Anne Chao, Kai-Hsiang Hu
Institute of Statistics,
National Tsing Hua University, Hsin-Chu, Taiwan 30043
iNEXT.3D (INterpolation and EXTrapolation for three dimensions of
biodiversity) is a sequel to
iNEXT (Hsieh
et al., 2016). Here the three dimensions (3D) of diversity include
taxonomic diversity (TD), phylogenetic diversity (PD) and functional
diversity (FD). An online version “iNEXT.3D Online”
(https://chao.shinyapps.io/iNEXT_3D/) 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 to quantify 3D. In this framework, TD quantifies the effective number of species, PD quantifies the effective total branch length, 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. (2014) for the basic standardization theory for TD, and Chao et al. (2021) for a review of the unified theory for 3D.
For each of the three dimensions of biodiversity, iNEXT.3D features
two statistical analyses (non-asymptotic and asymptotic):
- A non-asymptotic approach based on interpolation and extrapolation for 3D diversity (i.e., Hill-Chao numbers)
iNEXT.3D computes the estimated 3D diversity for standardized samples
with a common sample size or sample completeness. This approach aims to
compare diversity estimates for equally-large (with a common sample
size) or equally-complete (with a common sample coverage) samples; it is
based on the seamless rarefaction and extrapolation (R/E) sampling
curves of Hill-Chao numbers for q = 0, 1 and 2. For each dimension of
biodiversity, iNEXT.3D offers three types of R/E sampling curves:
-
Sample-size-based (or size-based) R/E sampling curves: This type of sampling curve plots the diversity estimates with respect to sample size.
-
Coverage-based R/E sampling curves: This type of sampling curve plots the diversity estimates with respect to sample coverage.
-
Sample completeness curve: This curve depicts how sample coverage varies with sample size. The sample completeness curve provides a bridge between the size- and coverage-based R/E sampling curves.
- An asymptotic approach to infer asymptotic 3D diversity (i.e., Hill-Chao numbers)
iNEXT.3D computes the estimated asymptotic 3D diversity and also plots
3D diversity profiles (q-profiles) for q between 0 and 2, in comparison
with the observed diversity. Typically, the asymptotic estimates for q ≥
1 are reliable, but for q < 1 (especially for q = 0, species richness),
the asymptotic estimates represent only lower bounds. iNEXT.3D also
features a time-profile (which depicts the observed and asymptotic
estimate of PD or mean PD with respect to reference times), and a
tau-profile (which depicts the observed and asymptotic estimate of FD
with respect to threshold level tau).
If you publish your work based on results from iNEXT.3D package, you
should make references to the following methodology paper and the
package:
-
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. and Hu, K.-H. (2023). The iNEXT.3D package: interpolation and extrapolation for three dimensions of biodiversity. R package available from CRAN.
- Required: R
- Suggested: RStudio IDE
The iNEXT.3D package can be downloaded from CRAN or Anne Chao’s
iNEXT.3D_github using the
commands below. For a first-time installation, some additional packages
must be installed and loaded; see package manual.
## install iNEXT.3D package from CRAN
install.packages("iNEXT.3D")
## or install the latest version from github
install.packages('devtools')
library(devtools)
install_github('AnneChao/iNEXT.3D')
## import packages
library(iNEXT.3D)There are six main functions in this package:
Two functions for non-asymptotic analysis with graphical displays:
-
iNEXT3D computes standardized 3D diversity estimates of order q = 0, 1 and 2 for rarefied and extrapolated samples at specified sample coverage values and sample sizes.
-
ggiNEXT3D visualizes the output from the function
iNEXT3D.
Two functions for point estimation and basic data information
-
estimate3D computes 3D diversity of order q = 0, 1 and 2 with a particular set of user-specified level of sample sizes or sample coverage values.
-
DataInfo3D provides basic data information based on the observed data.
Two functions for asymptotic analysis with graphical displays:
-
ObsAsy3D computes observed and asymptotic diversity of order q between 0 and 2 (in increments of 0.2) for 3D diversity; it also computes observed and asymptotic PD for specified reference times, and observed and asymptotic FD for specified threshold levels.
-
ggObsAsy3D visualizes the output from the function
ObsAsy3D.
Although species identities/names are not required to assess TD or
compare TD across individual assemblages (as in the iNEXT package),
they are required for PD and FD. Thus, for iNEXT.3D package,
information on species identity (or any unique identification code) and
assemblage affiliation is required. Two types of species
abundance/incidence data are supported:
-
Individual-based abundance data (
datatype = "abundance"): When there are multiple assemblages, in addition to the assemblage/site names (as column names) and the species names (as row names), species abundance data (reference sample) can be input as a species (in rows) by assemblage (in columns) matrix/data.frame or a list of species abundance vectors. In the special case that there is only one assemblage, all data should be read in one column. -
Sampling-unit-based incidence data: Incidence-raw data (
datatype = "incidence_raw"): for each assemblage, input data for a reference sample consist of a species-by-sampling-unit matrix, in addition to the sampling-unit names (as column names) and the species names (as row names). When there are N assemblages, input data consist of N lists of matrices, and each matrix is a species-by-sampling-unit matrix. Each element in the incidence raw matrix is 1 for a detection, and 0 for a non-detection. Input a matrix which combines data for all assemblages is allowed, but the argumentnTin the functioniNEXT3Dmust be specified so that the number of sampling units in each assemblage is specified.
For example, the dataset Brazil_rainforest_abun_data included in the
iNEXT.3D package consists of species sample abundances of two
assemblages/habitats: “Edge” and “Interior”. Run the following code to
view the first 15 rows of the abundance data.
data("Brazil_rainforest_abun_data")
Brazil_rainforest_abun_data Edge Interior
Carpotroche_brasiliensis 11 21
Astronium_concinnum 110 11
Astronium_graveolens 36 7
Spondias_macrocarpa 12 1
Spondias_venulosa 2 0
Tapirira_guianensis 7 1
Thyrsodium_spruceanum 11 11
Anaxagorea_silvatica 1 13
Annona_acutiflora 1 1
Annona_cacans 0 2
Annona_dolabripetala 3 3
Annona_sp 0 1
Duguetia_chrysocarpa 1 1
Ephedranthus_sp1 1 0
Ephedranthus_sp2 0 1
We use data (Fish_incidence_data) collected from two time periods,
namely "2013-2015" and "2016-2018", as an example. Each time period
is designated as an assemblage. The purpose was to compare 3D diversity
of the two time periods. In each time period, species
incidence/occurrence was recorded in 36 sampling units in each
assemblage; each sampling unit represents a sampling date. Thus, there
are 36 columns in each time period. Run the following code to view the
first 7 rows and 7 columns for each matrix.
data("Fish_incidence_data")
Fish_incidence_data$`2013-2015`
17/01/2013 18/02/2013 19/03/2013 17/04/2013 16/05/2013 14/06/2013 15/07/2013
Agonus_cataphractus 0 1 1 1 0 0 0
Alosa_fallax 0 0 0 0 0 0 0
Ammodytes_tobianus 0 0 0 0 0 0 0
Anguilla_anguilla 0 1 1 0 0 0 0
Aphia_minuta 0 0 0 0 1 1 0
Arnoglossus_laterna 0 0 0 0 0 0 0
Atherina_boyeri 0 0 0 0 0 0 0
$`2016-2018`
18/01/2016 15/02/2016 16/03/2016 14/04/2016 12/05/2016 10/06/2016 11/07/2016
Agonus_cataphractus 1 1 1 1 1 0 0
Alosa_fallax 0 0 0 0 0 0 0
Ammodytes_tobianus 0 0 0 0 0 0 0
Anguilla_anguilla 0 0 0 0 0 0 1
Aphia_minuta 0 0 0 0 1 0 0
Arnoglossus_laterna 0 0 0 0 0 0 0
Atherina_boyeri 0 1 0 0 1 1 0
To perform PD analysis, the phylogenetic tree (in Newick format) spanned
by species observed in the pooled data is required. For the dataset
Fish_incidence_data, the phylogenetic tree for all observed species
(including species in both time periods) is stored in the file
fish_phylo_tree; for the dataset Brazil_rainforest_abun_data, the
phylogenetic tree for all observed species (including species in both
Edge and Interior habitats) is stored in the file
Brazil_rainforest_phylo_tree. A partial list of the tip labels and
node labels are shown below.
data("Brazil_rainforest_phylo_tree")
Brazil_rainforest_phylo_tree
Phylogenetic tree with 425 tips and 205 internal nodes.
Tip labels:
Carpotroche_brasiliensis, Casearia_ulmifolia, Casearia_sp4, Casearia_sylvestris, Casearia_sp2, Casearia_sp3, ...
Node labels:
magnoliales_to_asterales, poales_to_asterales, , , , celastrales_to_malpighiales, ...
Rooted; includes branch lengths.To perform FD analysis, the species-pairwise distance matrix (Gower
distance computed from species traits) for species observed in the
pooled data is required in a matrix/data.frame format. For the dataset
Fish_incidence_data, the distance matrix for all observed species
(including species in both time periods) is stored in the file
fish_dist_matrix; for the dataset Brazil_rainforest_abun_data, the
distance matrix for all species (including species in both Edge and
Interior habitats) is stored in the file
Brazil_rainforest_dist_matrix. The distance matrix for the first 3
Brazil rainforest tree species is shown below.
data("Brazil_rainforest_distance_matrix")
Brazil_rainforest_distance_matrix 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 iNEXT3D() with default arguments:
iNEXT3D(data, diversity = 'TD', q = c(0,1,2), datatype = "abundance",
size = NULL, endpoint = NULL, knots = 40, nboot = 50, conf = 0.95, nT = NULL,
PDtree = NULL, PDreftime = NULL, PDtype = 'meanPD',
FDdistM, FDtype = 'AUC', FDtau = NULL, FDcut_number = 50)The arguments of this function are briefly described below, and will be
explained in more details by illustrative examples in later text. This
main function computes standardized 3D diversity estimates of order q =
0, 1 and 2, the sample coverage estimates, and related statistics for K
(if knots = K in the specified argument) evenly-spaced knots (sample
sizes) between size 1 and the endpoint, where the endpoint is
described below. Each knot represents a particular sample size for which
3D diversity estimates will be calculated. By default, endpoint =
double the reference sample size for abundance data or double the total
sampling units for incidence data. For example, if endpoint = 10,
knot = 4 is specified, diversity estimates will be computed for a
sequence of samples with sizes (1, 4, 7, 10).
| Argument | Description |
|---|---|
| data |
|
| diversity |
selection of diversity type: ‘TD’ = Taxonomic
diversity, ‘PD’ = Phylogenetic diversity, and
‘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/occurrence matrix (datatype =
‘incidence_raw’) with all entries being 0 (non-detection) or
1 (detection).
|
| size |
an integer vector of sample sizes (number of individuals or sampling
units) for which diversity estimates will be computed. If
NULL, then diversity estimates will be computed for
those sample sizes determined by the specified/default
endpoint and knots.
|
| endpoint |
an integer specifying the sample size that is the
endpoint for rarefaction/extrapolation. If NULL, then
endpoint = double the reference sample
size.
|
| knots |
an integer specifying the number of equally-spaced
knots (say K, default is 40) between size 1 and the
endpoint; each knot represents a particular sample size
for which diversity estimate will be calculated. If the
endpoint is smaller than the reference sample size,
then iNEXT3D() computes only the rarefaction estimates
for approximately K evenly spaced knots. If the
endpoint is larger than the reference sample size, then
iNEXT3D() computes rarefaction estimates for
approximately K/2 evenly spaced knots between sample
size 1 and the reference sample size, and computes extrapolation
estimates for approximately K/2 evenly spaced knots
between the reference sample size and the endpoint.
|
| nboot | a positive integer specifying the number of bootstrap replications when assessing sampling uncertainty and constructing confidence intervals. Enter 0 to skip the bootstrap procedures. Default is 50. |
| conf | a positive number \< 1 specifying the level of confidence interval. Default is 0.95. |
| nT |
(required only when datatype = ‘incidence_raw’ and
input data in a single matrix/data.frame) a vector of nonnegative
integers specifying the number of sampling units in each assemblage.
