Anne Chao and Kai-Hsiang Hu
Institute of Statistics,
National Tsing Hua University, Hsin-Chu, Taiwan 30043
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 and their generalizations is adopted to quantify TD, PD and FD. 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 in the same units of species/lineage equivalents and can be meaningfully compared; 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 (alpha, beta and gamma) of 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 the size-based beta diversity is not a statistically valid measure (Chao et al. 2023b) and thus the corresponding 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
.
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. and Hu, K.-H. (2023). The iNEXT.beta3D package: interpolation and extrapolation with beta diversity for three dimensions of biodiversity. R package available from CRAN.
- Required: R
- Suggested: RStudio IDE
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, an additional
visualization extension package (ggplot2
frm CRAN) and (iNEXT.3D
from Anne Chao’s github) 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.
To assess beta diversity among assemblages, information on shared/unique species and their abundances is required. Thus, species identity (or any unique identification code) and assemblage affiliation must be provided in the data. In any input dataset, set row name of the data to be species name (or identification code) and column name to be assemblage name. Two types of species abundance/incidence data are supported:
-
Individual-based abundance data (
datatype = "abundance"
): Input data for a single dataset with N assemblages consist of a species-by-assemblage abundancematrix/data.frame
. Users can input several datasets which may represent data collected from various localities, regions, plots, time periods, …, etc. Input data for multiple datasets then consist of a list of matrices; each matrix represents a species-by-assemblage abundance matrix for one of the datasets. Different datasets can have different numbers of assemblages.iNEXTbeta3D
computes beta diversity and dissimilarity among assemblages within each dataset. -
Sampling-unit-based incidence raw data (
datatype = "incidence_raw"
): Input data for a dataset with N assemblages consist of a list of matrices/data.frames, with each matrix representing a species-by-sampling-unit incidence raw matrix for one of the N assemblages; each element in the incidence raw matrix is 1 for a detection, and 0 for a non-detection. Users can input several datasets. Input data then consist of multiple lists with each list comprising a list of species-by-sampling-unit incidence matrices; see an example below. The number of sampling units can vary with datasets (but within a dataset, the number of sampling units in each assemblage must be the same).iNEXTbeta3D
computes beta diversity and dissimilarity among assemblages within each dataset based on incidence-based frequency counts obtained from all sampling units.
We use the tree species abundance data collected from two rainforest
fragments/localities in Brazil to assess beta diversity between Edge and
Interior assemblages/habitats within each fragment; see Chao et
al. (2023b) for analysis details. The data (named
"Brazil_rainforests"
) consist of a list of two matrices (for two
fragments named “Marim” and “Rebio2”, respectively); each matrix
represents a species-by-assemblage abundance matrix, and there are two
assemblages (“Edge” and “Interior”) in each fragment. The demo data are
slightly different from those analyzed in Chao et al. (2023b) because
seven species are removed from the original pooled data due to lack of
phylogenetic information. Run the following code to view the data: (Here
we only show the first 15 rows for each matrix.)
data(Brazil_rainforests)
Brazil_rainforests
$Marim
Edge Interior
Acosmium_lentiscifolium 1 0
Allophylus_petiolulatus 5 0
Alseis_involuta 2 0
Ampelocera_glabra 1 0
Andira_legalis 0 1
Andira_ormosioides 0 1
Apuleia_leiocarpa 1 0
Aspidosperma_illustre 0 3
Astrocaryum_aculeatissimum 1 0
Astronium_concinnum 4 1
Barnebydendron_riedelii 0 2
Bauhinia_forficata 1 0
Brosimum_glaucum 4 0
Calyptranthes_lucida 0 4
Campomanesia_lineatifolia 1 0
$Rebio2
Edge Interior
Albizia_polycephala 1 0
Allophylus_petiolulatus 3 3
Alseis_involuta 1 0
Amaioua_intermedia 0 1
Ampelocera_glabra 0 3
Anaxagorea_silvatica 0 6
Annona_dolabripetala 1 0
Aspidosperma_cylindrocarpon 2 0
Astrocaryum_aculeatissimum 7 1
Astronium_concinnum 12 1
Astronium_graveolens 13 1
Beilschmiedia_linharensis 1 0
Brosimum_glaucum 2 2
Brosimum_sp1 0 1
Calyptranthes_lucida 2 1
We use tree species data collected from two second-growth rainforests, namely Cuatro Rios (CR) and Juan Enriquez (JE) in Costa Rica, as demo data to assess temporal beta diversity between two years (2005 and 2017) within each forest. Each year is designated as an assemblage. The data in each forest were collected from a 1-ha (50 m x 200 m) forest plot. Because individual trees of some species may exhibit intra-specific aggregation within a 1 ha area, they may not be suitable for modelling as independent sampling units. In this case, it is statistically preferable to first convert species abundance records in each forest to occurrence or incidence (detection/non-detection) data in subplots/quadrats; see Chao et al. (2023b) for analysis details.
