Description Usage Arguments Details Value Author(s) References See Also Examples
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).
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y |
A community matrix. |
x |
A matrix with same number of rows as in |
formula |
A two sided model formula in the form |
data |
A data frame where to look for variables defined in the right hand side
of |
index |
Character, the entropy index to be calculated (see Details). |
relative |
Logical, if |
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 permutation to use if |
... |
Other arguments passed to |
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
randomisation of the community data matrix. This is done by the "r2dtable"
method
in oecosimu
by default.
An object of class 'multipart' with same structure as 'oecosimu' objects.
Péter Sólymos, solymos@ualberta.ca
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 adipart
for additive diversity partitioning,
hiersimu
for hierarchical null model testing
and oecosimu
for permutation settings and calculating p-values.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ## 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 <- data.frame(
l1=1:nrow(mite),
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)))
## 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)
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