iNEXT.4steps (Four-Step Biodiversity Analysis based on
iNEXT) expands iNEXT (Chao et al. 2014) to include the
estimation of sample completeness and evenness under a unified framework
of Hill numbers. iNEXT.4steps links sample completeness,
diversity estimation, interpolation and extrapolation
(iNEXT), and evenness in a fully integrated approach. The
pertinent background for the four-step methodology is provided in Chao
et al. (2020). The four-step procedures are described in the
following:
- Step 1: Assessment of sample completeness
profile
Before performing biodiversity analysis, it is important to first
quantify the sample completeness of a biological survey. Chao et
al. (2020) generalized the conventional sample completeness to a class
of measures parametrized by an order q ≥ 0. When q = 0, sample
completeness reduces to the conventional measure of completeness, i.e.,
the ratio of the observed species richness to the true richness
(observed plus undetected). When q = 1, the measure reduces to the
sample coverage (the proportion of the total number of individuals in
the entire assemblage that belong to detected species), a concept
original developed by Alan Turing in his cryptographic analysis during
WWII. When q = 2, it represents a generalized sample coverage with each
species being proportionally weighted by its squared species abundance
(i.e., each individual being proportionally weighted by its species
abundance); this measure thus is disproportionally sensitive to highly
abundant species. For a general order q ≥ 0 (not necessarily to be an
integer) , the sample completeness of order q quantifies the proportion
of the assemblage’s individuals belonging to detected species, with each
individual being proportionally weighted by the (q-1)th power of its
abundance. Sample completeness profile depicts its estimate with respect
to order q ≥ 0; this profile fully characterizes the sample completeness
of a biological survey.
iNEXT.4steps features the estimated profile for all
orders of q ≥ 0 based on the methodology developed in Chao et
al. (2020). All estimates are theoretically between 0 and 1. If the
estimated sample completeness profile is a horizontal line at the level
of unity for all orders of q ≥ 0, then the survey is complete, implying
there is no undetected diversity. In most applications, the estimated
profile increases with order q, revealing the existence of undetected
diversity. The sample completeness estimate for q = 0 provides an upper
bound for the proportion of observed species; its complement represents
a lower bound for the proportion of undetected species. This
interpretation is mainly because data typically do not contain
sufficient information to accurately estimate species richness and only
a lower bound of species richness can be well estimated. By contrast,
for q ≥ 1, when data are not sparse, the sample completeness value for q
≥ 1 can be very accurately estimated measures. The values for q ≥ 2
typically are very close to unity, signifying that almost all highly
abundant species (for abundance data) or highly frequent species (for
incidence data) had been detected in the reference sample.
- STEP 2. Analysis of the size-based rarefaction and
extrapolation sampling curves, and the asymptotic diversity profile for
0 ≤ q ≤ 2.
(STEP 2a). For each dataset, first examine the
pattern of the size-based rarefaction and extrapolation sampling curve
up to double the reference sample size for q = 0, 1 and 2. If the curve
stays at a fixed level (this often occurs for the measures of q = 1 and
2), then our asymptotic estimate presented in Step 2b can be used to
accurately infer the true diversity of the entire assemblage. Otherwise,
our asymptotic diversity estimate represents only a lower bound (this
often occurs for the measures of q = 0).
(STEP 2b). When the true diversity can be accurately
inferred, the extent of undetected diversity within each dataset is
obtained by comparing the estimated asymptotic diversity profile and
empirical profile; the difference in diversity between any two
assemblages can be evaluated and tested for significance.
- STEP 3. Analysis of non-asymptotic coverage-based
rarefaction and extrapolation analysis for orders q = 0, 1 and
2.
When sampling data do not contain sufficient information to
accurately infer true diversity, fair comparisons of diversity across
multiple assemblages should be made by standardizing the sample coverage
(i.e., comparing diversity for a standardized fraction of an
assemblage’s individuals). This comparison can be done based on seamless
integration of coverage-based rarefaction and extrapolation sampling
curves up to a maximum coverage (Cmax = the minimum sample coverage
among all samples extrapolated to double reference sizes).
