adipart: Additive Diversity Partitioning and Hierarchical Null Model...
In vegan: Community Ecology Package
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
adipart(...)
## Default S3 method:
adipart(y, x, index=c("richness", "shannon", "simpson"),
weights=c("unif", "prop"), relative = FALSE, nsimul=99, ...)
## S3 method for class 'formula'
adipart(formula, data, index=c("richness", "shannon", "simpson"),
weights=c("unif", "prop"), relative = FALSE, nsimul=99, ...)
hiersimu(...)
## Default S3 method:
hiersimu(y, x, FUN, location = c("mean", "median"),
relative = FALSE, drop.highest = FALSE, nsimul=99, ...)
## S3 method for class 'formula'
hiersimu(formula, data, FUN, location = c("mean", "median"),
relative = FALSE, drop.highest = FALSE, nsimul=99, ...)
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 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.
...
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
## 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)
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
adipart object
Call: adipart(y = mite, index = "richness", nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index richness, weights unif
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 15.114 -43.353 22.316 22.044 22.300 22.603 0.05 *
gamma 35.000 0.000 35.000 35.000 35.000 35.000 1.00
beta.1 19.886 43.353 12.684 12.397 12.700 12.956 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
adipart object
Call: adipart(formula = mite ~ ., data = levsm, index = "richness",
nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index richness, weights unif
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 15.114 -41.7895 22.33383 21.98786 22.35714 22.5629 0.05 *
alpha.2 29.750 -22.9498 34.82895 34.36250 35.00000 35.0000 0.05 *
alpha.3 33.000 0.0000 35.00000 35.00000 35.00000 35.0000 0.05 *
gamma 35.000 0.0000 35.00000 35.00000 35.00000 35.0000 1.00
beta.1 14.636 7.4536 12.49511 11.90250 12.51429 12.9186 0.05 *
beta.2 3.250 13.9126 0.17105 0.00000 0.00000 0.6375 0.05 *
beta.3 2.000 0.0000 0.00000 0.00000 0.00000 0.0000 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(y = mite, FUN = diversity, relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
level_1 0.76064 -60.388 0.93935 0.93477 0.93962 0.945 0.05 *
leve_2 1.00000 0.000 1.00000 1.00000 1.00000 1.000 1.00
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(formula = mite ~ ., data = levsm, FUN = diversity,
relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
l1 0.76064 -72.186 0.93833 0.93520 0.93754 0.9423 0.05 *
l2 0.89736 -133.460 0.99807 0.99691 0.99801 0.9995 0.05 *
l3 0.92791 -492.633 0.99936 0.99909 0.99938 0.9996 0.05 *
l4 1.00000 0.000 1.00000 1.00000 1.00000 1.0000 1.00
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(formula = mite ~ ., data = levsm, FUN = morfun,
drop.highest = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
l1 0.52070 5.8049 0.35934 0.31216 0.36452 0.4048 0.05 *
l2 0.60234 13.9170 0.15898 0.10812 0.15947 0.2111 0.05 *
l3 0.67509 21.8738 -0.18455 -0.27930 -0.17545 -0.1364 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.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Author(s) References See Also Examples
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | adipart(...)
## Default S3 method:
adipart(y, x, index=c("richness", "shannon", "simpson"),
weights=c("unif", "prop"), relative = FALSE, nsimul=99, ...)
## S3 method for class 'formula'
adipart(formula, data, index=c("richness", "shannon", "simpson"),
weights=c("unif", "prop"), relative = FALSE, nsimul=99, ...)
hiersimu(...)
## Default S3 method:
hiersimu(y, x, FUN, location = c("mean", "median"),
relative = FALSE, drop.highest = FALSE, nsimul=99, ...)
## S3 method for class 'formula'
hiersimu(formula, data, FUN, location = c("mean", "median"),
relative = FALSE, drop.highest = FALSE, nsimul=99, ...)
|
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 diversity index to be calculated (see Details). |
weights |
Character, |
relative |
Logical, if |
nsimul |
Number of permutations to use if |
FUN |
A function to be used by |
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
|
... |
Other arguments passed to functions, e.g. base of
logarithm for Shannon diversity, or |
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ## 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)
|
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
adipart object
Call: adipart(y = mite, index = "richness", nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index richness, weights unif
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 15.114 -43.353 22.316 22.044 22.300 22.603 0.05 *
gamma 35.000 0.000 35.000 35.000 35.000 35.000 1.00
beta.1 19.886 43.353 12.684 12.397 12.700 12.956 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
adipart object
Call: adipart(formula = mite ~ ., data = levsm, index = "richness",
nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
options: index richness, weights unif
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
alpha.1 15.114 -41.7895 22.33383 21.98786 22.35714 22.5629 0.05 *
alpha.2 29.750 -22.9498 34.82895 34.36250 35.00000 35.0000 0.05 *
alpha.3 33.000 0.0000 35.00000 35.00000 35.00000 35.0000 0.05 *
gamma 35.000 0.0000 35.00000 35.00000 35.00000 35.0000 1.00
beta.1 14.636 7.4536 12.49511 11.90250 12.51429 12.9186 0.05 *
beta.2 3.250 13.9126 0.17105 0.00000 0.00000 0.6375 0.05 *
beta.3 2.000 0.0000 0.00000 0.00000 0.00000 0.0000 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(y = mite, FUN = diversity, relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
level_1 0.76064 -60.388 0.93935 0.93477 0.93962 0.945 0.05 *
leve_2 1.00000 0.000 1.00000 1.00000 1.00000 1.000 1.00
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(formula = mite ~ ., data = levsm, FUN = diversity,
relative = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
l1 0.76064 -72.186 0.93833 0.93520 0.93754 0.9423 0.05 *
l2 0.89736 -133.460 0.99807 0.99691 0.99801 0.9995 0.05 *
l3 0.92791 -492.633 0.99936 0.99909 0.99938 0.9996 0.05 *
l4 1.00000 0.000 1.00000 1.00000 1.00000 1.0000 1.00
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hiersimu object
Call: hiersimu(formula = mite ~ ., data = levsm, FUN = morfun,
drop.highest = TRUE, nsimul = 19)
nullmodel method 'r2dtable' with 19 simulations
alternative hypothesis: statistic is less or greater than simulated values
statistic SES mean 2.5% 50% 97.5% Pr(sim.)
l1 0.52070 5.8049 0.35934 0.31216 0.36452 0.4048 0.05 *
l2 0.60234 13.9170 0.15898 0.10812 0.15947 0.2111 0.05 *
l3 0.67509 21.8738 -0.18455 -0.27930 -0.17545 -0.1364 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.