Each 1-ha forest was divided into 100 subplots (each with 0.01 ha) and
only species’ incidence records in each subplot were used to compute the
incidence frequency for a species (i.e., the number of subplots in which
that species occurred). By treating the incidence frequency of each
species among subplots as a “proxy” for its abundance, the
iNEXT.beta3D
standardization can be adapted to deal with spatially
aggregated data and to avoid the effect of intra-specific aggregation.
The data (named "Second_growth_forests"
) consist of two lists (for two
forests named “CR 2005 vs. 2017” and “JE 2005 vs. 2017”, respectively).
Each list consists of two matrices; the first matrix represents the
species-by-subplot incidence data in 2005, and the second matrix
represents the species-by-subplots incidence data in 2017. Run the
following code to view the incidence raw data: (Here we only show the
first ten rows and six columns for each matrix; there are 100
columns/subplots in each forest and each year.)
data(Second_growth_forests)
Second_growth_forests
$`CR 2005 vs. 2017`
$`CR 2005 vs. 2017`$Year_2005
Subplot_1 Subplot_2 Subplot_3 Subplot_4 Subplot_5 Subplot_6
Abaade 0 0 0 0 0 0
Alcflo 0 0 0 0 0 0
Alclat 0 1 0 0 0 0
Aliatl 0 0 0 0 0 0
Ampmac 0 0 0 0 0 0
Anacra 0 1 0 0 0 1
Annama 0 1 0 0 0 0
Annpap 0 0 0 0 0 0
Apemem 0 0 0 0 0 0
Ardfim 0 0 0 0 0 0
$`CR 2005 vs. 2017`$Year_2017
Subplot_1 Subplot_2 Subplot_3 Subplot_4 Subplot_5 Subplot_6
Abaade 0 0 0 0 0 0
Alcflo 0 0 0 0 0 0
Alclat 0 1 0 0 0 0
Aliatl 0 0 0 0 0 0
Ampmac 0 0 0 0 0 0
Anacra 0 1 1 0 1 1
Annama 0 0 0 0 0 0
Annpap 0 0 0 0 0 0
Apemem 0 0 0 0 0 0
Ardfim 0 0 0 0 0 0
$`JE 2005 vs. 2017`
$`JE 2005 vs. 2017`$Year_2005
Subplot_1 Subplot_2 Subplot_3 Subplot_4 Subplot_5 Subplot_6
Alccos 0 0 0 0 0 0
Alcflo 0 0 0 0 0 0
Alclat 0 0 0 0 0 0
Annpap 0 0 0 0 0 0
Apemem 0 0 0 0 0 0
Astcon 0 0 0 0 0 0
Bacgas 0 0 0 0 0 0
Brogui 0 0 0 0 0 0
Brolac 0 0 0 0 0 0
Byrcra 0 0 0 0 1 0
$`JE 2005 vs. 2017`$Year_2017
Subplot_1 Subplot_2 Subplot_3 Subplot_4 Subplot_5 Subplot_6
Alccos 0 0 0 0 0 0
Alcflo 0 0 0 0 0 0
Alclat 0 0 0 0 0 0
Annpap 0 0 0 0 0 0
Apemem 0 0 0 0 0 0
Astcon 0 0 0 0 0 0
Bacgas 0 0 0 0 0 0
Brogui 0 0 0 0 0 0
Brolac 0 0 0 0 0 0
Byrcra 0 0 0 0 0 0
To perform PD analysis, the phylogenetic tree (in Newick format) spanned
by species observed in all datasets must be stored in a data file. For
example, the phylogenetic tree for all observed species (including
species in both “Marim” and “Rebio2” fragments) is stored in a data file
named "Brazil_tree"
for demonstration purpose. A partial list of the
tip labels and node labels are shown below.
data(Brazil_tree)
Brazil_tree
Phylogenetic tree with 185 tips and 117 internal nodes.
Tip labels:
Carpotroche_brasiliensis, Casearia_ulmifolia, Casearia_sp2, Casearia_oblongifolia, Casearia_commersoniana, Rinorea_bahiensis, ...
Node labels:
magnoliales_to_asterales, poales_to_asterales, , , , , ...
Rooted; includes branch lengths.
To perform FD analysis, the species-pairwise distance matrix (Gower
distance computed from species traits) for species observed in all
datasets must be stored in a matrix/data.frame format. Typically, the
distance between any two species is computed from species traits using
the Gower distance. In our demo data, the distance matrix for all
species (including species in both “Marim” and “Rebio2” fragments) is
stored in a data file named "Brazil_distM"
for demonstration purpose.
Here we only show the first three rows and three columns of the distance
matrix.
data(Brazil_distM)
Brazil_distM
Carpotroche_brasiliensis Astronium_concinnum Astronium_graveolens
Carpotroche_brasiliensis 0.000 0.522 0.522
Astronium_concinnum 0.522 0.000 0.000
Astronium_graveolens 0.522 0.000 0.000
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 = "meanPD",
FDdistM = NULL, FDtype = "AUC", FDtau = NULL, FDcut_number = 30)
The arguments of this function are briefly described below, and will be
explained in more details by 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.