- STEP 4. Assessment of evenness profiles
Chao and Ricotta (2019) developed five classes of evenness measures
parameterized by an order q > 0. (For q = 0, species abundances are
disregarded, so it is not meaningful to evaluate evenness among
abundances specifically for q = 0. As q tends to 0, all evenness values
tend to 1 as a limiting value.) All classes of evenness measures are
functions of diversity and species richness, and all are standardized to
the range of [0, 1] to adjust for the effect of differing species
richness. Evenness profile depicts evenness estimate with respect to
order q ≥ 0. Because true species richness typically cannot be
accurately estimated, evenness profile typically can only be accurately
measured when both diversity and richness are computed at a fixed level
of sample coverage up to a maximum coverage Cmax defined in Step 3.
iNEXT.4steps shows, by default, the relevant statistics and
plot for only one class of evenness measure (based on the normalized
slope of a diversity profile), but all the five classes are
featured.
NOTE 1: Sufficient data are required
to perform the 4-step analysis. If there are only a few species in
users’ data, it is likely that data are too sparse to use
iNEXT.4steps.
NOTE 2: The analyses in STEPs 2a, 2b
and 3 are mainly based on package iNEXT available from
CRAN. Thus, iNEXT.4steps expands iNEXT to
include the estimation of sample completeness and evenness.
NOTE 3: As with iNEXT,
iNEXT.4steps only deals with taxonomic/species diversity.
Researchers who are interested in phylogenetic diversity and functional
diversity should use package iNEXT.3D available from CRAN
and see the relevant paper (Chao et al. 2021) for methodology.
NOTE 4: iNEXT.4steps
aims to compare within-assemblage diversity. If the goal is to assess
the extent of differentiation among assemblages or to infer species
compositional shift and abundance changes, users should use
iNEXT.beta3D available from CRAN and see the relevant paper
(Chao et al. 2023) for methodology.
How to cite
If you publish your work based on results from iNEXT.4steps package,
you should make references to the following methodology paper and the
package:
Chao, A., Kubota, Y., Zelený, D., Chiu, C.-H., Li, C.-F.,
Kusumoto, B., Yasuhara, M., Thorn, S., Wei, C.-L., Costello, M. J. and
Colwell, R. K. (2020). Quantifying sample completeness and comparing
diversities among assemblages. Ecological Research, 35,
292-314.
Chao, A. and Hu, K.-H. (2024). The iNEXT.4steps package:
Four-Step Biodiversity Analysis based on iNEXT. R package available from
CRAN.
SOFTWARE NEEDED TO RUN iNEXT.4STEPS IN R
HOW TO RUN INEXT.4STEPS:
The iNEXT.4steps package can be downloaded from CRAN or
Anne Chao’s iNEXT.4steps_github.
For a first-time installation, some additional packages must be
installed and loaded; see package manual.
## install iNEXT.4steps package from CRAN
install.packages("iNEXT.4steps")
## install the latest version from github
install.packages('devtools')
library(devtools)
install_github('AnneChao/iNEXT.4steps')
## import packages
library(iNEXT.4steps)
An online version of iNEXT.4steps (https://chao.shinyapps.io/iNEXT_4steps/) is also
available for users without an R background.
MAIN FUNCTION iNEXT4steps()
We first describe the main function iNEXT4steps() with
default arguments:
iNEXT4steps(data, q = seq(0, 2, 0.2), datatype = "abundance",
nboot = 30, conf = 0.95, nT = NULL, details = FALSE)
The arguments of this function are briefly described below, and will
explain details by illustrative examples in later text.
data
|
- For
datatype = "abundance", data can be input as a
vector of species abundances (for a single assemblage),
matrix/data.frame (species by assemblages), or a list of species
abundance vectors.
- For
datatype = "incidence_raw", data can be input as a
list of matrix/data.frame (species by sampling units); data can also be
input as a matrix/data.frame by merging all sampling units across
assemblages based on species identity; in this case, the number of
sampling units (nT, see below) must be input.
|
q
|
a numerical vector specifying the orders of q that will be used to
compute sample completeness and evenness as well as plot the relevant
profiles. Default is seq(0, 2, by = 0.2).
|
datatype
|
data type of input data: individual-based abundance data
(datatype = "abundance") or species by sampling-units
incidence matrix (datatype = "incidence_raw") with all
entries being 0 (non-detection) or 1 (detection)
|
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 30.
|
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 positive 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.
|
details
|
a logical variable to indicate whether the detailed numerical values for
each step are displayed. Default is FALSE.
|
The output of iNEXT4steps will have three parts (if
details = TRUE): $summary,
$figure, and $details. It may take some time
to compute when data size is large or nboot is large.
iNEXT.4steps VIA EXAMPLES
First, we use the data Data_spider to illustrate the
complete 4-step analysis.
