The package iNEXT.beta3D (iNterpolation and
EXTrapolation with beta diversity for three dimensions of biodiversity)
is a sequel to iNEXT. The three dimensions (3D) of
biodiversity include taxonomic diversity
(TD), phylogenetic diversity (PD) and
functional diversity (FD). This document
provides an introduction demonstrating how to run
iNEXT.beta3D. An online version iNEXT.beta3D Online
is also available for users without an R background.
A unified framework based on Hill numbers (for TD) and their
generalizations, Hill-Chao numbers (for PD and FD), is adopted in the
package. TD quantifies the effective number of species, mean-PD (PD
divided by tree depth) quantifies the effective number of lineages, and
FD quantifies the effective number of virtual functional groups (or
functional “species”). Thus, TD, mean-PD, and FD are all expressed in
comparable units of species/lineage equivalents, allowing meaningful
comparisons across the three dimensions of biodiversity; see Chao et
al. (2021) for a review of the unified framework.
For each of the three dimensions, iNEXT.beta3D focuses
on the multiplicative diversity decomposition (beta = gamma/alpha) for
orders q = 0, 1 and 2 based on sampling data. Beta diversity quantifies
the extent of among-assemblage differentiation, or the changes in
species/lineages/functional-groups composition and abundance among
assemblages. iNEXT.beta3D features standardized 3D
estimates with a common sample size (for alpha and gamma diversity) or
sample coverage (for alpha, beta and gamma diversity).
iNEXT.beta3D also features coverage-based standardized
estimates of four classes of dissimilarity measures.
Based on the rarefaction and extrapolation (R/E) method for Hill
numbers (TD) of orders q = 0, 1 and 2, Chao et al. (2023b) developed the
pertinent R/E theory for taxonomic beta diversity with applications to
real-world spatial, temporal and spatio-temporal data. An application to
Gentry’s global forest data along with a concise description of the
theory is provided in Chao et al. (2023a). The extension to phylogenetic
and functional beta diversity is generally parallel.
The iNEXT.beta3D package features two types of R/E
sampling curves:
Sample-size-based (or size-based) R/E sampling curves: This type
of sampling curve plots standardized 3D gamma and
alpha diversity with respect to sample size. Note that
sample-size-based beta diversity is not generally a statistically valid
measure (Chao et al. 2023b); therefore, the corresponding beta diversity
sampling curve is not provided.
Sample-coverage-based (or coverage-based) R/E sampling curves:
This type of sampling curve plots standardized 3D
gamma, alpha, and beta diversity as well as
four classes of dissimilarity measures with respect to sample coverage
(an objective measure of sample completeness).
Sufficient data are needed to run iNEXT.beta3D. If your
data comprise only a few species and their
abundances/phylogenies/traits, it is probable that the data lack
sufficient information to run iNEXT.beta3D.
HOW TO CITE iNEXT.beta3D
If you publish your work based on results from
iNEXT.beta3D, you should make reference to at least one of
the following methodology papers (2023a, b) and also cite the
iNEXT.beta3D package:
Chao, A., Chiu, C.-H., Hu, K.-H., and Zeleny, D. (2023a).
Revisiting Alwyn H. Gentry’s forest transect data: a statistical
sampling-model-based approach. Japanese Journal of Statistics and
Data Science, 6, 861-884. (https://doi.org/10.1007/s42081-023-00214-1)
Chao, A., Thorn, S., Chiu, C.-H., Moyes, F., Hu, K.-H., Chazdon,
R. L., Wu, J., Magnago, L. F. S., Dornelas, M., Zeleny, D., Colwell, R.
K., and Magurran, A. E. (2023b). Rarefaction and extrapolation with beta
diversity under a framework of Hill numbers: the iNEXT.beta3D
standardization. Ecological Monographs e1588.(https://doi.org/10.1002/ecm.1588)
Chao, A., Lee, Y.-T., Lin, K.-L., and Chuang, P.-Y. (2026). The
iNEXT.beta3D package: interpolation and extrapolation with beta
diversity for three dimensions of biodiversity. R package version
1.1.0.