Argument | Description |
---|---|
data |
|
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-units
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 sized-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 If users set |
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 `nbbot = 100 (or`nbbot = 200\`). |
conf |
a positive number \< 1 specifying the level of confidence interval.
Default is conf = 0.95 .
|
PDtree |
(required argument only for diversity = ‘PD’ ), a
phylogenetic tree in Newick format for all observed species in the
pooled assemblage.
|
PDreftime |
(argument only for diversity = ‘PD’ ), a numerical value
specifying reference time for PD. Default is PDreftime =
NULL (i.e., the age of the root of PDtree ).
|
PDtype |
(argument only for diversity = ‘PD’ ), select PD type:
PDtype = ‘PD’ (effective total branch length) or
PDtype = ‘meanPD’ (effective number of equally divergent
lineages). Default is PDtype = ‘meanPD’ , where
meanPD = PD/tree depth.
|
FDdistM |
(required argument only 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 numeric number to cut \[0, 1\] interval into
equal-spaced sub-intervals to obtain the AUC value 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 set to obtain more
accurate AUC value.
|
This function returns an "iNEXTbeta3D"
object which can be further
used to make plots using the function ggiNEXTbeta3D()
to be described
below.
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.
The function ggiNEXTbeta3D()
with default arguments is described as
follows:
ggiNEXTbeta3D(output, type = "B")
Argument | Description |
---|---|
output |
output from the function iNEXTbeta3D .
|
type |
(argument only for
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 a 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
.
First, we run the iNEXTbeta3D()
function with Brazil_rainforests
abundance data to compute coverage-based taxonomic gamma, alpha, beta
diversity, and four dissimilarity indices under base = 'coverage'
by
running the following code:
## R/E Analysis with taxonomic diversity for abundance data
data(Brazil_rainforests)
output_TDc_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'TD',
datatype = "abundance", base = 'coverage', nboot = 10)
output_TDc_abun
The output contains seven data frames: gamma
, alpha
, beta
, 1-C
,
1-U
, 1-V
, 1-S
. For each data frame, it includes the name of
dataset (Dataset
), the diversity order of q (Order.q
), the target
standardized coverage value (SC
), the corresponding sample size
(Size
), the estimated diversity/dissimilarity estimate
(Alpha/Beta/Gamma/Dissimilarity
), Method
(Rarefaction, Observed, or
Extrapolation, depending on whether the target coverage is less than,
equal to, or greater than the coverage of the reference sample),
standard error of standardized estimate (s.e.
), the bootstrap lower
and upper confidence limits for the diversity/dissimilarity with a
default significance level of 0.95 (LCL
, UCL
). These estimates with
confidence intervals in the output are then used for plotting
rarefaction and extrapolation curves.
Our diversity/dissimilarity estimates and related statistics in the
default output are displayed for the standardized coverage value from
0.5 to the coverage value of twice the reference sample size (for q =
0), or from 0.5 to 1.0 (for q = 1 and 2), in increments of 0.025. In
addition, the results for the following four coverage value are also
added: SC(n, alpha)
, SC(2n, alpha)
, SC(n, gamma)
and
SC(2n, gamma)
if these values are in the above-specified range. Here
SC(n, alpha)
and SC(2n, alpha)
represent, respectively, the coverage
estimate for the alpha reference sample size n and the extrapolated
sample with size 2n in the joint assemblage. These values can be found
as SC(n)
and SC(2n)
for "Joint assemblage (for alpha)"
in the
column “Assemblage” from the output of the function DataInfobeta3D
;
see later text. Similar definitions pertain to SC(n, gamma)
and
SC(2n, gamma)
for the gamma reference sample; these two values can
also be found as SC(n)
and SC(2n)
for
"Pooled assemblage (for gamma)"
in the column “Assemblage” from the
output of the function DataInfobeta3D
. For beta diversity and
dissimilarity, the observed sample coverage and extrapolation limit are
defined the same as the alpha diversity. The corresponding coverage
values for incidence data are denoted as, respectively, SC(T, alpha)
,
SC(2T, alpha)
, SC(T, gamma)
and SC(2T, gamma)
in the output.
Because all the diversity/dissimilarity estimates are computed for the
standardized coverage range values starting from 0.5, the default
setting with level = NULL
does not work if the observed sample
coverage in the alpha/gamma reference sample is less than 50%. In this
case, readers should specify sample coverage values using the argument
level
, instead of using level = NULL
. The suggested maximum coverage
value that readers can specify is SC(2n, alpha)
. Beyond the limit,
beta diversity and dissimilarity estimates may be subject to some bias.
Below we show the output for taxonomic beta diversity between the “Edge”
and “Interior” habitats in the “Marim” fragment.