If assemblage names are not specified(i.e., names(nT) =
NULL), then assemblages are automatically named as
‘assemblage1’, ‘assemblage2’,…, etc.
|
| PDtree |
(required argument for diversity = ‘PD’), a
phylogenetic tree in Newick format for all observed species in the
pooled assemblage.
|
| PDreftime |
(argument only for diversity = ‘PD’), a vector of
numerical values specifying reference times for PD. Default is
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 ‘meanPD’, where
meanPD = PD/tree depth.
|
| 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_values’ for FD under specified threshold
values, 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 ‘AUC’.
|
| FDtau |
(argument only for diversity = ‘FD’ and FDtype =
‘tau_values’), a numerical vector between 0 and 1 specifying
tau values (threshold levels). If NULL (default), then
threshold is set to be the mean distance between any two individuals
randomly selected from the pooled assemblage (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 = 50. A larger value can be set to obtain
more accurate AUC value.
|
For each dimension of diversity (TD, PD, FD), the main function
iNEXT3D() returns the iNEXT3D object, which can be further used to
make plots using the function ggiNEXT3D() to be described below. The
"iNEXT3D" object includes three lists:
-
$TDInfo($PDInfo,or$FDInfo) for summarizing data information. -
$TDiNextEst($PDiNextEst, or$FDiNextEst) for showing diversity estimates along with related statistics for a series of rarefied and extrapolated samples; there are two data frames ($size_basedand$coverage_based) conditioning on standardized sample size or sample coverage, respectively. -
$TDAsyEst($PDAsyEst, or$FDAsyEst) for showing asymptotic diversity estimates along with related statistics.
The function ggiNEXT3D(), which extends ggplot2 with default
arguments, is described as follows:
ggiNEXT3D(output, type = 1:3, facet.var = "Assemblage", color.var = "Order.q") Here output is the iNEXT3D() object. Three types of curves are
allowed for 3D diversity:
-
Sample-size-based R/E curve (
type = 1): This curve plots diversity estimates with confidence intervals as a function of sample size. -
Sample completeness curve (
type = 2): This curve plots the sample coverage with respect to sample size. -
Coverage-based R/E curve (
type = 3): This curve plots the diversity estimates with confidence intervals as a function of sample coverage.
The argument facet.var = "Order.q", facet.var = "Assemblage",
facet.var = "Both", or facet.var = "None" is used to create a
separate plot for each value of the specified variable.
The ggiNEXT3D() function is a wrapper with the package ggplot2 to
create a rarefaction/extrapolation sampling curve in a single line of
code. The figure object is of class "ggplot", so it can be manipulated
by using the ggplot2 tools.
Based on the dataset (Brazil_rainforest_abun_data) included in the
package, the following commands return all numerical results for TD.
The first list of the output ($TDInfo) returns basic data information
including the name of the Assemblage, sample size (n), observed
species richness (S.obs), sample coverage estimate of the reference
sample with size n (SC(n)), sample coverage estimate of the
extrapolated sample with size 2n (SC(2n)) as well as the first five
species abundance frequency counts in the reference sample (f1-f5).
The output is identical to that based on the function DataInfo3D() by
specifying diversity = 'TD' and datatype = "abundance"; see later
text). Thus, if only data information is required, the simpler function
DataInfo3D() (see later text) can be used to obtain the same output.
More information about the observed diversity (for any order q between 0
and 2) can be obtained by function ObsAsy3D(), which will be
introduced later.
data(Brazil_rainforest_abun_data)
output_TD_abun <- iNEXT3D(Brazil_rainforest_abun_data, diversity = 'TD', q = c(0,1,2),
datatype = "abundance")
output_TD_abun$TDInfo$TDInfo
Assemblage n S.obs SC(n) SC(2n) f1 f2 f3 f4 f5
1 Edge 1794 319 0.939 0.974 110 48 38 28 13
2 Interior 2074 356 0.941 0.973 123 48 41 32 19
The second list of the output ($TDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the “Edge” assemblage,
corresponding to the target sample size m = 1, 95, 189, …, 1699, 1794,
1795, 1899, …, 3588), which locates the reference sample size at the
mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target sample size (m),
the Method (Rarefaction, Observed, or Extrapolation, depending
on whether the size m is less than, equal to, or greater than the
reference sample size), the diversity estimate of order q (qTD), the
lower and upper confidence limits of diversity (qTD.LCL and qTD.UCL)
conditioning on the sample size, and the corresponding sample coverage
estimate (SC) along with the lower and upper confidence limits of
sample coverage (SC.LCL and SC.UCL). These sample coverage estimates
with confidence intervals are used for plotting the sample completeness
curve. If the argument nboot is greater than zero, then a bootstrap
method is applied to obtain the confidence intervals for the diversity
and sample coverage estimates. Otherwise, all confidence intervals will
not be computed. Here only the first six rows of the $size_based
output are displayed:
output_TD_abun$TDiNextEst$size_based Assemblage Order.q m Method qTD qTD.LCL qTD.UCL SC SC.LCL SC.UCL
1 Edge 0 1 Rarefaction 1.000 1.000 1.000 0.012 0.010 0.013
2 Edge 0 95 Rarefaction 66.306 64.878 67.734 0.484 0.467 0.501
3 Edge 0 189 Rarefaction 106.743 103.952 109.535 0.638 0.622 0.653
4 Edge 0 284 Rarefaction 137.029 133.062 140.996 0.718 0.705 0.732
5 Edge 0 378 Rarefaction 161.010 156.022 165.998 0.768 0.756 0.781
6 Edge 0 472 Rarefaction 181.073 175.177 186.970 0.803 0.792 0.814
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding sample size (m), the Method
(Rarefaction, Observed, or Extrapolation, depending on whether the
coverage SC is less than, equal to, or greater than the reference
sample coverage), the diversity estimate of order q (qTD), the lower
and upper confidence limits of diversity (qTD.LCL and qTD.UCL)
conditioning on the target sample coverage value. Here only the first
six rows of the $coverage_based output are displayed below: (Note for
a fixed coverage value, the confidence interval in the $coverage_based
table is wider than the corresponding interval in the $size_based
table. This is because, for a given coverage value, the sample size
needed to attain a fixed coverage value varies with bootstrap
replication, leading to higher uncertainty on the resulting diversity
estimate.)
output_TD_abun$TDiNextEst$coverage_based Assemblage Order.q SC m Method qTD qTD.LCL qTD.UCL
1 Edge 0 0.012 1 Rarefaction 1.000 0.958 1.042
2 Edge 0 0.484 95 Rarefaction 66.306 61.580 71.032
3 Edge 0 0.638 189 Rarefaction 106.743 99.839 113.647
4 Edge 0 0.718 284 Rarefaction 137.029 128.379 145.680
5 Edge 0 0.768 378 Rarefaction 161.010 150.914 171.107
6 Edge 0 0.803 472 Rarefaction 181.073 169.728 192.419
The third list of the output ($TDAsyEst) includes the name of the
Assemblage, diversity label (qTD, species richness for q = 0, Shannon
diversity for q = 1, and Simpson diversity for q = 2), the observed
diversity (TD_obs), asymptotic diversity estimate (TD_asy) and its
estimated bootstrap standard error (s.e.) as well as the confidence
intervals for asymptotic diversity (qTD.LCL and qTD.UCL). These
statistics are computed only for q = 0, 1 and 2. More detailed
information about asymptotic and observed diversity estimates for any
order q between 0 and 2 can be obtained from function ObsAsy3D(). The
output for $TDAsyEst is shown below:
output_TD_abun$TDAsyEst Assemblage qTD TD_obs TD_asy s.e. qTD.LCL qTD.UCL
1 Edge Species richness 319.000 444.971 24.053 397.828 492.115
2 Edge Shannon diversity 155.386 178.000 4.865 168.464 187.535
3 Edge Simpson diversity 82.023 85.905 4.205 77.664 94.147
4 Interior Species richness 356.000 513.518 26.493 461.593 565.442
5 Interior Shannon diversity 163.514 186.983 5.925 175.371 198.595
6 Interior Simpson diversity 72.153 74.718 4.790 65.330 84.105
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) is given below:
# TD sample-size-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_TD_abun, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# TD sample-size-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_TD_abun, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors represent different
assemblages.
# Sample completeness curves for abundance data, separating by "Assemblage"
ggiNEXT3D(output_TD_abun, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# TD coverage-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_TD_abun, type = 3, facet.var = "Assemblage")
# TD coverage-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_TD_abun, type = 3, facet.var = "Order.q")
Based on the dataset (Fish_incidence_data) included in the package,
the following commands return all numerical results for TD. The first
list of the output ($TDInfo) returns basic data information including
the name of the Assemblage, number of sampling units (T), total number
of incidences (U), observed species richness (S.obs), sample
coverage estimate of the reference sample with size T (SC(T)), sample
coverage estimate of the extrapolated sample with size 2T (SC(2T)) as
well as the first five species incidence frequency counts in the
reference sample (Q1-Q5). The output is identical to that based on the
function DataInfo3D() by specifying diversity = 'TD' and
datatype = "incidence_raw"; see later text). Thus, if only data
information is required, the simpler function DataInfo3D() (see later
text) can be used to obtain the same output. More information about the
observed diversity (for any order q between 0 and 2) can be obtained by
function ObsAsy3D(), which will be introduced later.
data(Fish_incidence_data)
output_TD_inci <- iNEXT3D(Fish_incidence_data, diversity = 'TD', q = c(0, 1, 2),
datatype = "incidence_raw")
output_TD_inci$TDInfo$TDInfo
Assemblage T U S.obs SC(T) SC(2T) Q1 Q2 Q3 Q4 Q5
1 2013-2015 36 532 50 0.980 0.993 11 6 4 1 3
2 2016-2018 36 522 53 0.976 0.989 13 5 5 2 3
The second list of the output ($TDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the "2013-2015" time
period, corresponding to the target number of sample units mT = 1, 2,
4, …, 34, 36, 37, 38, …, 72), which locates the reference sampling units
at the mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target number of sampling
units (mT), the Method (Rarefaction, Observed, or
Extrapolation, depending on whether the target number of sample units
mT is less than, equal to, or greater than the number of sampling
units in the reference sample), the diversity estimate of order q
(qTD), the lower and upper confidence limits of diversity (qTD.LCL
and qTD.UCL) conditioning on the sample size, and the corresponding
sample coverage estimate (SC) along with the lower and upper
confidence limits of sample coverage (SC.LCL and SC.UCL). These
sample coverage estimates with confidence intervals are used for
plotting the sample completeness curve. If the argument nboot is
greater than zero, then a bootstrap method is applied to obtain the
confidence intervals for the diversity and sample coverage estimates.