SOFTWARE NEEDED TO RUN iNEXT.beta3D IN R
HOW TO RUN iNEXT.beta3D:
The iNEXT.beta3D package is available from CRAN and can
be downloaded from Anne Chao’s GitHub iNEXT.beta3D_github
using the following commands. For a first-time installation, additional
visualization extension package (ggplot2 from CRAN) and
relevant package (iNEXT.3D from CRAN) must be installed and
loaded.
## install iNEXT.beta3D package from CRAN
install.packages("iNEXT.beta3D")
## install the latest version from GitHub
install.packages('devtools')
library(devtools)
install_github('AnneChao/iNEXT.beta3D')
## import packages
library(iNEXT.beta3D)
There are three main functions in this package:
iNEXTbeta3D: computes standardized 3D estimates
with a common sample size (for alpha and gamma diversity) or sample
coverage (for alpha, beta and gamma diversity) for default sample sizes
or coverage values. This function also computes coverage-based
standardized 3D estimates of four classes of dissimilarity measures for
default coverage values. In addition, this function also computes
standardized 3D estimates with a particular vector of user-specified
sample sizes or coverage values.
ggiNEXTbeta3D: Visualizes the output from the
function iNEXTbeta3D.
DataInfobeta3D: Provides basic data information
for (1) the reference sample in each assemblage, (2) the gamma reference
sample in the pooled assemblage, and (3) the alpha reference sample in
the joint assemblage.
MAIN FUNCTION: iNEXTbeta3D()
We first describe the main function iNEXTbeta3D() with
default arguments:
iNEXTbeta3D(data, diversity = "TD", q = c(0, 1, 2), datatype = "abundance",
base = "coverage", level = NULL, nboot = 10, conf = 0.95,
PDtree = NULL, PDreftime = NULL, PDtype = 'AUC', PDcut_number = 30,
FDdistM = NULL, FDtype = "AUC", FDtau = NULL, FDcut_number = 30,
by_pair = FALSE)
The arguments of this function are briefly described below, and will
be explained in more detail through illustrative examples in later text.
By default (with the standardization base = “coverage”),
this function computes coverage-based standardized 3D gamma, alpha, beta
diversity, and four dissimilarity indices for coverage up to one (for q
= 1, 2) or up to the coverage of double the reference sample size (for q
= 0). If users set the standardization base to base=“size”,
this function computes size-based standardized 3D gamma and alpha
diversity estimates up to double the reference sample size in each
dataset. In addition, this function also computes standardized 3D
estimates with a particular vector of user-specified sample sizes or
coverage values.
data
|
- For
datatype = “abundance”, species abundance data for
a single dataset can be input as a matrix/data.frame
(species-by-assemblage); data for multiple datasets can be input as a
list of matrices/data.frames, with each matrix
representing a species-by-assemblage abundance matrix for one of the
datasets.
- For
datatype = “incidence_raw”, data for a single
dataset with N assemblages can be input as a list of
matrices/data.frames, with each matrix representing a
species-by-sampling-unit incidence matrix for one of the assemblages;
data for multiple datasets can be input as multiple lists.
|
diversity
|
selection of diversity type: diversity = “TD” =
Taxonomic diversity, diversity =
“PD” = Phylogenetic diversity, and
diversity = “FD” = Functional
diversity.
|
q
|
a numerical vector specifying the diversity orders. Default is
c(0, 1, 2).
|
datatype
|
data type of input data: individual-based abundance data (datatype
= “abundance”) or species-by-sampling-unit incidence matrix
(datatype = “incidence_raw”) with all entries being 0
(non-detection) or 1 (detection).
|
base
|
standardization base: coverage-based rarefaction and extrapolation for
gamma, alpha, beta diversity, and four classes of dissimilarity indices
(base = “coverage”), or size-based rarefaction and
extrapolation for gamma and alpha diversity (base =
“size”). Default is base = “coverage”.
|
level
|
A numerical vector specifying the particular values of sample
coverage (between 0 and 1 when base = “coverage”) or sample
sizes (base = “size”) that will be used to compute
standardized diversity/dissimilarity. Asymptotic diversity estimator can
be obtained by setting level = 1 (i.e., complete coverage
for base = “coverage”).
By default (with base = “coverage”), this function
computes coverage-based standardized 3D gamma, alpha, beta diversity,
and four dissimilarity indices for coverage from 0.5 up to one (for
q = 1, 2) or up to the coverage of double the reference
sample size (for q = 0), in increments of 0.025. The
extrapolation limit for beta diversity is defined as that for alpha
diversity.