EXAMPLE 1: Complete 4 steps for abundance data
In the spider data, species abundances of epigeal spiders were
recorded in two forest stands (“closed” and “open”). In the open forest,
there were 1760 individuals representing 74 species, whereas in the
closed forest, there were 1411 individuals representing 44 species. In
the pooled habitat, a total of 3171 individuals belonging to 85 species
are recorded.
Run the following code to obtain the numerical output and six figures
including five individual figures (for STEPs 1, 2a, 2b, 3 and 4,
respectively) and a complete set of five plots. (Here only show the
complete set of five plot; all five individual plots are omitted.)
data(Data_spider)
Four_Steps_out1 <- iNEXT4steps(data = Data_spider, datatype = "abundance")
Four_Steps_out1$summary
$`STEP 1. Sample completeness profiles`
Assemblage q = 0 q = 1 q = 2
1 Closed 0.61 0.99 1
2 Open 0.77 0.99 1
$`STEP 2b. Observed diversity values and asymptotic estimates`
Assemblage qTD TD_obs TD_asy s.e. qTD.LCL qTD.UCL
1 Closed Species richness 44.00 72.11 22.00 28.98 115.2
2 Closed Shannon diversity 10.04 10.30 0.29 9.74 10.9
3 Closed Simpson diversity 5.71 5.73 0.24 5.26 6.2
4 Open Species richness 74.00 96.31 13.00 70.82 121.8
5 Open Shannon diversity 16.34 16.84 0.70 15.46 18.2
6 Open Simpson diversity 9.41 9.46 0.38 8.72 10.2
$`STEP 3. Non-asymptotic coverage-based rarefaction and extrapolation analysis`
Cmax = 0.994 q = 0 q = 1 q = 2
1 Closed 55.6 10.2 5.72
2 Open 86.5 16.6 9.43
$`STEP 4. Evenness among species abundances of orders q = 1 and 2 at Cmax based on the normalized slope of a diversity profile`
Cmax = 0.994 Pielou J' q = 1 q = 2
1 Closed 0.58 0.17 0.09
2 Open 0.63 0.18 0.10
Four_Steps_out1$figure[[6]]
$summary: numerical tables for STEPs 1, 2b, 3 and 4.
Assemblage = the assemblage names.qTD = ‘Species richness’ represents the taxonomic
diversity of order q=0; ‘Shannon diversity’ represents the taxonomic
diversity of order q=1, ‘Simpson diversity’ represents the taxonomic
diversity of order q=2.TD_obs = the observed taxonomic diversity value of
order q.TD_asy = the estimated asymptotic diversity value of
order q.s.e. = the bootstrap standard error of the estimated
asymptotic diversity of order q.qTD.LCL, qTD.UCL = the bootstrap lower and
upper confidence limits for the estimated asymptotic diversity of order
q at the specified level in the setting (with a default value of
0.95).Pielou J' = a widely used evenness measure based on
Shannon entropy.
$figure: six figures including five individual figures
(for STEPS 1, 2a, 2b, 3 and 4 respectively) and a complete set of five
plots.
$details: (only when details = TRUE). The
numerical output for plotting all figures.
EXAMPLE 2: Complete 4 steps for incidence data
In the “Woody_plant” data, species incidence-raw data were recorded
in two forest vegetation types (“Monsoon” and “Upper_cloud” forest). In
the monsoon forest, 329 species and 6814 incidences were recorded in 191
plots. In the upper cloud forest, 239 species and 3371 incidences were
recorded in 153 plots (each 20×20-m plot is regarded as a sampling
unit). Because spatial clustering prevails in woody plants, individual
plants cannot be regarded as independent sampling units, violating the
basic sampling assumptions for the model based on abundance data. Thus,
it is statistically preferable to use incidence data to avoid this
violation.
Run the following code to obtain the numerical output and six figures
including five individual figures (for STEPs 1, 2a, 2b, 3 and 4,
respectively) and a complete set of five plots. (Here only show the
complete set of five plot; all five individual plots are omitted.)