Dataset Order.q SC Size Beta Method s.e. LCL UCL
1 Marim 0 0.500 148 1.11 Rarefaction 0.069 0.976 1.25
2 Marim 0 0.525 162 1.11 Rarefaction 0.069 0.973 1.24
3 Marim 0 0.550 178 1.10 Rarefaction 0.068 0.971 1.24
4 Marim 0 0.575 195 1.10 Rarefaction 0.067 0.970 1.23
5 Marim 0 0.600 213 1.10 Rarefaction 0.066 0.970 1.23
6 Marim 0 0.625 233 1.09 Rarefaction 0.063 0.971 1.22
7 Marim 0 0.650 255 1.09 Rarefaction 0.060 0.974 1.21
8 Marim 0 0.675 279 1.09 Rarefaction 0.057 0.977 1.20
9 Marim 0 0.696 302 1.09 Observed_SC(n, alpha) 0.054 0.980 1.19
10 Marim 0 0.700 306 1.09 Extrapolation 0.054 0.981 1.19
11 Marim 0 0.725 336 1.08 Extrapolation 0.051 0.985 1.18
12 Marim 0 0.750 368 1.08 Extrapolation 0.050 0.986 1.18
13 Marim 0 0.775 403 1.08 Extrapolation 0.053 0.981 1.19
14 Marim 0 0.800 443 1.09 Extrapolation 0.058 0.973 1.20
15 Marim 0 0.825 488 1.09 Extrapolation 0.066 0.961 1.22
16 Marim 0 0.850 541 1.09 Extrapolation 0.074 0.948 1.24
17 Marim 0 0.855 552 1.09 Observed_SC(n, gamma) 0.076 0.944 1.24
18 Marim 0 0.875 602 1.09 Extrapolation 0.083 0.932 1.26
19 Marim 0 0.876 604 1.09 Extrap_SC(2n, alpha) 0.083 0.932 1.26
20 Marim 1 0.500 148 1.11 Rarefaction 0.063 0.987 1.23
21 Marim 1 0.525 162 1.11 Rarefaction 0.063 0.985 1.23
22 Marim 1 0.550 178 1.11 Rarefaction 0.062 0.984 1.23
23 Marim 1 0.575 195 1.10 Rarefaction 0.061 0.983 1.22
24 Marim 1 0.600 213 1.10 Rarefaction 0.060 0.984 1.22
25 Marim 1 0.625 233 1.10 Rarefaction 0.058 0.985 1.21
26 Marim 1 0.650 255 1.10 Rarefaction 0.056 0.988 1.21
27 Marim 1 0.675 279 1.09 Rarefaction 0.053 0.991 1.20
28 Marim 1 0.696 302 1.09 Observed_SC(n, alpha) 0.051 0.994 1.19
29 Marim 1 0.700 306 1.09 Extrapolation 0.051 0.994 1.19
30 Marim 1 0.725 336 1.09 Extrapolation 0.048 0.997 1.19
31 Marim 1 0.750 368 1.09 Extrapolation 0.047 0.998 1.18
32 Marim 1 0.775 403 1.09 Extrapolation 0.047 0.995 1.18
33 Marim 1 0.800 443 1.08 Extrapolation 0.049 0.988 1.18
34 Marim 1 0.825 488 1.08 Extrapolation 0.050 0.981 1.18
35 Marim 1 0.850 541 1.07 Extrapolation 0.052 0.972 1.18
36 Marim 1 0.855 552 1.07 Observed_SC(n, gamma) 0.053 0.970 1.18
37 Marim 1 0.875 602 1.07 Extrapolation 0.054 0.963 1.17
38 Marim 1 0.876 604 1.07 Extrap_SC(2n, alpha) 0.054 0.963 1.17
39 Marim 1 0.900 678 1.06 Extrapolation 0.055 0.957 1.17
40 Marim 1 0.925 775 1.06 Extrapolation 0.056 0.953 1.17
41 Marim 1 0.950 912 1.06 Extrapolation 0.056 0.954 1.17
42 Marim 1 0.969 1075 1.07 Extrap_SC(2n, gamma) 0.054 0.959 1.17
43 Marim 1 0.975 1147 1.07 Extrapolation 0.054 0.963 1.17
44 Marim 1 1.000 Inf 1.10 Extrapolation 0.045 1.016 1.19
45 Marim 2 0.500 148 1.10 Rarefaction 0.053 0.996 1.21
46 Marim 2 0.525 162 1.10 Rarefaction 0.053 0.995 1.20
47 Marim 2 0.550 178 1.10 Rarefaction 0.052 0.995 1.20
48 Marim 2 0.575 195 1.09 Rarefaction 0.051 0.995 1.19
49 Marim 2 0.600 213 1.09 Rarefaction 0.049 0.995 1.19
50 Marim 2 0.625 233 1.09 Rarefaction 0.048 0.996 1.18
51 Marim 2 0.650 255 1.09 Rarefaction 0.046 0.998 1.18
52 Marim 2 0.675 279 1.09 Rarefaction 0.044 0.999 1.17
53 Marim 2 0.696 302 1.08 Observed_SC(n, alpha) 0.043 1.000 1.17
54 Marim 2 0.700 306 1.08 Extrapolation 0.043 1.001 1.17
55 Marim 2 0.725 336 1.08 Extrapolation 0.042 1.002 1.17
56 Marim 2 0.750 368 1.08 Extrapolation 0.042 1.002 1.17
57 Marim 2 0.775 403 1.09 Extrapolation 0.044 1.001 1.17
58 Marim 2 0.800 443 1.09 Extrapolation 0.045 0.999 1.18
59 Marim 2 0.825 488 1.09 Extrapolation 0.047 0.998 1.18
60 Marim 2 0.850 541 1.09 Extrapolation 0.048 0.997 1.18
61 Marim 2 0.855 552 1.09 Observed_SC(n, gamma) 0.048 0.997 1.18
62 Marim 2 0.875 602 1.09 Extrapolation 0.049 0.996 1.19