Otherwise, all confidence intervals will not be computed. Here only the
first six rows of the $size_based output are displayed:
output_TD_inci$TDiNextEst$size_based Assemblage Order.q mT Method qTD qTD.LCL qTD.UCL SC SC.LCL SC.UCL
1 2013-2015 0 1 Rarefaction 14.778 14.035 15.521 0.606 0.574 0.637
2 2013-2015 0 2 Rarefaction 20.603 19.639 21.567 0.749 0.726 0.772
3 2013-2015 0 4 Rarefaction 27.079 25.703 28.455 0.851 0.834 0.867
4 2013-2015 0 6 Rarefaction 31.121 29.430 32.813 0.894 0.880 0.908
5 2013-2015 0 8 Rarefaction 34.042 32.095 35.989 0.919 0.907 0.931
6 2013-2015 0 10 Rarefaction 36.319 34.149 38.488 0.934 0.923 0.945
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding number of sampling units (mT), the
Method (Rarefaction, Observed, or Extrapolation, depending on
whether the coverage SC is less than, equal to, or greater than the
reference sample coverage), the diversity estimate of order q (qTD),
the lower and upper confidence limits of diversity (qTD.LCL and
qTD.UCL) conditioning on the target sample coverage value. Here only
the first six rows of the $coverage_based output are displayed below:
(Note for a fixed coverage value, the confidence interval in the
$coverage_based table is wider than the corresponding interval in the
$size_based table. This is because, for a given coverage value, the
sample size needed to attain a fixed coverage value varies with
bootstrap replication, leading to higher uncertainty on the resulting
diversity estimate.)
output_TD_inci$TDiNextEst$coverage_based Assemblage Order.q SC mT Method qTD qTD.LCL qTD.UCL
1 2013-2015 0 0.606 1 Rarefaction 14.778 13.999 15.556
2 2013-2015 0 0.749 2 Rarefaction 20.603 19.158 22.049
3 2013-2015 0 0.851 4 Rarefaction 27.079 24.966 29.193
4 2013-2015 0 0.894 6 Rarefaction 31.121 28.553 33.690
5 2013-2015 0 0.919 8 Rarefaction 34.042 31.102 36.982
6 2013-2015 0 0.934 10 Rarefaction 36.319 33.010 39.628
The third list of the output ($TDAsyEst) includes the name of the
Assemblage, diversity label (qTD, species richness for q = 0, Shannon
diversity for q = 1, and Simpson diversity for q = 2), the observed
diversity (TD_obs), asymptotic diversity estimate (TD_asy) and its
estimated bootstrap standard error (s.e.) as well as the confidence
intervals for asymptotic diversity (qTD.LCL and qTD.UCL). These
statistics are computed only for q = 0, 1 and 2. More detailed
information about asymptotic and observed diversity estimates for any
order q between 0 and 2 can be obtained from function ObsAsy3D(). The
output is shown below:
output_TD_inci$TDAsyEst Assemblage qTD TD_obs TD_asy s.e. qTD.LCL qTD.UCL
1 2013-2015 Species richness 50.000 59.803 8.208 43.716 75.890
2 2013-2015 Shannon diversity 30.089 31.542 1.185 29.219 33.864
3 2013-2015 Simpson diversity 23.961 24.394 0.754 22.915 25.873
4 2016-2018 Species richness 53.000 69.431 10.444 48.961 89.900
5 2016-2018 Shannon diversity 31.534 33.393 1.252 30.940 35.847
6 2016-2018 Simpson diversity 24.889 25.409 0.738 23.963 26.855
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) for incidence data is given below:
# TD sample-size-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_TD_inci, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# TD sample-size-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_TD_inci, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors are used for different
assemblages.
# Sample completeness curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_TD_inci, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# TD coverage-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_TD_inci, type = 3, facet.var = "Assemblage")
# TD coverage-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_TD_inci, type = 3, facet.var = "Order.q")
Based on the dataset (Brazil_rainforest_abun_data) and the phylogentic
tree (Brazil_rainforest_phylo_tree) included in the package, the
following commands return all numerical results for PD. The first list
of the output ($PDInfo) returns basic data information including the
name of the Assemblage, sample size (n), observed species richness
(S.obs), sample coverage estimate of the reference sample with size n
(SC(n)), sample coverage estimate of the extrapolated sample with size
2n (SC(2n)), the observed total branch length in the phylogenetic tree
spanned by all observed specise (PD.obs), the number of singletons and
doubletons in the node/branch abundance set (f1*,f2*), the total
branch length of those singletons and doubletons in the node/branch
abundance set (g1,g2), and the reference time (Reftime). The output
is identical to that based on the function DataInfo3D() by specifying
diversity = 'PD' and datatype = "abundance"; see later text). Thus,
if only data information is required, the simpler function
DataInfo3D() (see later text) can be used to obtain the same output.
More information about the observed diversity (for any order q between 0
and 2) can be obtained by function ObsAsy3D(), which will be
introduced later.
The required argument for performing PD analysis is PDtree. For
example, the phylogenetic tree for all observed species (including
species in both Edge and Interior habitats) is stored in
Brazil_rainforest_phylo_tree. Then we enter the argument
PDtree = Brazil_rainforest_phylo_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.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_phylo_tree)
data <- Brazil_rainforest_abun_data
tree <- Brazil_rainforest_phylo_tree
output_PD_abun <- iNEXT3D(data, diversity = 'PD', q = c(0, 1, 2), datatype = "abundance",
nboot = 20, PDtree = tree)
output_PD_abun$PDInfo$PDInfo
# A tibble: 2 x 11
Assemblage n S.obs `SC(n)` `SC(2n)` PD.obs `f1*` `f2*` g1 g2 Reftime
<chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Edge 1794 319 0.939 0.974 24516 110 52 6578 2885 400
2 Interior 2074 356 0.941 0.973 27727 123 56 7065 3656 400
The second list of the output ($PDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the “Edge” assemblage,
corresponding to the target sample size m = 1, 95, 189, …, 1699, 1794,
1795, 1899, …, 3588), which locates the reference sample size at the
mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target sample size (m),
the Method (Rarefaction, Observed, or Extrapolation, depending
on whether the size m is less than, equal to, or greater than the
reference sample size), the diversity estimate of order q (qPD), the
lower and upper confidence limits of diversity (qPD.LCL and qPD.UCL)
conditioning on the sample size, the corresponding sample coverage
estimate (SC) along with the lower and upper confidence limits of
sample coverage (SC.LCL and SC.UCL), the reference time (Reftime)
and the type of PD (Type). These sample coverage estimates with
confidence intervals are used for plotting the sample completeness
curve. If the argument nboot is greater than zero, then a bootstrap
method is applied to obtain the confidence intervals for the diversity
and sample coverage estimates. Otherwise, all confidence intervals will
not be computed. Here only the first six rows of the $size_based
output are displayed:
output_PD_abun$PDiNextEst$size_based Assemblage Order.q m Method qPD qPD.LCL qPD.UCL SC SC.LCL SC.UCL Reftime Type
1 Edge 0 1 Rarefaction 1.000 0.989 1.011 0.012 0.011 0.013 400 meanPD
2 Edge 0 95 Rarefaction 18.547 18.090 19.004 0.484 0.470 0.498 400 meanPD
3 Edge 0 189 Rarefaction 26.723 26.039 27.407 0.638 0.625 0.650 400 meanPD
4 Edge 0 284 Rarefaction 32.305 31.458 33.153 0.718 0.707 0.730 400 meanPD
5 Edge 0 378 Rarefaction 36.498 35.522 37.475 0.768 0.758 0.779 400 meanPD
6 Edge 0 472 Rarefaction 39.882 38.791 40.972 0.803 0.792 0.814 400 meanPD
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding sample size (m), the Method
(Rarefaction, Observed, or Extrapolation, depending on whether the
coverage SC is less than, equal to, or greater than the reference
sample coverage), the diversity estimate of order q (qPD), the lower
and upper confidence limits of diversity (qPD.LCL and qPD.UCL)
conditioning on the target sample coverage value, the reference times
(Reftime) and the type of PD (Type). Here only the first six rows of
the $coverage_based output are displayed below: (Note for a fixed
coverage value, the confidence interval in the $coverage_based table
is wider than the corresponding interval in the $size_based table.
This is because, for a given coverage value, the sample size needed to
attain a fixed coverage value varies with bootstrap replication, leading
to higher uncertainty on the resulting diversity estimate.)
output_PD_abun$PDiNextEst$coverage_based Assemblage Order.q SC m Method qPD qPD.LCL qPD.UCL Reftime Type
1 Edge 0 0.012 1 Rarefaction 1.000 0.977 1.023 400 meanPD
2 Edge 0 0.484 95 Rarefaction 18.547 17.705 19.388 400 meanPD
3 Edge 0 0.638 189 Rarefaction 26.723 25.592 27.854 400 meanPD
4 Edge 0 0.718 284 Rarefaction 32.305 30.931 33.679 400 meanPD
5 Edge 0 0.768 378 Rarefaction 36.498 34.900 38.097 400 meanPD
6 Edge 0 0.803 472 Rarefaction 39.882 38.070 41.693 400 meanPD
The third list of the output ($PDAsyEst) includes the name of the
Assemblage, PD (or meanPD) for q = 0, 1, and 2 (qPD), the observed
diversity (PD_obs), asymptotic diversity estimates (PD_asy),
estimated asymptotic bootstrap standard error (s.e.) as well as the
confidence intervals for asymptotic diversity with q = 0, 1, and 2
(qPD.LCL and qPD.UCL), the reference times (Reftime) and the type
of PD (Type). These statistics are computed only for q = 0, 1 and 2.