data(Data_woody_plant)
Four_Steps_out2 <- iNEXT4steps(data = Data_woody_plant, datatype = "incidence_raw")
Four_Steps_out2$summary
$`STEP 1. Sample completeness profiles`
Assemblage q = 0 q = 1 q = 2
1 Monsoon 0.78 0.99 1
2 Upper_cloud 0.78 0.98 1
$`STEP 2b. Observed diversity values and asymptotic estimates`
Assemblage qTD TD_obs TD_asy s.e. qTD.LCL qTD.UCL
1 Monsoon Species richness 329.0 421.7 21.37 379.8 463.6
2 Monsoon Shannon diversity 145.7 150.2 1.75 146.7 153.6
3 Monsoon Simpson diversity 102.3 103.3 1.21 101.0 105.7
4 Upper_cloud Species richness 239.0 307.8 19.22 270.1 345.4
5 Upper_cloud Shannon diversity 105.5 110.5 1.90 106.8 114.2
6 Upper_cloud Simpson diversity 71.2 72.2 1.37 69.5 74.9
$`STEP 3. Non-asymptotic coverage-based rarefaction and extrapolation analysis`
Cmax = 0.993 q = 0 q = 1 q = 2
1 Monsoon 360 147 102.7
2 Upper_cloud 279 109 71.7
$`STEP 4. Evenness among species abundances of orders q = 1 and 2 at Cmax based on the normalized slope of a diversity profile`
Cmax = 0.993 Pielou J' q = 1 q = 2
1 Monsoon 0.85 0.41 0.28
2 Upper_cloud 0.83 0.39 0.25
Four_Steps_out2$figure[[6]]
Completeness and ggCompleteness: MAIN
FUNCTIONS FOR STEP 1
Function Completeness() computes sample completeness
estimates of orders q = 0 to q = 2 in increments of 0.2 (by default),
and function ggCompleteness is used to plot the
corresponding sample completeness profiles. These two functions are
specifically for users who only require sample completeness estimates
and profiles. The two functions with arguments are described below:
Completeness(data, q = seq(0, 2, 0.2), datatype = "abundance", nboot = 30,
conf = 0.95, nT = NULL)
All the arguments in these two functions are the same as those in the
main fnction iNEXT4steps for details.
Sample completeness estimates and profiles for abundance data
Run the following code to obtain sample completeness estimates based
on the abundance data Data_spider:
data(Data_spider)
SC_out1 <- Completeness(data = Data_spider, datatype = "abundance")
SC_out1
Order.q Estimate.SC s.e. SC.LCL SC.UCL Assemblage
1 0.0 0.768 8.67e-02 0.598 0.938 Open
2 0.2 0.818 6.42e-02 0.692 0.944 Open
3 0.4 0.877 3.87e-02 0.801 0.953 Open
4 0.6 0.930 1.83e-02 0.894 0.966 Open
5 0.8 0.966 6.87e-03 0.953 0.980 Open
6 1.0 0.986 2.21e-03 0.981 0.990 Open
7 1.2 0.994 6.72e-04 0.993 0.996 Open
8 1.4 0.998 2.28e-04 0.998 0.998 Open
9 1.6 0.999 9.28e-05 0.999 0.999 Open
10 1.8 1.000 4.02e-05 1.000 1.000 Open
11 2.0 1.000 1.71e-05 1.000 1.000 Open
12 0.0 0.610 1.21e-01 0.373 0.848 Closed
13 0.2 0.718 9.12e-02 0.540 0.897 Closed
14 0.4 0.834 5.31e-02 0.730 0.938 Closed
15 0.6 0.922 2.27e-02 0.877 0.966 Closed
16 0.8 0.969 7.54e-03 0.954 0.984 Closed
17 1.0 0.989 2.16e-03 0.985 0.994 Closed
18 1.2 0.997 6.17e-04 0.995 0.998 Closed
19 1.4 0.999 2.06e-04 0.999 0.999 Closed
20 1.6 1.000 7.84e-05 1.000 1.000 Closed
21 1.8 1.000 3.04e-05 1.000 1.000 Closed
22 2.0 1.000 1.14e-05 1.000 1.000 Closed
Order.q: the order of sample completeness.Estimate.SC: the estimated sample completeness of order
q.s.e.: standard error of sample completeness
estimate.SC.LCL, SC.UCL: the bootstrap lower and
upper confidence limits for the sample completeness of order q at the
specified level (with a default value of 0.95).Assemblage: the assemblage name.
Run the following code to plot sample completeness profiles for q
between 0 to 2, along with confidence intervals.