63 Marim 2 0.876 604 1.09 Extrap_SC(2n, alpha) 0.049 0.996 1.19
64 Marim 2 0.900 678 1.09 Extrapolation 0.049 0.997 1.19
65 Marim 2 0.925 775 1.09 Extrapolation 0.049 0.998 1.19
66 Marim 2 0.950 912 1.09 Extrapolation 0.048 0.999 1.19
67 Marim 2 0.969 1075 1.09 Extrap_SC(2n, gamma) 0.048 1.000 1.19
68 Marim 2 0.975 1147 1.09 Extrapolation 0.048 1.000 1.19
69 Marim 2 1.000 Inf 1.09 Extrapolation 0.048 0.994 1.18
Run the following code to display the two types of curves:
## Coverage-based R/E curves for taxonomic gamma, alpha and beta diversity
ggiNEXTbeta3D(output_TDc_abun, type = 'B')
## Coverage-based R/E curves for four taxonomic dissimilarity indices
ggiNEXTbeta3D(output_TDc_abun, type = 'D')
The following commands return the size-based R/E sampling curves for gamma and alpha taxonomic diversity:
## Size-based R/E curves for taxonomic gamma and alpha diversity
output_TDs_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'TD',
datatype = 'abundance', base = "size", nboot = 10)
ggiNEXTbeta3D(output_TDs_abun)
In addition to the default sample sizes or coverage values,
iNEXTbeta3D
also computes standardized 3D estimates with a particular
vector of user-specified sample sizes or coverage values. The following
commands return the TD estimates with two user-specified levels of
sample coverage (e.g., 85% and 90%). Only the output for gamma, alpha
and beta is shown below in each dataset; the output for 1-C, 1-U, 1-V,
1-S is omitted.
## R/E Analysis with taxonomic diversity for abundance data
data(Brazil_rainforests)
output_TDc_abun_byuser = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'TD',
datatype = "abundance", base = 'coverage', nboot = 10,
level = c(0.85, 0.9))
output_TDc_abun_byuser
$Marim
$Marim$gamma
Dataset Order.q SC Size Gamma Method s.e. LCL UCL
1 Order q = 0
2 Marim 0 0.85 295.313 118.011 Rarefaction 5.727 106.786 129.237
3 Marim 0 0.9 374.487 127.8 Extrapolation 7.546 113.01 142.59
4 Order q = 1
5 Marim 1 0.85 295.313 90.988 Rarefaction 5.307 80.587 101.388
6 Marim 1 0.9 374.487 97.277 Extrapolation 5.834 85.843 108.712
7 Order q = 2
8 Marim 2 0.85 295.313 67.621 Rarefaction 6.049 55.764 79.477
9 Marim 2 0.9 374.487 71.019 Extrapolation 6.55 58.181 83.857
$Marim$alpha
Dataset Order.q SC Size Alpha Method s.e. LCL UCL
1 Order q = 0
2 Marim 0 0.85 540.613 108.036 Extrapolation 6.704 94.896 121.175
3 Marim 0 0.9 677.745 116.503 Extrapolation 7.776 101.262 131.745
4 Order q = 1
5 Marim 1 0.85 540.613 84.693 Extrapolation 5.1 74.697 94.688
6 Marim 1 0.9 677.745 91.384 Extrapolation 5.546 80.515 102.254
7 Order q = 2
8 Marim 2 0.85 540.613 61.998 Extrapolation 5.479 51.26 72.737
9 Marim 2 0.9 677.745 64.996 Extrapolation 5.965 53.304 76.688
$Marim$beta
Dataset Order.q SC Size Beta Method s.e. LCL UCL
1 Order q = 0
2 Marim 0 0.85 540.613 1.092 Extrapolation 0.092 0.912 1.273
3 Marim 0 0.9 677.745 1.097 Extrapolation 0.105 0.891 1.303
4 Order q = 1
5 Marim 1 0.85 540.613 1.074 Extrapolation 0.072 0.933 1.216
6 Marim 1 0.9 677.745 1.064 Extrapolation 0.077 0.913 1.216
7 Order q = 2
8 Marim 2 0.85 540.613 1.091 Extrapolation 0.071 0.951 1.231
9 Marim 2 0.9 677.745 1.093 Extrapolation 0.073 0.95 1.235
$Rebio2
$Rebio2$gamma
Dataset Order.q SC Size Gamma Method s.e. LCL UCL
1 Order q = 0
2 Rebio2 0 0.85 434.58 135.297 Extrapolation 12.851 110.109 160.485
3 Rebio2 0 0.9 657.113 162.764 Extrapolation 15.015 133.335 192.192
4 Order q = 1
5 Rebio2 1 0.85 434.58 84.77 Extrapolation 5.664 73.668 95.871
6 Rebio2 1 0.9 657.113 94.373 Extrapolation 6.327 81.972 106.773
7 Order q = 2
8 Rebio2 2 0.85 434.58 57.565 Extrapolation 3.397 50.906 64.223