More detailed information about asymptotic and observed diversity
estimates for any order q between 0 and 2 can be obtained from function
ObsAsy3D(). The output is shown below:
output_PD_abun$PDAsyEst Assemblage qPD PD_obs PD_asy s.e. qPD.LCL qPD.UCL Reftime Type
1 Edge q = 0 PD 61.290 80.027 4.638 70.936 89.118 400 meanPD
2 Edge q = 1 PD 5.246 5.372 0.147 5.084 5.660 400 meanPD
3 Edge q = 2 PD 1.797 1.798 0.032 1.735 1.860 400 meanPD
4 Interior q = 0 PD 69.318 86.375 4.199 78.145 94.605 400 meanPD
5 Interior q = 1 PD 5.721 5.854 0.121 5.616 6.092 400 meanPD
6 Interior q = 2 PD 1.914 1.915 0.031 1.854 1.975 400 meanPD
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) is given below:
# PD sample-size-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_PD_abun, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# PD sample-size-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_PD_abun, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors are used for different
assemblages.
# Sample completeness curves for abundance data, separating by "Assemblage"
ggiNEXT3D(output_PD_abun, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# PD coverage-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_PD_abun, type = 3, facet.var = "Assemblage")
# PD coverage-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_PD_abun, type = 3, facet.var = "Order.q")
Based on the dataset (Fish_incidence_data) included in the package and
the phylogentic tree (Fish_phylo_tree), the following commands return
all numerical results for PD. The first list of the output ($PDInfo)
returns basic data information including the name of the Assemblage,
number of sampling units (T), total number of incidences (U),
observed species richness (S.obs), sample coverage estimate of the
reference sample with size T (SC(T)), sample coverage estimate of the
extrapolated sample with size 2T (SC(2T)), the observed total branch
length in the phylogenetic tree spanned by all observed species
(PD.obs), the singletons/doubletons in the sample branch incidence
(Q1*,Q2*), the total branch length of those singletons/doubletons in
the sample branch incidence (R1,R2), and the reference time
(Reftime). The output is identical to that based on the function
DataInfo3D() by specifying diversity = 'PD' and
datatype = "incidence_raw"; see later text). Thus, if only data
information is required, the simpler function DataInfo3D() (see later
text) can be used to obtain the same output. More information about the
observed diversity (for any order q between 0 and 2) can be obtained by
function ObsAsy3D(), which will be introduced later.
The required argument for performing PD analysis is PDtree. For
example, the phylogenetic tree for all observed species (including
species in both "2013-2015" and "2016-2018" time periods) is stored
in Fish_phylo_tree. Then we enter the argument
PDtree = Fish_phylo_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.
data(Fish_incidence_data)
data(Fish_phylo_tree)
data <- Fish_incidence_data
tree <- Fish_phylo_tree
output_PD_inci <- iNEXT3D(data, diversity = 'PD', q = c(0, 1, 2),
datatype = "incidence_raw", nboot = 20, PDtree = tree)
output_PD_inci$PDInfo$PDInfo
# A tibble: 2 x 12
Assemblage T U S.obs `SC(T)` `SC(2T)` PD.obs `Q1*` `Q2*` R1 R2 Reftime
<chr> <int> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 2013-2015 36 532 50 0.98 0.993 9.62 11 7 0.69 1.23 0.977
2 2016-2018 36 522 53 0.976 0.989 9.44 13 6 0.368 0.345 0.977
The second list of the output ($PDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the "2013-2015" time
period, corresponding to the target number of sample units mT = 1, 2,
4, …, 34, 36, 37, 38, …, 72), which locates the reference sampling units
at the mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target number of sample
units (mT), the Method (Rarefaction, Observed, or
Extrapolation, depending on whether the target number of sample units
mT is less than, equal to, or greater than the number of sampling
units in the reference sample), the diversity estimate of order q
(qPD), the lower and upper confidence limits of diversity (qPD.LCL
and qPD.UCL) conditioning on the sample size, the corresponding sample
coverage estimate (SC) along with the lower and upper confidence
limits of sample coverage (SC.LCL and SC.UCL), the reference time
(Reftime) and the type of PD (Type). These sample coverage estimates
with confidence intervals are used for plotting the sample completeness
curve. If the argument nboot is greater than zero, then a bootstrap
method is applied to obtain the confidence intervals for the diversity
and sample coverage estimates. Otherwise, all confidence intervals will
not be computed. Here only the first six rows of the $size_based
output are displayed:
output_PD_inci$PDiNextEst$size_based Assemblage Order.q mT Method qPD qPD.LCL qPD.UCL SC SC.LCL SC.UCL Reftime Type
1 2013-2015 0 1 Rarefaction 5.744 5.518 5.969 0.606 0.576 0.635 0.977 meanPD
2 2013-2015 0 2 Rarefaction 6.813 6.551 7.075 0.749 0.731 0.767 0.977 meanPD
3 2013-2015 0 4 Rarefaction 7.716 7.447 7.986 0.851 0.840 0.861 0.977 meanPD
4 2013-2015 0 6 Rarefaction 8.130 7.813 8.446 0.894 0.886 0.903 0.977 meanPD
5 2013-2015 0 8 Rarefaction 8.389 8.012 8.767 0.919 0.911 0.927 0.977 meanPD
6 2013-2015 0 10 Rarefaction 8.589 8.151 9.027 0.934 0.926 0.941 0.977 meanPD
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding number of sample units (mT), the
Method (Rarefaction, Observed, or Extrapolation, depending on
whether the coverage SC is less than, equal to, or greater than the
reference sample coverage), the diversity estimate of order q (qPD),
the lower and upper confidence limits of diversity (qPD.LCL and
qPD.UCL) conditioning on the target sample coverage value, the
reference time (Reftime) and the type of PD (Type). Here only the
first six rows of the $coverage_based output are displayed below:
(Note for a fixed coverage value, the confidence interval in the
$coverage_based table is wider than the corresponding interval in the
$size_based table. This is because, for a given coverage value, the
sample size needed to attain a fixed coverage value varies with
bootstrap replication, leading to higher uncertainty on the resulting
diversity estimate.)
output_PD_inci$PDiNextEst$coverage_based Assemblage Order.q SC mT Method qPD qPD.LCL qPD.UCL Reftime Type
1 2013-2015 0 0.606 1 Rarefaction 5.744 5.504 5.983 0.977 meanPD
2 2013-2015 0 0.749 2 Rarefaction 6.813 6.557 7.069 0.977 meanPD
3 2013-2015 0 0.851 4 Rarefaction 7.716 7.455 7.978 0.977 meanPD
4 2013-2015 0 0.894 6 Rarefaction 8.130 7.811 8.448 0.977 meanPD
5 2013-2015 0 0.919 8 Rarefaction 8.389 8.003 8.776 0.977 meanPD
6 2013-2015 0 0.934 10 Rarefaction 8.589 8.138 9.041 0.977 meanPD
The third list of the output ($PDAsyEst) includes the name of the
Assemblage, PD (or meanPD) for q = 0, 1, and 2 (qPD), the observed
diversity (PD_obs), asymptotic diversity estimate (PD_asy) and its
estimated bootstrap standard error (s.e.), the confidence intervals
for asymptotic diversity (qPD.LCL and qPD.UCL), the reference time
(Reftime) and the type of PD (Type) . These statistics are computed
only for q = 0, 1 and 2. More detailed information about asymptotic and
observed diversity estimates for any order q between 0 and 2 can be
obtained from function ObsAsy3D(). The output is shown below:
output_PD_inci$PDAsyEst Assemblage qPD PD_obs PD_asy s.e. qPD.LCL qPD.UCL Reftime Type
1 2013-2015 q = 0 PD 9.847 10.039 0.651 8.764 11.315 0.977 meanPD
2 2013-2015 q = 1 PD 7.635 7.729 0.169 7.397 8.061 0.977 meanPD
3 2013-2015 q = 2 PD 7.013 7.057 0.160 6.744 7.371 0.977 meanPD
4 2016-2018 q = 0 PD 9.659 9.854 1.309 7.288 12.420 0.977 meanPD
5 2016-2018 q = 1 PD 7.781 7.859 0.194 7.478 8.240 0.977 meanPD
6 2016-2018 q = 2 PD 7.202 7.244 0.185 6.882 7.606 0.977 meanPD
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) is given below:
# PD sample-size-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_PD_inci, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# PD sample-size-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_PD_inci, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors are used for different
assemblages.
# Sample completeness curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_PD_inci, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# PD coverage-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_PD_inci, type = 3, facet.var = "Assemblage")
# PD coverage-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_PD_inci, type = 3, facet.var = "Order.q")
Based on the dataset (Brazil_rainforest_abun_data) and the the
distance matrix (Brazil_rainforest_distance_matrix) included in the
package, the following commands return all numerical results for FD.
The first list of the output ($FDInfo) returns basic data information
including the name of the Assemblage, sample size (n), observed
species richness (S.obs), sample coverage estimate of the reference
sample with size n (SC(n)), sample coverage estimate of the
extrapolated sample with size 2n (SC(2n)), and the minimum, mean, and
maximum distance among all non-diagonal elements in the distance
matrix(dmin, dmean, dmax). The output is identical to that based on
the function DataInfo3D() by specifying diversity = 'FD' and
datatype = "abundance"; see later text). Thus, if only data
information is required, the simpler function DataInfo3D() (see later
text) can be used to obtain the same output. More information about the
observed diversity (for any order q between 0 and 2) can be obtained by
function ObsAsy3D(), which will be introduced later.
The required argument for performing FD analysis is FDdistM. For
example, the distance matrix for all species (including species in both
Edge and Interior habitats) is stored in
Brazil_rainforest_distance_matrix. Then we enter the argument
FDdistM = Brazil_rainforest_distance_matrix 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_values" means FD is
computed under specific threshold values 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_values" 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 data (i.e., quadratic entropy).
