multipart: Multiplicative Diversity Partitioning
In vegan: Community Ecology Package
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
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
1
2
3
4
5
6
7
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 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.
...
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
randomisation 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
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 <- 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)
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
multipart object
Call: multipart(y = mite, x = levsm, index = "renyi", scales = 1,
nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -57.642 12.19732 12.08629 12.21029 12.3135 0.05 *
alpha.2 11.2353 -80.659 14.09259 14.02745 14.09644 14.1556 0.05 *
alpha.3 12.0064 -304.976 14.13633 14.12600 14.13761 14.1489 0.05 *
gamma 14.1603 0.000 14.16027 14.16027 14.16027 14.1603 1.00
beta.1 1.3568 25.650 1.15877 1.14627 1.15961 1.1703 0.05 *
beta.2 1.0710 27.762 1.00311 0.99855 1.00270 1.0077 0.05 *
beta.3 1.1794 359.115 1.00169 1.00080 1.00160 1.0024 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -69.574 12.1712 12.0881 12.1628 12.2884 0.05 *
alpha.2 11.2353 -90.855 14.0714 14.0289 14.0710 14.1307 0.05 *
alpha.3 12.0064 -483.106 14.1347 14.1271 14.1340 14.1416 0.05 *
gamma 14.1603 0.000 14.1603 14.1603 14.1603 14.1603 1.00
beta.1 1.3568 27.375 1.1604 1.1445 1.1620 1.1689 0.05 *
beta.2 1.0710 32.363 1.0045 1.0004 1.0044 1.0071 0.05 *
beta.3 1.1794 568.722 1.0018 1.0013 1.0019 1.0023 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.055481 -66.238 12.178840 12.111465 12.179886 12.2923 0.05 *
alpha.2 11.235261 -107.566 14.081574 14.038939 14.082429 14.1210 0.05 *
alpha.3 12.006443 -293.102 14.135137 14.123732 14.136415 14.1463 0.05 *
gamma 14.160271 0.000 14.160271 14.160271 14.160271 14.1603 1.00
beta.1 0.078594 23.389 0.068437 0.067709 0.068512 0.0691 0.05 *
beta.2 0.535514 35.425 0.501908 0.500405 0.502146 0.5034 0.05 *
beta.3 0.589695 345.059 0.500889 0.500494 0.500844 0.5013 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, global = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global TRUE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -57.118 12.2037 12.0819 12.2163 12.3333 0.05 *
alpha.2 11.2353 -106.017 14.0854 14.0419 14.0797 14.1237 0.05 *
alpha.3 12.0064 -403.394 14.1344 14.1257 14.1348 14.1419 0.05 *
gamma 14.1603 0.000 14.1603 14.1603 14.1603 14.1603 1.00
beta.1 1.7578 86.542 1.1604 1.1481 1.1591 1.1720 0.05 *
beta.2 1.2603 132.886 1.0053 1.0026 1.0057 1.0084 0.05 *
beta.3 1.1794 474.860 1.0018 1.0013 1.0018 1.0024 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
vegan documentation built on May 2, 2019, 5:51 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
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
1 2 3 4 5 6 7 |
Arguments
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 |
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
randomisation 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
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 <- 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)
|
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
multipart object
Call: multipart(y = mite, x = levsm, index = "renyi", scales = 1,
nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -57.642 12.19732 12.08629 12.21029 12.3135 0.05 *
alpha.2 11.2353 -80.659 14.09259 14.02745 14.09644 14.1556 0.05 *
alpha.3 12.0064 -304.976 14.13633 14.12600 14.13761 14.1489 0.05 *
gamma 14.1603 0.000 14.16027 14.16027 14.16027 14.1603 1.00
beta.1 1.3568 25.650 1.15877 1.14627 1.15961 1.1703 0.05 *
beta.2 1.0710 27.762 1.00311 0.99855 1.00270 1.0077 0.05 *
beta.3 1.1794 359.115 1.00169 1.00080 1.00160 1.0024 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -69.574 12.1712 12.0881 12.1628 12.2884 0.05 *
alpha.2 11.2353 -90.855 14.0714 14.0289 14.0710 14.1307 0.05 *
alpha.3 12.0064 -483.106 14.1347 14.1271 14.1340 14.1416 0.05 *
gamma 14.1603 0.000 14.1603 14.1603 14.1603 14.1603 1.00
beta.1 1.3568 27.375 1.1604 1.1445 1.1620 1.1689 0.05 *
beta.2 1.0710 32.363 1.0045 1.0004 1.0044 1.0071 0.05 *
beta.3 1.1794 568.722 1.0018 1.0013 1.0019 1.0023 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global FALSE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.055481 -66.238 12.178840 12.111465 12.179886 12.2923 0.05 *
alpha.2 11.235261 -107.566 14.081574 14.038939 14.082429 14.1210 0.05 *
alpha.3 12.006443 -293.102 14.135137 14.123732 14.136415 14.1463 0.05 *
gamma 14.160271 0.000 14.160271 14.160271 14.160271 14.1603 1.00
beta.1 0.078594 23.389 0.068437 0.067709 0.068512 0.0691 0.05 *
beta.2 0.535514 35.425 0.501908 0.500405 0.502146 0.5034 0.05 *
beta.3 0.589695 345.059 0.500889 0.500494 0.500844 0.5013 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
multipart object
Call: multipart(formula = mite ~ ., data = levsm, index = "renyi",
scales = 1, global = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index renyi, scales 1, global TRUE
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 8.0555 -57.118 12.2037 12.0819 12.2163 12.3333 0.05 *
alpha.2 11.2353 -106.017 14.0854 14.0419 14.0797 14.1237 0.05 *
alpha.3 12.0064 -403.394 14.1344 14.1257 14.1348 14.1419 0.05 *
gamma 14.1603 0.000 14.1603 14.1603 14.1603 14.1603 1.00
beta.1 1.7578 86.542 1.1604 1.1481 1.1591 1.1720 0.05 *
beta.2 1.2603 132.886 1.0053 1.0026 1.0057 1.0084 0.05 *
beta.3 1.1794 474.860 1.0018 1.0013 1.0018 1.0024 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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