If users set base = “size”, this function computes
size-based standardized 3D gamma and alpha diversity estimates based on
40 equally-spaced sample sizes/knots from sample size 1 up to double the
reference sample size.
|
nboot
|
a positive integer specifying the number of bootstrap replications when
assessing sampling uncertainty and constructing confidence intervals.
Bootstrap replications are generally time consuming. Set
nboot = 0 to skip the bootstrap procedures. Default is
nboot = 10. If more accurate results are required, set
nboot = 100 (or nboot = 200).
|
conf
|
a positive number < 1 specifying the level of confidence interval.
Default is conf = 0.95.
|
PDtree
|
(required argument for diversity = “PD”), a phylogenetic
tree in Newick format spanned by all observed species across the input
datasets.
|
PDreftime
|
(argument only for diversity = “PD” and PDtype =
“PD” or PDtype = “meanPD”), a numerical value
specifying a fixed time reference point for phylogenetic diversity.
Default is PDreftime = NULL, in which case the age of the
root of the phylogenetic tree spanned by the pooled observed species is
used.
|
PDtype
|
(argument only for diversity = “PD”), select PD type:
PDtype = “PD” for effective total branch length,
PDtype = “meanPD” for effective number of equally divergent
lineages, or PDtype = “AUC” for an overall measure that
integrates mean phylogenetic diversity over all time reference points
from zero to the age of the root. Default is PDtype =
“AUC”.
|
PDcut_number
|
(argument only for diversity = “PD” and PDtype =
“AUC”), a positive integer greater than one specifying the number
of equally spaced time reference points between zero and the age of the
root used to numerically approximate the AUC. Default is
PDcut_number = 30. A larger value can be used to obtain a
more accurate AUC approximation.
|
FDdistM
|
(required argument for diversity = “FD”), a species
pairwise distance matrix for all species in the pooled assemblage.
|
FDtype
|
(argument only for diversity = “FD”), select FD type:
FDtype = “tau_value” for FD under a specified threshold
value, or FDtype = “AUC” (area under the curve of
tau-profile) for an overall FD which integrates all threshold values
between zero and one. Default is FDtype = “AUC”.
|
FDtau
|
(argument only for diversity = “FD” and
FDtype=“tau_value”),
a numerical value between 0 and 1 specifying the tau value (threshold
level) that will be used to compute FD. If FDtau = NULL
(default), then the threshold level is set to be the mean distance
between any two individuals randomly selected from the pooled dataset
(i.e., quadratic entropy).
|
FDcut_number
|
(argument only for diversity = “FD” and
FDtype=“AUC”), a positive integer specifying the number of
equally spaced sub-intervals used to partition the [0, 1] interval for
numerical approximation of the AUC by integrating the tau-profile.
Equivalently, the number of tau values that will be considered to
compute the integrated AUC value. Default is FDcut_number =
30. A larger value can be used to obtain a more accurate AUC
approximation.
|
by_pair
|
a logical variable specifying whether diversity decomposition is
performed for all assemblages as a whole or for every pair of
assemblages. If by_pair = FALSE, alpha/beta/gamma diversity
and dissimilarity are computed for all assemblages within each dataset
as a whole; if by_pair = TRUE, the corresponding output is
computed for every pair of assemblages. Default is FALSE.
|
This function returns an "iNEXTbeta3D" object which can
be further used to make plots using the function
ggiNEXTbeta3D() to be described below. Note that
ggiNEXTbeta3D() only accepts output from
iNEXTbeta3D() when by_pair = FALSE.
Output of the main function iNEXTbeta3D()
By default (with base = 'coverage'), the
iNEXTbeta3D() function for each of the three dimensions
(TD, PD, and FD) returns the "iNEXTbeta3D" object including
seven data frames for each dataset:
- gamma (standardized gamma diversity)
- alpha (standardized alpha diversity)
- beta (standardized beta diversity)
- 1-C (standardized Sorensen-type non-overlap index)
- 1-U (standardized Jaccard-type non-overlap index)
- 1-V (standardized Sorensen-type turnover index)
- 1-S (standardized Jaccard-type turnover index)
When users set base = 'size', the
iNEXTbeta3D() function for each of the three dimensions
(TD, PD, and FD) returns the "iNEXTbeta3D" object including
two data frames for each dataset:
- gamma (size-based standardized gamma diversity)
- alpha (size-based standardized alpha diversity)
Size-based beta diversity and dissimilarity indices are not
statistically valid measures and thus are not provided.