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_distance_matrix)
data <- Brazil_rainforest_abun_data
distM <- Brazil_rainforest_distance_matrix
output_FD_abun <- iNEXT3D(data, diversity = 'FD', datatype = "abundance", nboot = 10,
FDdistM = distM, FDtype = 'AUC')
output_FD_abun$FDInfo$FDInfo
Assemblage n S.obs SC(n) SC(2n) dmin dmean dmax
1 Edge 1794 319 0.939 0.974 0 0.372 0.776
2 Interior 2074 356 0.941 0.973 0 0.329 0.776
The second list of the output ($FDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the “Edge” assemblage,
corresponding to the target sample size m = 1, 95, 189, …, 1699, 1794,
1795, 1899, …, 3588), which locates the reference sample size at the
mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target sample size (m),
the Method (Rarefaction, Observed, or Extrapolation, depending
on whether the size m is less than, equal to, or greater than the
reference sample size), the diversity estimate of order q (qFD), the
lower and upper confidence limits of diversity (qFD.LCL and qFD.UCL)
conditioning on the sample size, and the corresponding sample coverage
estimate (SC) along with the lower and upper confidence limits of
sample coverage (SC.LCL and SC.UCL). These sample coverage estimates
with confidence intervals are used for plotting the sample completeness
curve. If the argument nboot is greater than zero, then a bootstrap
method is applied to obtain the confidence intervals for the diversity
and sample coverage estimates. Otherwise, all confidence intervals will
not be computed. Here only the first six rows of the $size_based
output are displayed:
output_FD_abun$FDiNextEst$size_based Assemblage Order.q m Method qFD qFD.LCL qFD.UCL SC SC.LCL SC.UCL
1 Edge 0 1 Rarefaction 1.000 1.000 1.000 0.012 0.010 0.013
2 Edge 0 95 Rarefaction 10.900 10.585 11.215 0.484 0.466 0.502
3 Edge 0 189 Rarefaction 12.993 12.453 13.532 0.638 0.625 0.650
4 Edge 0 284 Rarefaction 14.129 13.405 14.853 0.718 0.710 0.727
5 Edge 0 378 Rarefaction 14.860 13.982 15.738 0.768 0.762 0.775
6 Edge 0 472 Rarefaction 15.383 14.369 16.397 0.803 0.797 0.809
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding sample size (m), the Method
(Rarefaction, Observed, or Extrapolation, depending on whether the
coverage SC is less than, equal to, or greater than the reference
sample coverage), the diversity estimate of order q (qFD), and the
lower and upper confidence limits of diversity (qFD.LCL and qFD.UCL)
conditioning on the target sample coverage value. Here only the first
six rows of the $coverage_based output are displayed below: (Note for
a fixed coverage value, the confidence interval in the $coverage_based
table is wider than the corresponding interval in the $size_based
table. This is because, for a given coverage value, the sample size
needed to attain a fixed coverage value varies with bootstrap
replication, leading to higher uncertainty on the resulting diversity
estimate.)
output_FD_abun$FDiNextEst$coverage_based Assemblage Order.q SC m Method qFD qFD.LCL qFD.UCL
1 Edge 0 0.012 1 Rarefaction 1.000 0.993 1.007
2 Edge 0 0.484 95 Rarefaction 10.900 10.497 11.303
3 Edge 0 0.638 189 Rarefaction 12.993 12.439 13.546
4 Edge 0 0.718 284 Rarefaction 14.129 13.431 14.827
5 Edge 0 0.768 378 Rarefaction 14.860 14.021 15.700
6 Edge 0 0.803 472 Rarefaction 15.383 14.398 16.368
The third list of the output ($FDAsyEst) includes the name of the
Assemblage, FD for q = 0, 1, and 2 (qFD), the observed diversity
(FD_obs), asymptotic diversity estimate (FD_asy) and its estimated
bootstrap standard error (s.e.) as well as the confidence intervals
for asymptotic diversity (qFD.LCL and qFD.UCL). These statistics are
computed only for q = 0, 1 and 2. More detailed information about
asymptotic and observed diversity estimates for any order q between 0
and 2 can be obtained from function ObsAsy3D(). The output is shown
below:
output_FD_abun$FDAsyEst Assemblage qFD FD_obs FD_asy s.e. qFD.LCL qFD.UCL
1 Edge q = 0 FD(AUC) 17.851 19.008 6.753 5.771 32.244
2 Edge q = 1 FD(AUC) 11.781 12.037 0.420 11.214 12.860
3 Edge q = 2 FD(AUC) 9.139 9.228 0.292 8.657 9.800
4 Interior q = 0 FD(AUC) 17.168 18.208 10.050 0.000 37.907
5 Interior q = 1 FD(AUC) 9.716 9.922 0.429 9.081 10.763
6 Interior q = 2 FD(AUC) 7.007 7.055 0.184 6.694 7.416
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) is given below:
# FD sample-size-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_FD_abun, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# FD sample-size-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_FD_abun, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors are used for different
assemblages.
# Sample completeness curves for abundance data, separating by "Assemblage"
ggiNEXT3D(output_FD_abun, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# FD coverage-based R/E curves, separating by "Assemblage"
ggiNEXT3D(output_FD_abun, type = 3, facet.var = "Assemblage")
# FD coverage-based R/E curves, separating by "Order.q"
ggiNEXT3D(output_FD_abun, type = 3, facet.var = "Order.q")
Based on the dataset (Fish_incidence_data) and the the distance matrix
(Fish_distance_matrix) included in the package, the following commands
return all numerical results for FD. The first list of the output
($FDInfo) returns basic data information including the name of the
Assemblage, number of sampling units (T), total number of incidences
(U), observed species richness (S.obs), sample coverage estimate of
the reference sample with size T (SC(T)), sample coverage estimate of
the reference sample with size 2T (SC(2T)), and the minimum, mean, and
maximum distance among all non-diagonal elements in the distance
matrix(dmin, dmean, dmax). The output is identical to that based on
the function DataInfo3D() by specifying diversity = 'FD' and
datatype = "incidence_raw"; see later text). Thus, if only data
information is required, the simpler function DataInfo3D() (see later
text) can be used to obtain the same output. More information about the
observed diversity (for any order q between 0 and 2) can be obtained by
function ObsAsy3D(), which will be introduced later.
The required argument for performing FD analysis is FDdistM. For
example, the distance matrix for all species (including species in both
"2013-2015" and "2016-2018" time periods) is stored in
Fish_distance_matrix. Then we enter the argument
FDdistM = Fish_distance_matrix 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_values" means FD is computed under
specific threshold values 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_values" 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 data (i.e., quadratic entropy).
data(Fish_incidence_data)
data(Fish_distance_matrix)
data <- Fish_incidence_data
distM <- Fish_distance_matrix
output_FD_inci <- iNEXT3D(data, diversity = 'FD', datatype = "incidence_raw", nboot = 20,
FDdistM = distM, FDtype = 'AUC')
output_FD_inci$FDInfo$FDInfo
Assemblage T U S.obs SC(T) SC(2T) dmin dmean dmax
1 2013-2015 36 532 50 0.980 0.993 0.006 0.240 0.733
2 2016-2018 36 522 53 0.976 0.989 0.006 0.237 0.733
The second list of the output ($FDiNextEst) includes size- and
coverage-based standardized diversity estimates and related statistics
computed for 40 knots by default (for example in the "2013-2015" time
period, corresponding to the target number of sample units mT = 1, 2,
4, …, 34, 36, 37, 38, …, 72), which locates the reference sampling units
at the mid-point of the selected knots. There are two data frames
($size_based and $coverage_based).
The first data frame ($size_based) includes the name of the
Assemblage, diversity order (Order.q), the target number of sample
units (mT), the Method (Rarefaction, Observed, or
Extrapolation, depending on whether the target number of sample units
mT is less than, equal to, or greater than the number of sampling
units in the reference sample), the diversity estimate of order q
(qFD), the lower and upper confidence limits of diversity (qFD.LCL
and qFD.UCL) conditioning on the sample size, and the corresponding
sample coverage estimate (SC) along with the lower and upper
confidence limits of sample coverage (SC.LCL and SC.UCL). These
sample coverage estimates with confidence intervals are used for
plotting the sample completeness curve. If the argument nboot is
greater than zero, then a bootstrap method is applied to obtain the
confidence intervals for the diversity and sample coverage estimates.
Otherwise, all confidence intervals will not be computed. Here only the
first six rows of the $size_based output are displayed:
output_FD_inci$FDiNextEst$size_based Assemblage Order.q mT Method qFD qFD.LCL qFD.UCL SC SC.LCL SC.UCL
1 2013-2015 0 1 Rarefaction 14.778 13.788 15.768 0.606 0.573 0.638
2 2013-2015 0 2 Rarefaction 15.318 14.309 16.328 0.749 0.720 0.778
3 2013-2015 0 4 Rarefaction 15.888 14.855 16.920 0.851 0.829 0.873
4 2013-2015 0 6 Rarefaction 16.224 15.171 17.276 0.894 0.876 0.912
5 2013-2015 0 8 Rarefaction 16.463 15.386 17.539 0.919 0.903 0.934
6 2013-2015 0 10 Rarefaction 16.652 15.549 17.755 0.934 0.920 0.947
The second data frame ($coverage_based) includes the name of
assemblage, the diversity order (Order.q), the target sample coverage
value (SC), the corresponding number of sample units (mT), the
Method (Rarefaction, Observed, or Extrapolation, depending on
whether the coverage SC is less than, equal to, or greater than the
reference sample coverage), the diversity estimate of order q (qFD),
and the lower and upper confidence limits of diversity (qFD.LCL and
qFD.UCL) conditioning on the target sample coverage value. Here only
the first six rows of the $coverage_based output are displayed below:
(Note for a fixed coverage value, the confidence interval in the
$coverage_based table is wider than the corresponding interval in the
$size_based table. This is because, for a given coverage value, the
sample size needed to attain a fixed coverage value varies with
bootstrap replication, leading to higher uncertainty on the resulting
diversity estimate.)
output_FD_inci$FDiNextEst$coverage_based Assemblage Order.q SC mT Method qFD qFD.LCL qFD.UCL
1 2013-2015 0 0.606 1 Rarefaction 14.778 13.904 15.652
2 2013-2015 0 0.749 2 Rarefaction 15.318 14.455 16.182
3 2013-2015 0 0.851 4 Rarefaction 15.888 14.999 16.776
4 2013-2015 0 0.894 6 Rarefaction 16.224 15.299 17.148
5 2013-2015 0 0.919 8 Rarefaction 16.463 15.491 17.434
6 2013-2015 0 0.934 10 Rarefaction 16.652 15.629 17.675
The third list of the output ($FDAsyEst) includes the name of the
Assemblage, FD for q = 0, 1, and 2 (qFD), the observed diversity
(FD_obs), asymptotic diversity estimate (FD_asy) and its estimated
bootstrap standard error (s.e.), and the confidence intervals for
asymptotic diversity (qFD.LCL and qFD.UCL). These statistics are
computed only for q = 0, 1 and 2. More detailed information about
asymptotic and observed diversity estimates for any order q between 0
and 2 can be obtained from function ObsAsy3D(). The output is shown
below:
output_FD_inci$FDAsyEst Assemblage qFD FD_obs FD_asy s.e. qFD.LCL qFD.UCL
1 2013-2015 q = 0 FD(AUC) 17.904 18.906 2.659 13.693 24.118
2 2013-2015 q = 1 FD(AUC) 15.944 16.043 0.454 15.154 16.932
3 2013-2015 q = 2 FD(AUC) 15.463 15.490 0.441 14.625 16.355
4 2016-2018 q = 0 FD(AUC) 17.739 19.770 3.201 13.495 26.045
5 2016-2018 q = 1 FD(AUC) 15.749 15.867 0.473 14.940 16.795
6 2016-2018 q = 2 FD(AUC) 15.275 15.305 0.443 14.436 16.174
The ggiNEXT3D function can be used to make graphical displays for
rarefaction and extrapolation sampling curves. When
facet.var = "Assemblage" is specified in the ggiNEXT3D function, it
creates a separate plot for each assemblage; within each assemblage,
different color curves represent diversity of different orders. An
example for showing sample-size-based rarefaction/extrapolation curves
(type = 1) is given below:
# FD sample-size-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_FD_inci, type = 1, facet.var = "Assemblage")
When facet.var = "Order.q" is specified in the ggiNEXT3D function,
it creates a separate plot for each diversity order; within each plot,
different color curves represent different assemblages. An example is
shown below:
# FD sample-size-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_FD_inci, type = 1, facet.var = "Order.q")
The following commands return the sample completeness (sample coverage)
curve (type = 2) in which different colors are used for different
assemblages.
