
    ## Default S3 method:
    multipart(y, x, index=c("renyi", "tsallis"), scales = 1,
        global = FALSE, relative = FALSE, nsimul=99, method = "r2dtable", ...)
    ## S3 method for class 'formula'
    multipart(formula, data, index=c("renyi", "tsallis"), scales = 1,
        global = FALSE, relative = 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, two levels are assumed: each row is a group in the first level, and all rows are in the same group in the second level.
`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 entropy index to be calculated (see Details).
`relative` | Logical, if `TRUE` then beta diversity is standardized by its maximum (see Details).
`scales` | Numeric, of length 1, the order of the generalized diversity index to be used.
`global` | Logical, indicates the calculation of beta diversity values, see Details.
`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.
`...` | Other arguments passed to `oecosimu`, i.e. `method`, `thin` or `burnin`.

### Details

Multiplicative diversity partitioning is based on Whittaker's (1972) ideas, that has recently been generalised to one parametric diversity families (i.e. Rényi and Tsallis) by Jost (2006, 2007). Jost recommends to use the numbers equivalents (Hill numbers), instead of pure diversities, and proofs, that this satisfies the multiplicative partitioning requirements.

The current implementation of `multipart` calculates Hill numbers based on the functions `renyi` and `tsallis` (provided as `index` argument). If values for more than one `scales` are desired, it should be done in separate runs, because it adds extra dimensionality to the implementation, which has not been resolved efficiently.

Alpha diversities are then the averages of these Hill numbers for each hierarchy levels, the global gamma diversity is the alpha value calculated for the highest hierarchy level. When `global = TRUE`, beta is calculated relative to the global gamma value:

beta_i = gamma / alpha_i

when `global = FALSE`, beta is calculated relative to local gamma values (local gamma means the diversity calculated for a particular cluster based on the pooled abundance vector):

beta_ij = alpha_(i+1)j / mean(alpha_i)

where j is a particular cluster at hierarchy level i. Then beta diversity value for level i is the mean of the beta values of the clusters at that level, β_{i} = mean(β_{ij}).

If `relative = TRUE`, the respective beta diversity values are standardized by their maximum possible values (mean(β_{ij}) / β_{max,ij}) given as β_{max,ij} = n_{j} (the number of lower level units in a given cluster j).

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

### Value

An object of class 'multipart' with same structure as 'oecosimu' objects.

### Author(s)

Péter Sólymos, solymos@ualberta.ca

### References

Jost, L. (2006). Entropy and diversity. Oikos, 113, 363–375.

Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427–2439.

Whittaker, R. (1972). Evolution and measurement of species diversity. Taxon, 21, 213–251.

### See Also

See `adipart` for additive diversity partitioning, `hiersimu` for hierarchical null model testing and `oecosimu` for permutation settings and calculating p-values.

### 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))))
    ## Multiplicative diversity partitioning
    multipart(mite, levsm, index="renyi", scales=1, nsimul=19)
    multipart(mite ~ ., levsm, index="renyi", scales=1, nsimul=19)
    multipart(mite ~ ., levsm, index="renyi", scales=1, nsimul=19, relative=TRUE)
    multipart(mite ~ ., levsm, index="renyi", scales=1, nsimul=19, global=TRUE)

[Package vegan version 2.4-3 Index]