GRAPHIC DISPLAYS: FUNCTION
ggiNEXTbeta3D()
The function ggiNEXTbeta3D() with default arguments is
described as follows. This function only accepts output from
iNEXTbeta3D when by_pair = FALSE.
ggiNEXTbeta3D(output, type = "B")
output
|
output from the function iNEXTbeta3D.
|
type
|
(argument only for base = "coverage"),
type = ‘B’ for plotting the rarefaction and
extrapolation sampling curves for gamma, alpha, and beta diversity;
type = ‘D’ for plotting the rarefaction and
extrapolation sampling curves for four dissimilarity indices.
Skip the argument for plotting size-based rarefaction and extrapolation
sampling curves for gamma and alpha diversity.
|
The ggiNEXTbeta3D() function is a wrapper around the
ggplot2 package to create an R/E curve using a single line
of code. The resulting object is of class "ggplot", so it
can be manipulated using the ggplot2 tools. Users can
visualize the displays of coverage-based R/E sampling curves of gamma,
alpha and beta diversity as well as four classes of dissimilarity
indices by setting the parameter type.
DATA INFORMATION: FUNCTION
DataInfobeta3D()
The function DataInfobeta3D() provides basic data
information for (1) the reference sample in each individual assemblage,
(2) the gamma reference sample in the pooled assemblage, and (3) the
alpha reference sample in the joint assemblage. The function
DataInfobeta3D() with default arguments is shown below:
DataInfobeta3D(data, diversity = "TD", datatype = "abundance",
PDtree = NULL, PDreftime = NULL, PDtype = "meanPD",
FDdistM = NULL, FDtype = "AUC", FDtau = NULL, by_pair = FALSE)
Arguments shared by DataInfobeta3D() and
iNEXTbeta3D() have the same definitions as described above.
Running the DataInfobeta3D() function returns basic data
information including sample size, observed species richness, two sample
coverage estimates (SC(n) and SC(2n)) as well
as other relevant information in each of the three dimensions of
diversity. We use Brazil_rainforests data to demonstrate
the function for each dimension.
## Data information for taxonomic diversity
data(Brazil_rainforests)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'TD', datatype = 'abundance')
#> Dataset Assemblage n S.obs SC(n) SC(2n) f1 f2 f3 f4 f5
#> 1 Marim Edge 158 84 0.691 0.852 49 18 8 4 1
#> 2 Marim Interior 144 80 0.704 0.899 43 23 7 5 0
#> 3 Marim Pooled assemblage 302 119 0.855 0.969 44 34 17 9 7
#> 4 Marim Joint assemblage 302 164 0.696 0.876 92 41 15 9 1
#> 5 Rebio2 Edge 162 70 0.754 0.895 40 17 4 2 0
#> 6 Rebio2 Interior 168 74 0.763 0.877 40 13 8 4 4
#> 7 Rebio2 Pooled assemblage 330 118 0.819 0.901 60 18 15 5 3
#> 8 Rebio2 Joint assemblage 330 144 0.758 0.886 80 30 12 6 4
Output description:
Dataset = the input datasets.
Pair = combinations of assemblage pairs; this column
is included only when the analysis is performed for every pair of
assemblages.
Assemblage = Individual assemblages,
'Pooled assemblage' (for gamma) or
'Joint assemblage' (for alpha).
n = number of observed individuals in the reference
sample (sample size).
S.obs = number of observed species in the reference
sample.
SC(n) = sample coverage estimate of the reference
sample.
SC(2n) = sample coverage estimate of twice the
reference sample size.
f1-f5 = the first five species
abundance frequency counts in the reference sample.