Sample completeness estimates and profiles for incidence data
Similar procedures can be applied to incidence data
Data_woody_plant to infer sample completeness.
data(Data_woody_plant)
SC_out2 <- Completeness(data = Data_woody_plant, datatype = "incidence_raw")
SC_out2
Order.q Estimate.SC s.e. SC.LCL SC.UCL Assemblage
1 0.0 0.780 4.59e-02 0.690 0.870 Monsoon
2 0.2 0.849 3.01e-02 0.790 0.908 Monsoon
3 0.4 0.909 1.65e-02 0.876 0.941 Monsoon
4 0.6 0.951 7.68e-03 0.936 0.966 Monsoon
5 0.8 0.976 3.06e-03 0.970 0.982 Monsoon
6 1.0 0.989 1.08e-03 0.987 0.991 Monsoon
7 1.2 0.995 3.56e-04 0.994 0.996 Monsoon
8 1.4 0.998 1.44e-04 0.998 0.998 Monsoon
9 1.6 0.999 8.11e-05 0.999 0.999 Monsoon
10 1.8 1.000 4.82e-05 1.000 1.000 Monsoon
11 2.0 1.000 2.69e-05 1.000 1.000 Monsoon
12 0.0 0.777 6.09e-02 0.657 0.896 Upper_cloud
13 0.2 0.836 4.29e-02 0.752 0.920 Upper_cloud
14 0.4 0.892 2.58e-02 0.841 0.942 Upper_cloud
15 0.6 0.935 1.32e-02 0.910 0.961 Upper_cloud
16 0.8 0.965 5.85e-03 0.954 0.976 Upper_cloud
17 1.0 0.982 2.34e-03 0.978 0.987 Upper_cloud
18 1.2 0.992 9.12e-04 0.990 0.993 Upper_cloud
19 1.4 0.996 4.01e-04 0.995 0.997 Upper_cloud
20 1.6 0.998 2.13e-04 0.998 0.999 Upper_cloud
21 1.8 0.999 1.22e-04 0.999 0.999 Upper_cloud
22 2.0 1.000 6.85e-05 1.000 1.000 Upper_cloud
Run the following code to plot sample completeness profiles for q
between 0 to 2, along with confidence intervals.
Evenness and ggevenness: MAIN FUNCTIONS FOR
STEP 4
Evenness() computes standardized (or observed) evenness
of order q = 0 to q = 2 in increments of 0.2 (by default) based on five
classes of evenness measures, and function ggevenness is
used to plot the corresponding evenness profiles. These two functions
are specifically for users who only require evenness estimates and
profiles. The two functions with arguments are described below:
Evenness(data, q = seq(0, 2, 0.2), datatype = "abundance", method = "Estimated",
nboot = 30, conf = 0.95, nT = NULL, E.class = 1:5, SC = NULL)
There are only three arguments that are not used in the main function
iNEXT4steps; these three arguments are described below (see
iNEXT4steps for other arguments)
method
|
a binary selection of method with “Estimated” (evenness is
computed under a standardized coverage value) or “Observed”
(evenness is computed for the observed data).
|
E.class
|
an integer vector between 1 to 5 specifying which class(es) of evenness
measures are selected; default is 1:5 (select all five classes).
|
SC
|
(required only when method = “Estimated”) a standardized
coverage value for calculating estimated evenness. If
SC=NULL, then this function computes the diversity
estimates for the minimum sample coverage among all samples extrapolated
to double reference sizes (Cmax).
|
Two simple examples for demonstrating functions Evenness
and ggEvenness are given below.
Evenness estimates and profiles for abundance data with default
standardized coverage value (Cmax)
The dataset Data_spider is used to estimate evenness at
the default standardized sample coverage (SC = NULL).
Evenness estimates of order q = 0 to q = 2 in increments of 0.2 (by
default) will be computed based on five classes of evenness measures.
(For q = 0, species abundances are disregarded, so it is not meaningful
to evaluate evenness among abundances specifically for q = 0. As q tends
to 0, all evenness values tend to 1 as a limiting value.) Function
ggevenness is used to plot the corresponding evenness
profiles. Here only the evenness estimates are shown for the first class
of evenness measures. The corresponding numerical tables for the other
four classes of evenness measures are omitted. Users also can use
argument E.class to specify which class (e.g.,
E.class= 3) or classes are required.