# Sample completeness curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_FD_inci, type = 2, color.var = "Assemblage")
The following commands return the coverage-based
rarefaction/extrapolation sampling curves in which different color
curves represent three diversity orders within each assemblage
(facet.var = "Assemblage"), or represent two assemblages within each
diversity order (facet.var = "Order.q"), respectively.
# FD coverage-based R/E curves for incidence data, separating by "Assemblage"
ggiNEXT3D(output_FD_inci, type = 3, facet.var = "Assemblage")
# FD coverage-based R/E curves for incidence data, separating by "Order.q"
ggiNEXT3D(output_FD_inci, type = 3, facet.var = "Order.q")
The function DataInfo3D() provides basic data information for the
reference sample in each individual assemblage. The function
DataInfo3D() with default arguments is shown below:
DataInfo3D(data, diversity = "TD", datatype = "abundance",
nT = NULL, PDtree, PDreftime = NULL,
FDdistM, FDtype = "AUC", FDtau = NULL) All arguments in the above function are the same as those for the main
function iNEXT3D. Running the DataInfo3D() 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_rainforest_abun_data and Fish_incidence_data to demo the
function for each dimension of diversity.
data(Brazil_rainforest_abun_data)
DataInfo3D(Brazil_rainforest_abun_data, diversity = 'TD', datatype = "abundance") Assemblage n S.obs SC(n) SC(2n) f1 f2 f3 f4 f5
1 Edge 1794 319 0.939 0.974 110 48 38 28 13
2 Interior 2074 356 0.941 0.973 123 48 41 32 19
Output description:
-
Assemblage= assemblage name. -
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 with size n. -
SC(2n)= sample coverage estimate of the reference sample with size 2n. -
f1-f5= the first five species abundance frequency counts in the reference sample.
data(Fish_incidence_data)
DataInfo3D(Fish_incidence_data, diversity = 'TD', datatype = "incidence_raw") Assemblage T U S.obs SC(T) SC(2T) Q1 Q2 Q3 Q4 Q5
1 2013-2015 36 532 50 0.980 0.993 11 6 4 1 3
2 2016-2018 36 522 53 0.976 0.989 13 5 5 2 3
Output description:
-
Assemblage= assemblage name. -
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 with size T. -
SC(2T)= sample coverage estimate of the reference sample with size 2T. -
Q1-Q5= the first five species incidence frequency counts in the reference sample.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_phylo_tree)
data <- Brazil_rainforest_abun_data
tree <- Brazil_rainforest_phylo_tree
DataInfo3D(data, diversity = 'PD', datatype = "abundance", PDtree = tree)# A tibble: 2 x 11
Assemblage n S.obs `SC(n)` `SC(2n)` PD.obs `f1*` `f2*` g1 g2 Reftime
<chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Edge 1794 319 0.939 0.974 24516 110 52 6578 2885 400
2 Interior 2074 356 0.941 0.973 27727 123 56 7065 3656 400
Output description:
-
Assemblage,n,S.obs,SC(n)andSC(2n): definitions are the same as in the TD abundance output and thus are omitted. -
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(Fish_incidence_data)
data(Fish_phylo_tree)
data <- Fish_incidence_data
tree <- Fish_phylo_tree
DataInfo3D(data, diversity = 'PD', datatype = "incidence_raw", PDtree = tree)# A tibble: 2 x 12
Assemblage T U S.obs `SC(T)` `SC(2T)` PD.obs `Q1*` `Q2*` R1 R2 Reftime
<chr> <int> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 2013-2015 36 532 50 0.98 0.993 9.62 11 7 0.69 1.23 0.977
2 2016-2018 36 522 53 0.976 0.989 9.44 13 6 0.368 0.345 0.977
Output description:
-
Assemblage,T,U,S.obs,SC(T)andSC(2T): definitions are the same as in the TD incidence output and thus are omitted. -
PD.obs= the observed total branch length in the phylogenetic tree spanned by all observed species. -
Q1*,Q2*= the singletons/doubletons in the sample branch incidence. -
R1,R2= the total branch length of those singletons/doubletons in the sample branch incidence. -
Reftime= reference time.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_distance_matrix)
data <- Brazil_rainforest_abun_data
distM <- Brazil_rainforest_distance_matrix
DataInfo3D(data, diversity = 'FD', datatype = "abundance",
FDdistM = distM, FDtype = 'AUC') Assemblage n S.obs SC(n) SC(2n) dmin dmean dmax
1 Edge 1794 319 0.939 0.974 0 0.372 0.776
2 Interior 2074 356 0.941 0.973 0 0.329 0.776
Output description:
-
Assemblage,n,S.obs,SC(n)andSC(2n): definitions are the same as in TD abundance output 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.
data(Fish_incidence_data)
data(Fish_distance_matrix)
data <- Fish_incidence_data
distM <- Fish_distance_matrix
DataInfo3D(data, diversity = 'FD', datatype = "incidence_raw",
FDdistM = distM, FDtype = 'AUC') Assemblage T U S.obs SC(T) SC(2T) dmin dmean dmax
1 2013-2015 36 532 50 0.980 0.993 0.006 0.240 0.733
2 2016-2018 36 522 53 0.976 0.989 0.006 0.237 0.733
Output description:
-
Assemblage,T,U,S.obs,SC(T)andSC(2T): definitions are the same as in the TD incidence output 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.
estimate3D is used to compute 3D diversity (TD, PD, FD) estimates with
q = 0, 1, 2 under any specified levels of sample size (when
base = "size") and sample coverage values (when base = "coverage")
for abundance data (datatype = "abundance") or incidence data
(datatype = "incidence_raw"). When base = "size", level can be
specified with a particular vector of sample sizes (greater than 0); if
level = NULL, this function computes the diversity estimates for the
minimum sample size among all samples extrapolated to the double
reference sizes. When base = "coverage", level can be specified with
a particular vector of sample coverage values (between 0 and 1); if
level = NULL, this function computes the diversity estimates for the
minimum sample coverage among all samples extrapolated to the double
reference sizes. All arguments in the function are the same as those for
the main function iNEXT3D.
estimate3D(data, diversity = "TD", q = c(0, 1, 2), datatype = "abundance",
base = "coverage", level = NULL, nboot = 50, conf = 0.95,
nT = NULL, PDtree, PDreftime = NULL, PDtype = "meanPD",
FDdistM, FDtype = "AUC", FDtau = NULL, FDcut_number = 50) The following commands return the TD estimates with two specified levels
of sample coverage (93% and 97%) based on the
Brazil_rainforest_abun_data.
data(Brazil_rainforest_abun_data)
output_est_TD_abun <- estimate3D(Brazil_rainforest_abun_data, diversity = 'TD', q = c(0,1,2),
datatype = "abundance", base = "coverage", level = c(0.93, 0.97))
output_est_TD_abun Assemblage Order.q SC m Method qTD s.e. qTD.LCL qTD.UCL
1 Edge 0 0.93 1547.562 Rarefaction 302.879 8.892 285.450 320.308
2 Edge 0 0.97 3261.971 Extrapolation 383.307 17.598 348.816 417.798
3 Edge 1 0.93 1547.562 Rarefaction 152.374 3.819 144.889 159.860
4 Edge 1 0.97 3261.971 Extrapolation 166.837 4.443 158.130 175.544
5 Edge 2 0.93 1547.562 Rarefaction 81.437 4.048 73.503 89.372
6 Edge 2 0.97 3261.971 Extrapolation 83.726 4.304 75.290 92.163
7 Interior 0 0.93 1699.021 Rarefaction 331.917 14.476 303.545 360.289
8 Interior 0 0.97 3883.447 Extrapolation 433.807 22.432 389.840 477.773
9 Interior 1 0.93 1699.021 Rarefaction 159.330 4.873 149.779 168.882
10 Interior 1 0.97 3883.447 Extrapolation 175.739 5.536 164.890 186.589
11 Interior 2 0.93 1699.021 Rarefaction 71.611 4.173 63.432 79.789
12 Interior 2 0.97 3883.447 Extrapolation 73.326 4.412 64.678 81.973
The following commands return the TD estimates with two specified levels
of sample coverage (97.5% and 99%) for the Fish_incidence_data.
data(Fish_incidence_data)
output_est_TD_inci <- estimate3D(Fish_incidence_data, diversity = 'TD', q = c(0, 1, 2),
datatype = "incidence_raw", base = "coverage",
level = c(0.975, 0.99))
output_est_TD_inci Assemblage Order.q SC mT Method qTD s.e. qTD.LCL qTD.UCL
1 2013-2015 0 0.975 29.169 Rarefaction 47.703 3.144 41.542 53.865
2 2013-2015 0 0.990 58.667 Extrapolation 54.914 4.952 45.209 64.620
3 2013-2015 1 0.975 29.169 Rarefaction 29.773 1.000 27.813 31.732
4 2013-2015 1 0.990 58.667 Extrapolation 30.751 0.970 28.849 32.653
5 2013-2015 2 0.975 29.169 Rarefaction 23.861 0.768 22.356 25.367
6 2013-2015 2 0.990 58.667 Extrapolation 24.126 0.771 22.615 25.638
7 2016-2018 0 0.975 34.825 Rarefaction 52.574 5.922 40.968 64.180
8 2016-2018 0 0.990 76.971 Extrapolation 62.688 9.742 43.595 81.782
9 2016-2018 1 0.975 34.825 Rarefaction 31.479 1.298 28.935 34.022
10 2016-2018 1 0.990 76.971 Extrapolation 32.721 1.394 29.989 35.454
11 2016-2018 2 0.975 34.825 Rarefaction 24.872 0.742 23.418 26.325
12 2016-2018 2 0.990 76.971 Extrapolation 25.163 0.746 23.700 26.626
The following commands return the PD estimates with two specified levels
of sample sizes (1500 and 3500) for the Brazil_rainforest_abun_data.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_phylo_tree)
data <- Brazil_rainforest_abun_data
tree <- Brazil_rainforest_phylo_tree
output_est_PD_abun <- estimate3D(data, diversity = 'PD', datatype = "abundance",
base = "size", level = c(1500, 3500), PDtree = tree)
output_est_PD_abun Assemblage Order.q m Method SC qPD s.e. qPD.LCL qPD.UCL Reftime Type
1 Edge 0 1500 Rarefaction 0.928 58.370 1.280 55.861 60.880 400 meanPD
2 Edge 0 3500 Extrapolation 0.973 71.893 2.758 66.487 77.298 400 meanPD
3 Edge 1 1500 Rarefaction 0.928 5.224 0.109 5.011 5.437 400 meanPD
4 Edge 1 3500 Extrapolation 0.973 5.320 0.111 5.102 5.538 400 meanPD
5 Edge 2 1500 Rarefaction 0.928 1.797 0.024 1.749 1.844 400 meanPD
6 Edge 2 3500 Extrapolation 0.973 1.797 0.024 1.750 1.844 400 meanPD
7 Interior 0 1500 Rarefaction 0.922 63.555 1.066 61.466 65.645 400 meanPD
8 Interior 0 3500 Extrapolation 0.965 78.004 2.117 73.853 82.154 400 meanPD
9 Interior 1 1500 Rarefaction 0.922 5.675 0.133 5.414 5.936 400 meanPD
10 Interior 1 3500 Extrapolation 0.965 5.784 0.135 5.520 6.048 400 meanPD
11 Interior 2 1500 Rarefaction 0.922 1.913 0.032 1.850 1.977 400 meanPD
12 Interior 2 3500 Extrapolation 0.965 1.914 0.032 1.851 1.978 400 meanPD
The following commands return the PD estimates with two specified levels
of sample coverage (97.5% and 99%) for the Fish_incidence_data.