## Data information for mean phylogenetic diversity
data(Brazil_rainforests)
data(Brazil_tree)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'PD', datatype = 'abundance',
PDtype = 'meanPD', PDtree = Brazil_tree, PDreftime = NULL)
#> Dataset Assemblage n S.obs SC(n) SC(2n) PD.obs f1* f2* g1 g2 Reftime
#> 1 Marim Edge 158 84 0.691 0.852 8805 49 26 3278 2188 400
#> 2 Marim Interior 144 80 0.704 0.899 8436 43 28 2974 1935 400
#> 3 Marim Pooled assemblage 302 119 0.855 0.969 11842 44 39 3172 2995 400
#> 4 Marim Joint assemblage 302 164 0.696 0.876 17241 92 54 6252 4123 400
#> 5 Rebio2 Edge 162 70 0.754 0.895 7874 40 23 3648 1717 400
#> 6 Rebio2 Interior 168 74 0.763 0.877 8360 40 17 3365 1954 400
#> 7 Rebio2 Pooled assemblage 330 118 0.819 0.901 11979 60 23 5063 1637 400
#> 8 Rebio2 Joint assemblage 330 144 0.758 0.886 16234 80 40 7013 3671 400
For both PDtype = "PD" and
PDtype = "meanPD", the output information is described as
follows:
Dataset, Pair, Assemblage,
n, S.obs, SC(n) and
SC(2n): definitions are the same as in the TD
output.
PD.obs = the observed total branch length in the
phylogenetic tree spanned by all observed species.
f1*,f2* = the number of singletons and
doubletons in the node/branch abundance set.
g1,g2 = the total branch length of
those singletons/doubletons in the node/branch abundance set.
Reftime = the fixed time reference point for
phylogenetic diversity. If PDreftime = NULL, the age of the
root of the phylogenetic tree spanned by the pooled observed species is
used.
## Data information for phylogenetic diversity when all time reference points are considered
data(Brazil_rainforests)
data(Brazil_tree)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'PD',
datatype = 'abundance', PDtype = 'AUC',
PDtree = Brazil_tree)
#> Dataset Assemblage n S.obs SC(n) SC(2n) Tree.depth.min Tree.depth.max
#> 1 Marim Edge 158 84 0.691 0.852 0 400
#> 2 Marim Interior 144 80 0.704 0.899 0 400
#> 3 Marim Pooled assemblage 302 119 0.855 0.969 0 400
#> 4 Marim Joint assemblage 302 164 0.696 0.876 0 400
#> 5 Rebio2 Edge 162 70 0.754 0.895 0 400
#> 6 Rebio2 Interior 168 74 0.763 0.877 0 400
#> 7 Rebio2 Pooled assemblage 330 118 0.819 0.901 0 400
#> 8 Rebio2 Joint assemblage 330 144 0.758 0.886 0 400
For PDtype = "AUC" the output information is described
as follows:
Dataset, Pair, Assemblage,
n, S.obs, SC(n) and
SC(2n): definitions are the same as in the TD
output.
Tree.depth.min = the minimum time reference point
used for calculating the integrated mean phylogenetic diversity; this
value is zero.
Tree.depth.max = the maximum time reference point
used for calculating the integrated mean phylogenetic diversity; this
value is the age of the root of the phylogenetic tree spanned by the
pooled observed species.
## Data information for functional diversity (under a specified threshold level, FDtype = 'tau_value')
data(Brazil_rainforests)
data(Brazil_distM)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'FD', datatype = 'abundance',
FDdistM = Brazil_distM, FDtype = 'tau_value', FDtau = NULL)
#> Dataset Assemblage n S.obs SC(n) SC(2n) a1* a2* h1 h2 Tau
#> 1 Marim Edge 158 84 0.691 0.852 0 0 0 0 0.343
#> 2 Marim Interior 144 80 0.704 0.899 0 0 0 0 0.343
#> 3 Marim Pooled assemblage 302 119 0.855 0.969 0 0 0 0 0.343
#> 4 Marim Joint assemblage 302 164 0.696 0.876 0 0 0 0 0.343
#> 5 Rebio2 Edge 162 70 0.754 0.895 0 0 0 0 0.343
#> 6 Rebio2 Interior 168 74 0.763 0.877 0 0 0 0 0.343
#> 7 Rebio2 Pooled assemblage 330 118 0.819 0.901 0 0 0 0 0.343
#> 8 Rebio2 Joint assemblage 330 144 0.758 0.886 0 0 0 0 0.343
For FDtype = "tau_value" the output information is
described as follows:
Dataset, Pair, Assemblage,
n, S.obs, SC(n) and
SC(2n): definitions are the same as in the TD
output.
a1*,a2* = the number of singletons
(a1*) and of doubletons (a2*) among the
functionally indistinct set at the specified threshold level
'Tau'.
h1,h2 = the total contribution of
singletons (h1) and of doubletons (h2) at the
specified threshold level 'Tau'.