9 Rebio2 2 0.9 657.113 60.225 Extrapolation 3.646 53.079 67.372
$Rebio2$alpha
Dataset Order.q SC Size Alpha Method s.e. LCL UCL
1 Order q = 0
2 Rebio2 0 0.85 539.824 92.197 Extrapolation 6.656 79.15 105.243
3 Rebio2 0 0.9 717.89 103.188 Extrapolation 8.097 87.319 119.058
4 Order q = 1
5 Rebio2 1 0.85 539.824 58.713 Extrapolation 4.344 50.199 67.228
6 Rebio2 1 0.9 717.89 63.83 Extrapolation 4.871 54.283 73.377
7 Order q = 2
8 Rebio2 2 0.85 539.824 36.464 Extrapolation 3.957 28.708 44.219
9 Rebio2 2 0.9 717.89 37.713 Extrapolation 4.249 29.385 46.04
$Rebio2$beta
Dataset Order.q SC Size Beta Method s.e. LCL UCL
1 Order q = 0
2 Rebio2 0 0.85 539.824 1.467 Extrapolation 0.133 1.207 1.728
3 Rebio2 0 0.9 717.89 1.577 Extrapolation 0.149 1.285 1.869
4 Order q = 1
5 Rebio2 1 0.85 539.824 1.444 Extrapolation 0.093 1.261 1.627
6 Rebio2 1 0.9 717.89 1.478 Extrapolation 0.097 1.288 1.669
7 Order q = 2
8 Rebio2 2 0.85 539.824 1.579 Extrapolation 0.086 1.411 1.746
9 Rebio2 2 0.9 717.89 1.597 Extrapolation 0.082 1.437 1.757
The following commands return the TD estimates with two user-specified levels of sample sizes (e.g., 300 and 500).
## Size-based R/E for taxonomic gamma and alpha diversity
output_TDs_abun_byuser = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'TD',
datatype = 'abundance', base = "size", nboot = 10,
level = c(300, 500))
output_TDs_abun_byuser
$Marim
$Marim$gamma
Dataset Order.q Size SC Gamma Method s.e. LCL UCL
1 Order q = 0
2 Marim 0 300 0.854 118.708 Rarefaction 3.757 111.344 126.071
3 Marim 0 500 0.947 137.082 Extrapolation 6.075 125.176 148.989
4 Order q = 1
5 Marim 1 300 0.854 91.406 Rarefaction 3.446 84.651 98.16
6 Marim 1 500 0.947 104.649 Extrapolation 4.056 96.7 112.598
7 Order q = 2
8 Marim 2 300 0.854 67.861 Rarefaction 4.309 59.415 76.306
9 Marim 2 500 0.947 74.527 Extrapolation 5.03 64.669 84.385
$Marim$alpha
Dataset Order.q Size SC Alpha Method s.e. LCL UCL
1 Order q = 0
2 Marim 0 300 0.694 81.695 Rarefaction 2.144 77.493 85.897
3 Marim 0 500 0.831 104.795 Extrapolation 4.229 96.506 113.083
4 Order q = 1
5 Marim 1 300 0.694 66.473 Rarefaction 1.675 63.19 69.756
6 Marim 1 500 0.831 82.274 Extrapolation 2.441 77.49 87.059
7 Order q = 2
8 Marim 2 300 0.694 52.416 Rarefaction 2.235 48.036 56.796
9 Marim 2 500 0.831 60.871 Extrapolation 2.881 55.225 66.518
$Rebio2
$Rebio2$gamma
Dataset Order.q Size SC Gamma Method s.e. LCL UCL
1 Order q = 0
2 Rebio2 0 300 0.807 112.391 Rarefaction 6.596 99.462 125.319
3 Rebio2 0 500 0.867 144.556 Extrapolation 9.083 126.754 162.358
4 Order q = 1
5 Rebio2 1 300 0.807 76.38 Rarefaction 5.197 66.195 86.565
6 Rebio2 1 500 0.867 88.06 Extrapolation 6.633 75.06 101.06
7 Order q = 2
8 Rebio2 2 300 0.807 54.382 Rarefaction 3.763 47.007 61.757
9 Rebio2 2 500 0.867 58.564 Extrapolation 4.317 50.103 67.026
$Rebio2$alpha
Dataset Order.q Size SC Alpha Method s.e. LCL UCL
1 Order q = 0
2 Rebio2 0 300 0.741 68.239 Rarefaction 3.023 62.314 74.164
3 Rebio2 0 500 0.836 89.067 Extrapolation 4.694 79.867 98.267
4 Order q = 1
5 Rebio2 1 300 0.741 47.986 Rarefaction 3.23 41.654 54.317
6 Rebio2 1 500 0.836 57.286 Extrapolation 4.197 49.06 65.512
7 Order q = 2
8 Rebio2 2 300 0.741 32.948 Rarefaction 3.025 27.019 38.877
9 Rebio2 2 500 0.836 36.08 Extrapolation 3.52 29.18 42.98
We can also use incidence raw data (Second_growth_forests
) to compute
coverage-based standardized gamma, alpha, beta diversity, and four
dissimilarities under base = 'coverage'
, and also size-based
standardized gamma and alpha diversity. Run the following code to
perform incidence data analysis. The output data frame is similar to
that based on abundance data and thus is omitted.