data(Fish_incidence_data)
data(Fish_phylo_tree)
data <- Fish_incidence_data
tree <- Fish_phylo_tree
output_est_PD_inci <- estimate3D(data, diversity = 'PD', datatype = "incidence_raw",
base = "coverage", level = c(0.975, 0.99), PDtree = tree)
output_est_PD_inci Assemblage Order.q SC mT Method qPD s.e. qPD.LCL qPD.UCL Reftime Type
1 2013-2015 0 0.975 29.169 Rarefaction 9.672 0.406 8.876 10.469 0.9770115 meanPD
2 2013-2015 0 0.990 58.667 Extrapolation 10.018 0.718 8.611 11.426 0.9770115 meanPD
3 2013-2015 1 0.975 29.169 Rarefaction 7.612 0.125 7.368 7.857 0.9770115 meanPD
4 2013-2015 1 0.990 58.667 Extrapolation 7.680 0.127 7.431 7.929 0.9770115 meanPD
5 2013-2015 2 0.975 29.169 Rarefaction 7.003 0.121 6.765 7.240 0.9770115 meanPD
6 2013-2015 2 0.990 58.667 Extrapolation 7.030 0.122 6.792 7.268 0.9770115 meanPD
7 2016-2018 0 0.975 34.825 Rarefaction 9.646 0.413 8.838 10.455 0.9770115 meanPD
8 2016-2018 0 0.990 76.971 Extrapolation 9.831 0.704 8.451 11.211 0.9770115 meanPD
9 2016-2018 1 0.975 34.825 Rarefaction 7.779 0.135 7.513 8.044 0.9770115 meanPD
10 2016-2018 1 0.990 76.971 Extrapolation 7.835 0.141 7.558 8.112 0.9770115 meanPD
11 2016-2018 2 0.975 34.825 Rarefaction 7.201 0.135 6.936 7.465 0.9770115 meanPD
12 2016-2018 2 0.990 76.971 Extrapolation 7.224 0.136 6.957 7.491 0.9770115 meanPD
The following commands return the FD estimates with two specified levels
of sample coverage (93% and 97%) for the Brazil_rainforest_abun_data.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_distance_matrix)
data <- Brazil_rainforest_abun_data
distM <- Brazil_rainforest_distance_matrix
output_est_FD_abun <- estimate3D(data, diversity = 'FD', datatype = "abundance",
base = "coverage", level = c(0.93, 0.97), nboot = 10,
FDdistM = distM, FDtype = 'AUC')
output_est_FD_abun Assemblage Order.q SC m Method qFD s.e. qFD.LCL qFD.UCL
1 Edge 0 0.93 1547.562 Rarefaction 17.590 1.700 14.257 20.923
2 Edge 0 0.97 3261.971 Extrapolation 18.578 1.937 14.781 22.374
3 Edge 1 0.93 1547.562 Rarefaction 11.732 0.395 10.958 12.506
4 Edge 1 0.97 3261.971 Extrapolation 11.920 0.398 11.140 12.700
5 Edge 2 0.93 1547.562 Rarefaction 9.120 0.269 8.593 9.648
6 Edge 2 0.97 3261.971 Extrapolation 9.183 0.271 8.652 9.714
7 Interior 0 0.93 1699.021 Rarefaction 16.890 1.952 13.065 20.716
8 Interior 0 0.97 3883.447 Extrapolation 17.839 3.166 11.634 24.044
9 Interior 1 0.93 1699.021 Rarefaction 9.668 0.303 9.074 10.262
10 Interior 1 0.97 3883.447 Extrapolation 9.834 0.317 9.212 10.456
11 Interior 2 0.93 1699.021 Rarefaction 6.994 0.180 6.641 7.348
12 Interior 2 0.97 3883.447 Extrapolation 7.033 0.184 6.673 7.393
The following commands return the FD estimates with two specified levels
of sample sizes (30 and 70) for the Fish_incidence_data.
data(Fish_incidence_data)
data(Fish_distance_matrix)
data <- Fish_incidence_data
distM <- Fish_distance_matrix
output_est_FD_inci <- estimate3D(data, diversity = 'FD', datatype = "incidence_raw",
base = "size", level = c(30, 70), nboot = 10,
FDdistM = distM, FDtype = 'AUC')
output_est_FD_inci Assemblage Order.q mT Method SC qFD s.e. qFD.LCL qFD.UCL
1 2013-2015 0 30 Rarefaction 0.976 17.748 0.255 17.248 18.248
2 2013-2015 0 70 Extrapolation 0.993 18.550 0.582 17.410 19.691
3 2013-2015 1 30 Rarefaction 0.976 15.929 0.217 15.505 16.354
4 2013-2015 1 70 Extrapolation 0.993 16.006 0.210 15.594 16.417
5 2013-2015 2 30 Rarefaction 0.976 15.459 0.215 15.038 15.880
6 2013-2015 2 70 Extrapolation 0.993 15.477 0.215 15.056 15.898
7 2016-2018 0 30 Rarefaction 0.972 17.503 0.704 16.124 18.883
8 2016-2018 0 70 Extrapolation 0.988 18.705 1.135 16.480 20.930
9 2016-2018 1 30 Rarefaction 0.972 15.729 0.506 14.738 16.720
10 2016-2018 1 70 Extrapolation 0.988 15.816 0.515 14.808 16.825
11 2016-2018 2 30 Rarefaction 0.972 15.268 0.486 14.316 16.221
12 2016-2018 2 70 Extrapolation 0.988 15.290 0.486 14.337 16.242
ObsAsy3D(data, diversity = "TD", q = seq(0, 2, 0.2), datatype = "abundance",
nboot = 50, conf = 0.95, nT = NULL,
method = c("Asymptotic", "Observed"),
PDtree, PDreftime = NULL, PDtype = "meanPD",
FDdistM, FDtype = "AUC", FDtau = NULL, FDcut_number = 50
)All arguments in the above function are the same as those for the main
function iNEXT3D (except that the default of q here is
seq(0, 2, 0.2)). The function ObsAsy3D() computes observed and
asymptotic diversity of order q between 0 and 2 (in increments of 0.2)
for 3D diversity; these 3D values with different order q can be used to
depict a q-profile in the ggObsAsy3D function.
It also computes observed and asymptotic PD for various reference times
by specifying the argument PDreftime; these PD values with different
reference times can be used to depict a time-profile in the ggObsAsy3D
function.
It also computes observed and asymptotic FD for various threshold tau
levels by specifying the argument FDtau; these FD values with
different threshold levels can be used to depict a tau-profile in the
ggObsAsy3D function.
For each dimension, by default, both the observed and asymptotic diversity estimates will be computed.
ggObsAsy3D(output, profile = "q")ggObsAsy3D is a ggplot2 extension for an ObsAsy3D object to plot 3D
q-profile (which depicts the observed diversity and asymptotic diversity
estimate with respect to order q) for q between 0 and 2 (in increments
of 0.2).
It also plots time-profile (which depicts the observed and asymptotic
estimate of PD or mean PD with respect to reference times when
diversity = "PD" specified in the ObsAsy3D function), and tau-profile
(which depicts the observed and asymptotic estimate of FD with respect
to threshold level tau when diversity = "FD" and
FDtype = "tau_values" specified in the ObsAsy3D function) based on
the output from the function ObsAsy3D.
In the plot of profiles, only confidence intervals of the asymptotic diversity will be shown when both the observed and asymptotic diversity estimates are computed.
The following commands returns the observed and asymptotic taxonomic
diversity (‘TD’) for the Brazil_rainforest_abun_data, along with its
confidence interval for diversity order q between 0 to 2. Here only the
first ten rows of the output are shown.
data(Brazil_rainforest_abun_data)
output_ObsAsy_TD_abun <- ObsAsy3D(Brazil_rainforest_abun_data, diversity = 'TD',
datatype = "abundance")
output_ObsAsy_TD_abun Assemblage Order.q qTD s.e. qTD.LCL qTD.UCL Method
1 Edge 0.0 444.971 29.065 388.005 501.938 Asymptotic
2 Edge 0.2 375.270 20.145 335.787 414.754 Asymptotic
3 Edge 0.4 312.452 13.210 286.561 338.343 Asymptotic
4 Edge 0.6 258.379 8.563 241.595 275.164 Asymptotic
5 Edge 0.8 213.730 6.097 201.780 225.680 Asymptotic
6 Edge 1.0 178.000 5.154 167.898 188.101 Asymptotic
7 Edge 1.2 149.914 4.881 140.347 159.482 Asymptotic
8 Edge 1.4 127.945 4.803 118.532 137.357 Asymptotic
9 Edge 1.6 110.672 4.779 101.305 120.039 Asymptotic
10 Edge 1.8 96.948 4.784 87.571 106.325 Asymptotic
The following commands plot the corresponding q-profiles, along with its confidence interval for q between 0 to 2.