Tau = the specified threshold level of
distinctiveness. Default is dmean (the mean distance between any two
individuals randomly selected from the pooled data over all
datasets).
## Data information for functional diversity (FDtype = 'AUC')
data(Brazil_rainforests)
data(Brazil_distM)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'FD', datatype = 'abundance',
FDdistM = Brazil_distM, FDtype = 'AUC')
#> Dataset Assemblage n S.obs SC(n) SC(2n) dmin dmean dmax
#> 1 Marim Edge 158 84 0.691 0.852 0 0.329 0.755
#> 2 Marim Interior 144 80 0.704 0.899 0 0.313 0.663
#> 3 Marim Pooled assemblage 302 119 0.855 0.969 0 0.323 0.755
#> 4 Marim Joint assemblage 302 164 0.696 0.876 0 0.323 0.755
#> 5 Rebio2 Edge 162 70 0.754 0.895 0 0.376 0.659
#> 6 Rebio2 Interior 168 74 0.763 0.877 0 0.310 0.660
#> 7 Rebio2 Pooled assemblage 330 118 0.819 0.901 0 0.355 0.770
#> 8 Rebio2 Joint assemblage 330 144 0.758 0.886 0 0.355 0.770
For FDtype = "AUC" the output information is described
as follows:
Dataset, Pair, Assemblage,
n, S.obs, SC(n) and
SC(2n): definitions are the same as in TD and thus are
omitted.
dmin = the minimum distance among all non-diagonal
elements in the distance matrix.
dmean = the mean distance between any two
individuals randomly selected from each assemblage.
dmax = the maximum distance among all elements in
the distance matrix.
Below we use the demo dataset (Second-growth forests) to
show the output of the function DataInfobeta3D for
incidence data:
## Data information for taxonomic diversity with incidence data
data(Second_growth_forests)
DataInfobeta3D(data = Second_growth_forests, diversity = 'TD', datatype = 'incidence_raw',
by_pair = FALSE)
#> Dataset Assemblage T U S.obs SC(T) SC(2T) Q1 Q2 Q3 Q4 Q5
#> 1 CR_2005_2011_2017 Year_2005 100 787 135 0.919 0.953 64 17 16 6 4
#> 2 CR_2005_2011_2017 Year_2011 100 768 135 0.916 0.952 65 18 12 7 5
#> 3 CR_2005_2011_2017 Year_2017 100 768 134 0.917 0.956 64 20 11 8 3
#> 4 CR_2005_2011_2017 Pooled assemblage 100 929 152 0.926 0.961 69 22 15 6 6
#> 5 CR_2005_2011_2017 Joint assemblage 100 2323 404 0.917 0.953 193 55 39 21 12
#> 6 JE_2005_2011_2017 Year_2005 100 503 71 0.955 0.979 23 9 8 4 0
#> 7 JE_2005_2011_2017 Year_2011 100 631 88 0.942 0.962 37 8 4 6 7
#> 8 JE_2005_2011_2017 Year_2017 100 659 91 0.953 0.979 31 12 8 3 5
#> 9 JE_2005_2011_2017 Pooled assemblage 100 908 108 0.964 0.985 33 14 9 6 8
#> 10 JE_2005_2011_2017 Joint assemblage 100 1793 250 0.950 0.973 91 29 20 13 12
Information description:
Dataset = the input datasets.
Pair = combinations of assemblage pairs; this column
is included only when the analysis is performed for every pair of
assemblages.
Assemblage = Individual assemblages,
'Pooled assemblage' (for gamma) or
'Joint assemblage' (for alpha).
T = number of sampling units in the reference sample
(sample size for incidence data).
U = total number of incidences in the reference
sample.
S.obs = number of observed species in the reference
sample.
SC(T) = sample coverage estimate of the reference
sample.
SC(2T) = sample coverage estimate of twice the
reference sample size.
Q1-Q5 = the first five species
incidence frequency counts in the reference sample.