## R/E Analysis with taxonomic diversity for incidence raw data
data(Second_growth_forests)
output_TDc_inci = iNEXTbeta3D(data = Second_growth_forests, diversity = 'TD',
datatype = "incidence_raw", base = 'coverage', nboot = 10)
output_TDc_inci
The same procedures can be applied to incidence data. Based on the demo dataset, we display below the coverage-based R/E curves for comparing temporal beta diversity between 2005 and 2017 in two second-growth forests (CR and JE) by running the following code:
## Coverage-based R/E curves for taxonomic gamma, alpha and beta diversity
ggiNEXTbeta3D(output_TDc_inci, type = 'B')
The following commands return the size-based R/E sampling curves for gamma and alpha taxonomic diversity:
## Size-based R/E curves for taxonomic gamma and alpha diversity
output_TDs_inci = iNEXTbeta3D(data = Second_growth_forests, diversity = 'TD',
datatype = 'incidence_raw', base = "size", nboot = 10)
ggiNEXTbeta3D(output_TDs_inci)
As with abundance data, user can also specify sample sizes (i.e. number of sampling units) or coverage values to obtain the pertinent output. The code for examples is given below with two user-specified levels of sample coverage values (e.g., 90% and 95%), but the output is omitted.
## R/E Analysis with taxonomic diversity for incidence data
data(Second_growth_forests)
output_TDc_inci_byuser = iNEXTbeta3D(data = Second_growth_forests, diversity = 'TD',
datatype = 'incidence_raw', base = "coverage",
nboot = 10, level = c(0.9, 0.95))
output_TDc_inci_byuser
The following commands return the TD estimates with two user-specified levels of sample sizes (e.g., 100 and 200).
## Size-based R/E for taxonomic gamma and alpha diversity
data(Second_growth_forests)
output_TDs_inci_byuser = iNEXTbeta3D(data = Second_growth_forests, diversity = 'TD',
datatype = 'incidence_raw', base = "size",
nboot = 10, level = c(100, 200))
output_TDs_inci_byuser
As with taxonomic diversity, iNEXT.beta3D
computes coverage-based
standardized phylogenetic gamma, alpha, beta diversity as well as four
classes of phylogenetic dissimilarity indices; it also computes
size-based standardized phylogenetic gamma and alpha diversity. The
species names (or identification codes) in the phylogenetic tree must
exactly match with those in the corresponding species
abundance/incidence data. Two types of phylogenetic rarefaction and
extrapolation curves (coverage- and size-based sampling curves) are also
provided.
The required argument for performing PD analysis is PDtree
. For
example, the phylogenetic tree for all observed species (including
species in both Marim and Rebio2 fragments) is stored in a data file
named "Brazil_tree"
. Then we enter the argument
PDtree = Brazil_tree
. Two optional arguments are: PDtype
and
PDreftime
. There are two options for PDtype
: "PD"
(effective total
branch length) or "meanPD"
(effective number of equally divergent
lineages, meanPD = PD/tree depth). Default is PDtype = "meanPD"
.
PDreftime
is a numerical value specifying a reference time for
computing phylogenetic diversity. By default (PDreftime = NULL
), the
reference time is set to the tree depth, i.e., age of the root of the
phylogenetic tree. Run the following code to perform PD analysis. The
output data frame is similar to that based on abundance data and thus is
omitted.
## R/E Analysis with phylogenetic diversity for abundance data
data(Brazil_rainforests)
data(Brazil_tree)
output_PDc_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'PD',
datatype = "abundance", base = 'coverage', nboot = 10,
PDtree = Brazil_tree, PDreftime = NULL, PDtype = 'meanPD')
output_PDc_abun
Run the following code to display the R/E curves for phylogenetic gamma, alpha, and beta diversity:
## Coverage-based R/E sampling curves for phylogenetic gamma, alpha and beta diversity
ggiNEXTbeta3D(output_PDc_abun, type = 'B')
The following commands return the size-based R/E sampling curves for gamma and alpha phylogenetic diversity:
## Size-based R/E curves for phylogenetic gamma and alpha diversity
data(Brazil_rainforests)
data(Brazil_tree)
output_PDs_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'PD',
datatype = 'abundance', base = "size", nboot = 10,
PDtree = Brazil_tree, PDreftime = NULL, PDtype = 'meanPD')
ggiNEXTbeta3D(output_PDs_abun)
As with taxonomic and phylogenetic diversity, iNEXT.beta3D
computes
coverage-based standardized functional gamma, alpha, beta diversity as
well as four classes of functional dissimilarity indices; it also
computes size-based standardized functional gamma and alpha diversity.