# q-profile curves
ggObsAsy3D(output_ObsAsy_TD_abun)
The following commands return the observed and asymptotic taxonomic
diversity (‘TD’) estimates for the Fish_incidence_data, along with its
confidence interval for diversity order q between 0 to 2. Here only the
first ten rows of the output are shown.
data(Fish_incidence_data)
output_ObsAsy_TD_inci <- ObsAsy3D(Fish_incidence_data, diversity = 'TD',
datatype = "incidence_raw")
output_ObsAsy_TD_inci Assemblage Order.q qTD s.e. qTD.LCL qTD.UCL Method
1 2013-2015 0.0 59.803 11.767 36.740 82.867 Asymptotic
2 2013-2015 0.2 50.828 6.526 38.037 63.619 Asymptotic
3 2013-2015 0.4 43.790 3.500 36.930 50.651 Asymptotic
4 2013-2015 0.6 38.458 1.993 34.553 42.364 Asymptotic
5 2013-2015 0.8 34.490 1.343 31.858 37.121 Asymptotic
6 2013-2015 1.0 31.542 1.084 29.418 33.665 Asymptotic
7 2013-2015 1.2 29.328 0.966 27.434 31.222 Asymptotic
8 2013-2015 1.4 27.635 0.897 25.877 29.392 Asymptotic
9 2013-2015 1.6 26.312 0.846 24.655 27.969 Asymptotic
10 2013-2015 1.8 25.255 0.804 23.680 26.831 Asymptotic
The following commands plot the corresponding q-profiles, along with its confidence interval for q between 0 to 2.
# q-profile curves
ggObsAsy3D(output_ObsAsy_TD_inci)
The following commands return the observed and asymptotic phylogenetic
diversity (‘PD’) estimates for the Brazil_rainforest_abun_data, along
with its confidence interval for diversity order q = 0, 1, 2 under
reference times from 0.01 to 400 (tree height). Here only the first ten
rows of the output are shown.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_phylo_tree)
data <- Brazil_rainforest_abun_data
tree <- Brazil_rainforest_phylo_tree
output_ObsAsy_PD_abun <- ObsAsy3D(data, diversity = 'PD', q = c(0, 1, 2),
PDreftime = seq(0.01, 400, length.out = 20),
datatype = "abundance", nboot = 20, PDtree = tree)
output_ObsAsy_PD_abun Assemblage Order.q qPD s.e. qPD.LCL qPD.UCL Method Reftime Type
1 Edge 0 444.971 27.967 390.156 499.787 Asymptotic 0.100 meanPD
2 Edge 1 178.000 5.913 166.411 189.589 Asymptotic 0.100 meanPD
3 Edge 2 85.905 5.294 75.529 96.281 Asymptotic 0.100 meanPD
4 Interior 0 513.518 26.491 461.597 565.438 Asymptotic 0.100 meanPD
5 Interior 1 186.983 6.267 174.700 199.266 Asymptotic 0.100 meanPD
6 Interior 2 74.718 4.907 65.100 84.335 Asymptotic 0.100 meanPD
7 Edge 0 371.100 21.565 328.834 413.366 Asymptotic 10.354 meanPD
8 Edge 1 141.418 4.579 132.443 150.393 Asymptotic 10.354 meanPD
9 Edge 2 72.848 3.824 65.353 80.343 Asymptotic 10.354 meanPD
10 Interior 0 413.568 25.413 363.758 463.377 Asymptotic 10.354 meanPD
The argument profile = "time" in the ggObsAsy3D function creates a
separate plot for each diversity order q = 0, 1, and 2 with x-axis being
“Reference time”. Different assemblages will be represented by different
color lines.
# time-profile curves
ggObsAsy3D(output_ObsAsy_PD_abun, profile = "time")
The following commands return the observed and asymptotic taxonomic
diversity (‘PD’) estimates for the Fish_incidence_data, along with its
confidence interval for diversity order q between 0 to 2. Here only the
first ten rows of the output are shown.
data(Fish_incidence_data)
data(Fish_phylo_tree)
data <- Fish_incidence_data
tree <- Fish_phylo_tree
output_ObsAsy_PD_inci <- ObsAsy3D(data, diversity = 'PD', q = seq(0, 2, 0.2),
datatype = "incidence_raw", nboot = 20, PDtree = tree,
PDreftime = NULL)
output_ObsAsy_PD_inci Assemblage Order.q qPD s.e. qPD.LCL qPD.UCL Method Reftime Type
1 2013-2015 0.0 10.039 1.241 7.607 12.471 Asymptotic 0.977 meanPD
2 2013-2015 0.2 9.462 0.538 8.407 10.517 Asymptotic 0.977 meanPD
3 2013-2015 0.4 8.802 0.322 8.170 9.433 Asymptotic 0.977 meanPD
4 2013-2015 0.6 8.329 0.227 7.884 8.773 Asymptotic 0.977 meanPD
5 2013-2015 0.8 7.985 0.187 7.619 8.351 Asymptotic 0.977 meanPD
6 2013-2015 1.0 7.729 0.170 7.397 8.061 Asymptotic 0.977 meanPD
7 2013-2015 1.2 7.533 0.162 7.216 7.849 Asymptotic 0.977 meanPD
8 2013-2015 1.4 7.378 0.158 7.067 7.688 Asymptotic 0.977 meanPD
9 2013-2015 1.6 7.252 0.158 6.943 7.561 Asymptotic 0.977 meanPD
10 2013-2015 1.8 7.147 0.159 6.836 7.458 Asymptotic 0.977 meanPD
The following commands plot the corresponding q-profiles, along with its confidence interval for q between 0 to 2, for the default reference time = 0.977 (the tree depth).
# q-profile curves
ggObsAsy3D(output_ObsAsy_PD_inci, profile = "q")
The following commands returns observed and asymptotic functional
diversity (‘FD’) for Brazil_rainforest_abun_data, along with its
confidence interval at diversity order q = 0, 1, 2 under tau values from
0 to 1. Here only the first ten rows of the output are shown.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_distance_matrix)
data <- Brazil_rainforest_abun_data
distM <- Brazil_rainforest_distance_matrix
output_ObsAsy_FD_abun_tau <- ObsAsy3D(data, diversity = 'FD', q = c(0, 1, 2),
datatype = "abundance", nboot = 10, FDdistM = distM,
FDtype = 'tau_values', FDtau = seq(0, 1, 0.05))
output_ObsAsy_FD_abun_tau Assemblage Order.q qFD s.e. qFD.LCL qFD.UCL Method Tau
1 Edge 0 444.971 23.002 399.888 490.055 Asymptotic 0.00
2 Edge 1 178.000 6.655 164.956 191.043 Asymptotic 0.00
3 Edge 2 85.905 6.033 74.081 97.730 Asymptotic 0.00
4 Edge 0 79.904 16.209 48.135 111.673 Asymptotic 0.05
5 Edge 1 45.187 2.311 40.658 49.716 Asymptotic 0.05
6 Edge 2 32.092 1.727 28.707 35.477 Asymptotic 0.05
7 Edge 0 73.276 17.121 39.719 106.832 Asymptotic 0.10
8 Edge 1 42.200 2.228 37.832 46.567 Asymptotic 0.10
9 Edge 2 30.182 1.596 27.053 33.311 Asymptotic 0.10
10 Edge 0 35.372 19.020 0.000 72.651 Asymptotic 0.15
The following commands plot the corresponding tau-profiles, along with its confidence interval for diversity order q = 0, 1, 2.
# tau-profile curves
ggObsAsy3D(output_ObsAsy_FD_abun_tau, profile = "tau")
The following commands returns the observed and asymptotic taxonomic
diversity (‘FD’) for the Brazil_rainforest_abun_data, along with its
confidence interval for diversity order q between 0 to 2 with
FDtype = 'AUC'. Here only the first ten rows of the output are shown.
data(Brazil_rainforest_abun_data)
data(Brazil_rainforest_distance_matrix)
data <- Brazil_rainforest_abun_data
distM <- Brazil_rainforest_distance_matrix
output_ObsAsy_FD_abun <- ObsAsy3D(data, diversity = 'FD', q = seq(0, 2, 0.5),
datatype = "abundance", nboot = 10,
FDdistM = distM, FDtype = 'AUC')
output_ObsAsy_FD_abun Assemblage Order.q qFD s.e. qFD.LCL qFD.UCL Method
1 Edge 0.0 19.008 8.458 2.431 35.585 Asymptotic
2 Edge 0.5 14.698 1.114 12.515 16.882 Asymptotic
3 Edge 1.0 12.037 0.205 11.636 12.438 Asymptotic
4 Edge 1.5 10.345 0.128 10.094 10.597 Asymptotic
5 Edge 2.0 9.228 0.150 8.934 9.523 Asymptotic
6 Interior 0.0 18.208 6.907 4.671 31.745 Asymptotic
7 Interior 0.5 13.071 1.030 11.051 15.090 Asymptotic
8 Interior 1.0 9.922 0.228 9.475 10.369 Asymptotic
9 Interior 1.5 8.103 0.202 7.708 8.499 Asymptotic
10 Interior 2.0 7.055 0.196 6.671 7.440 Asymptotic
The following commands plot the corresponding q-profiles, along with its confidence interval for q between 0 to 2.
# q-profile curves
ggObsAsy3D(output_ObsAsy_FD_abun, profile = "q")
The following commands returns observed and asymptotic functional
diversity (‘FD’) for Fish_incidence_data, along with its confidence
interval at diversity order q from 0 to 2. Here only the first ten rows
of the output are shown.
data(Fish_incidence_data)
data(Fish_distance_matrix)
data <- Fish_incidence_data
distM <- Fish_distance_matrix
output_ObsAsy_FD_inci <- ObsAsy3D(data, diversity = 'FD', datatype = "incidence_raw",
nboot = 20, FDdistM = distM, FDtype = 'AUC')
output_ObsAsy_FD_inci Assemblage Order.q qFD s.e. qFD.LCL qFD.UCL Method
1 2013-2015 0.0 18.906 2.065 14.859 22.952 Asymptotic
2 2013-2015 0.2 17.826 0.907 16.048 19.604 Asymptotic
3 2013-2015 0.4 17.115 0.582 15.974 18.256 Asymptotic
4 2013-2015 0.6 16.624 0.469 15.706 17.543 Asymptotic
5 2013-2015 0.8 16.284 0.433 15.436 17.132 Asymptotic
6 2013-2015 1.0 16.043 0.418 15.223 16.863 Asymptotic
7 2013-2015 1.2 15.868 0.411 15.063 16.673 Asymptotic
8 2013-2015 1.4 15.736 0.406 14.941 16.532 Asymptotic
9 2013-2015 1.6 15.635 0.402 14.847 16.423 Asymptotic
10 2013-2015 1.8 15.555 0.399 14.773 16.338 Asymptotic
The following commands plot the corresponding q-profiles, along with its confidence interval for q between 0 to 2.
# q-profile curves
ggObsAsy3D(output_ObsAsy_FD_inci, profile = "q")
The iNEXT.3D package is licensed under the GPLv3. To help refine
iNEXT.3D, your comments or feedback would be welcome (please send them
to Anne Chao or report an issue on the iNEXT.3D github
iNEXT.3D_github.
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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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Hsieh, T. C., Ma, K-H, and Chao, A. (2016). iNEXT: An R package for rarefaction and extrapolation of species diversity (Hill numbers). Methods in Ecology and Evolution, 7, 1451-1456.