## Data information for taxonomic diversity for every pair of assemblages (incidence data)
data(Second_growth_forests)
DataInfobeta3D(data = Second_growth_forests, diversity = 'TD', datatype = 'incidence_raw',
by_pair = TRUE)
#> Dataset Pair Assemblage T U S.obs SC(T) SC(2T) Q1 Q2 Q3 Q4
#> 1 CR_2005_2011_2017 Year_2005 100 787 135 0.919 0.953 64 17 16 6
#> 2 CR_2005_2011_2017 Year_2011 100 768 135 0.916 0.952 65 18 12 7
#> 3 CR_2005_2011_2017 Year_2017 100 768 134 0.917 0.956 64 20 11 8
#> 4 CR_2005_2011_2017 Year_2005 vs. Year_2011 Pooled assemblage 100 860 145 0.920 0.954 69 19 13 5
#> 5 CR_2005_2011_2017 Year_2005 vs. Year_2011 Joint assemblage 100 1555 270 0.917 0.952 129 35 28 13
#> 6 CR_2005_2011_2017 Year_2005 vs. Year_2017 Pooled assemblage 100 923 151 0.925 0.959 70 21 14 6
#> 7 CR_2005_2011_2017 Year_2005 vs. Year_2017 Joint assemblage 100 1555 269 0.918 0.954 128 37 27 14
#> 8 CR_2005_2011_2017 Year_2011 vs. Year_2017 Pooled assemblage 100 837 142 0.923 0.958 65 20 15 7
#> 9 CR_2005_2011_2017 Year_2011 vs. Year_2017 Joint assemblage 100 1536 269 0.917 0.954 129 38 23 15
#> 10 JE_2005_2011_2017 Year_2005 100 503 71 0.955 0.979 23 9 8 4
#> 11 JE_2005_2011_2017 Year_2011 100 631 88 0.942 0.962 37 8 4 6
#> 12 JE_2005_2011_2017 Year_2017 100 659 91 0.953 0.979 31 12 8 3
#> 13 JE_2005_2011_2017 Year_2005 vs. Year_2011 Pooled assemblage 100 757 96 0.951 0.969 37 8 6 7
#> 14 JE_2005_2011_2017 Year_2005 vs. Year_2011 Joint assemblage 100 1134 159 0.947 0.970 60 17 12 10
#> 15 JE_2005_2011_2017 Year_2005 vs. Year_2017 Pooled assemblage 100 864 107 0.963 0.987 32 17 9 4
#> 16 JE_2005_2011_2017 Year_2005 vs. Year_2017 Joint assemblage 100 1162 162 0.954 0.979 54 21 16 7
#> 17 JE_2005_2011_2017 Year_2011 vs. Year_2017 Pooled assemblage 100 788 100 0.958 0.981 33 13 8 6
#> 18 JE_2005_2011_2017 Year_2011 vs. Year_2017 Joint assemblage 100 1290 179 0.948 0.971 68 20 12 9
Output description: definitions are the same as before and thus are
omitted.
License and feedback
The iNEXT.beta3D package is licensed under the GPLv3. To
help refine iNEXT.beta3D, users’ comments or feedback would
be welcome (please send them to Anne Chao or report an issue on the
iNEXT.beta3D GitHub iNEXT.beta3D_github).
References
Chao, A., Chiu, C.-H., Hu, K.-H., and Zeleny, D. (2023a).
Revisiting Alwyn H. Gentry’s forest transect data: a statistical
sampling-model-based approach. Japanese Journal of Statistics and
Data Science, 6, 861-884. (https://doi.org/10.1007/s42081-023-00214-1)
Chao, A., Henderson, P. A., Chiu, C.-H., Moyes, F., Hu, K.-H.,
Dornelas, M. and Magurran, A. E. (2021). Measuring temporal change in
alpha diversity: a framework integrating taxonomic, phylogenetic and
functional diversity and the iNEXT.3D standardization. Methods in
Ecology and Evolution, 12, 1926-1940.
Chao, A., Thorn, S., Chiu, C.-H., Moyes, F., Hu, K.-H., Chazdon,
R. L., Wu, J., Magnago, L. F. S., Dornelas, M., Zeleny, D., Colwell, R.
K., and Magurran, A. E. (2023b). Rarefaction and extrapolation with beta
diversity under a framework of Hill numbers: the iNEXT.beta3D
standardization. Ecological Monographs e1588.