The species names (or identification codes) in the distance matrix must
exactly match with those in the corresponding species
abundance/incidence data. Two types of functional rarefaction and
extrapolation curves (coverage- and size-based sampling curves) are also
provided.
The required argument for performing FD analysis is FDdistM
. For
example, the distance matrix for all species (including species in both
“Marim” and “Rebio2” fragments) is stored in a data file named
"Brazil_distM"
. Then we enter the argument FDdistM = Brazil_distM
.
Three optional arguments are (1) FDtype
: FDtype = "AUC"
means FD is
computed from the area under the curve of a tau-profile by integrating
all plausible threshold values between zero and one;
FDtype = "tau_value"
means FD is computed under a specific threshold
value to be specified in the argument FD_tau
. (2) FD_tau
: a
numerical value specifying the tau value (threshold level) that will be
used to compute FD. If FDtype = "tau_value"
and FD_tau = NULL
, then
the threshold level is set to be the mean distance between any two
individuals randomly selected from the pooled data over all datasets
(i.e., quadratic entropy). (3) FDcut_number
is a numeric number to cut
[0, 1] interval into equal-spaced sub-intervals to obtain the AUC
value. Default is FDcut_number = 30
. If more accurate integration is
desired, then use a larger integer. Run the following code to perform FD
analysis. The output data frame is similar to that based on abundance
data and thus is omitted; see later graphical display of the output.
## R/E Analysis with functional diversity for abundance data - FDtype = 'AUC' (area under curve)
## by considering all threshold values between zero and one
data(Brazil_rainforests)
data(Brazil_distM)
output_FDc_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'FD',
datatype = "abundance", base = 'coverage', nboot = 10,
FDdistM = Brazil_distM, FDtype = 'AUC', FDcut_number = 30)
output_FDc_abun
Run the following code to display the R/E curves for functional gamma, alpha, and beta diversity:
## Coverage-based R/E sampling curves for functional gamma, alpha and beta diversity
ggiNEXTbeta3D(output_FDc_abun, type = 'B')
The following commands return the size-based R/E sampling curves for gamma and alpha functional diversity:
## Size-based R/E curves for functional gamma and alpha diversity
data(Brazil_rainforests)
data(Brazil_distM)
output_FDs_abun = iNEXTbeta3D(data = Brazil_rainforests, diversity = 'FD',
datatype = 'abundance', base = "size", nboot = 10,
FDdistM = Brazil_distM, FDtype = 'AUC', FDcut_number = 30)
ggiNEXTbeta3D(output_FDs_abun)
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, FDdistM = NULL, FDtype = "AUC", FDtau = NULL)
All arguments in the above function are the same as those for the main
function iNEXTbeta3D
. 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 demo 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. -
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 phylogenetic diversity
data(Brazil_rainforests)
data(Brazil_tree)
DataInfobeta3D(data = Brazil_rainforests, diversity = 'PD', datatype = 'abundance',
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
Information description:
-
Dataset
,Assemblage
,n
,S.obs
,SC(n)
andSC(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
= reference time for phylogenetic diversity (the age of the root of phylogenetic tree).
## 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
Information description:
-
Dataset
,Assemblage
,n
,S.obs
,SC(n)
andSC(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
Information description:
-
Dataset
,Assemblage
,n
,S.obs
,SC(n)
andSC(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 (incidence data)
data(Second_growth_forests)
DataInfobeta3D(data = Second_growth_forests, diversity = 'TD', datatype = 'incidence_raw')
Dataset Assemblage T U S.obs SC(T) SC(2T) Q1 Q2 Q3 Q4 Q5
1 CR 2005 vs. 2017 Year_2005 100 787 135 0.919 0.953 64 17 16 6 4
2 CR 2005 vs. 2017 Year_2017 100 768 134 0.917 0.956 64 20 11 8 3
3 CR 2005 vs. 2017 Pooled assemblage 100 923 151 0.925 0.959 70 21 14 6 6
4 CR 2005 vs. 2017 Joint assemblage 100 1555 269 0.918 0.954 128 37 27 14 7
5 JE 2005 vs. 2017 Year_2005 100 503 71 0.955 0.979 23 9 8 4 0
6 JE 2005 vs. 2017 Year_2017 100 659 91 0.953 0.979 31 12 8 3 5
7 JE 2005 vs. 2017 Pooled assemblage 100 864 107 0.963 0.987 32 17 9 4 8
8 JE 2005 vs. 2017 Joint assemblage 100 1162 162 0.954 0.979 54 21 16 7 5
Information description:
-
Dataset
= the input datasets. -
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.
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.
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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)
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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.
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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.