data(Data_spider)
Even_out1_est <- Evenness(data = Data_spider, datatype = "abundance",
method = "Estimated", SC = NULL, E.class = 1:5)
Even_out1_est
$E1
Order.q Evenness s.e. Even.LCL Even.UCL Assemblage Method SC
1 0.0 1.000 0.00000 1.000 1.000 Open Estimated 0.994
2 0.2 0.728 0.02484 0.679 0.776 Open Estimated 0.994
3 0.4 0.601 0.03206 0.538 0.664 Open Estimated 0.994
4 0.6 0.563 0.03159 0.501 0.625 Open Estimated 0.994
5 0.8 0.580 0.02744 0.526 0.634 Open Estimated 0.994
6 1.0 0.630 0.02163 0.587 0.672 Open Estimated 0.994
7 1.2 0.694 0.01572 0.663 0.725 Open Estimated 0.994
8 1.4 0.760 0.01090 0.739 0.781 Open Estimated 0.994
9 1.6 0.819 0.00767 0.804 0.834 Open Estimated 0.994
10 1.8 0.867 0.00578 0.856 0.879 Open Estimated 0.994
11 2.0 0.904 0.00463 0.895 0.914 Open Estimated 0.994
12 0.0 1.000 0.00000 1.000 1.000 Closed Estimated 0.994
13 0.2 0.700 0.02592 0.649 0.750 Closed Estimated 0.994
14 0.4 0.567 0.03388 0.500 0.633 Closed Estimated 0.994
15 0.6 0.525 0.03421 0.458 0.592 Closed Estimated 0.994
16 0.8 0.537 0.03089 0.476 0.597 Closed Estimated 0.994
17 1.0 0.578 0.02586 0.527 0.628 Closed Estimated 0.994
18 1.2 0.633 0.02046 0.593 0.673 Closed Estimated 0.994
19 1.4 0.693 0.01573 0.662 0.723 Closed Estimated 0.994
20 1.6 0.749 0.01222 0.725 0.773 Closed Estimated 0.994
21 1.8 0.799 0.00992 0.779 0.818 Closed Estimated 0.994
22 2.0 0.840 0.00846 0.824 0.857 Closed Estimated 0.994
Order.q: the order of evenness.Evenness: the computed evenness value of order q.s.e.: standard error of evenness value.Even.LCL, Even.UCL: the bootstrap lower
and upper confidence limits for the evenness of order q at the specified
level (with a default value of 0.95).Assemblage: the assemblage name.Method: "Estimated" or
"Observed".SC: the standardized coverage value under which
evenness values are computed (only for
method = "Estimated")
The following commands plot the evenness profiles for all five
classes of even measures, along with their confidence intervals.
ggEvenness(Even_out1_est)
Evenness estimates and profiles for incidence data with user’s
specified coverage value of 0.98.
In the function Evenness, users can specify a particular
sample coverage value under which all five classes of evenness measures
will be computed. For example, instead of using the default standardized
coverage value, if users want to compute evenness estimates for 0.98
based on the incidence dataset Data_woody_plant, then the
argument SC=0.98 is used instead of SC=NULL,
as shown below. Here only the evenness estimates are displayed for the
first class of evenness measures. The corresponding numerical tables for
the other four classes of evenness measures are omitted.
data(Data_woody_plant)
Even_out2_est <- Evenness(data = Data_woody_plant, datatype = "incidence_raw",
method = "Estimated", SC = 0.98, E.class = 1:5)
Even_out2_est
$E1
Order.q Evenness s.e. Even.LCL Even.UCL Assemblage Method SC
1 0.0 1.000 0.000000 1.000 1.000 Monsoon Estimated 0.98
2 0.2 0.876 0.003865 0.868 0.883 Monsoon Estimated 0.98
3 0.4 0.821 0.005239 0.810 0.831 Monsoon Estimated 0.98
4 0.6 0.814 0.005136 0.804 0.824 Monsoon Estimated 0.98
5 0.8 0.839 0.004208 0.831 0.848 Monsoon Estimated 0.98
6 1.0 0.880 0.002970 0.874 0.886 Monsoon Estimated 0.98
7 1.2 0.921 0.001830 0.917 0.924 Monsoon Estimated 0.98
8 1.4 0.953 0.001005 0.951 0.955 Monsoon Estimated 0.98
9 1.6 0.975 0.000509 0.974 0.976 Monsoon Estimated 0.98
10 1.8 0.987 0.000246 0.987 0.988 Monsoon Estimated 0.98
11 2.0 0.994 0.000117 0.993 0.994 Monsoon Estimated 0.98
12 0.0 1.000 0.000000 1.000 1.000 Upper_cloud Estimated 0.98
13 0.2 0.861 0.004662 0.851 0.870 Upper_cloud Estimated 0.98
14 0.4 0.797 0.006403 0.784 0.810 Upper_cloud Estimated 0.98
15 0.6 0.787 0.006398 0.774 0.799 Upper_cloud Estimated 0.98
16 0.8 0.812 0.005366 0.801 0.822 Upper_cloud Estimated 0.98
17 1.0 0.855 0.003887 0.847 0.863 Upper_cloud Estimated 0.98
18 1.2 0.901 0.002469 0.896 0.906 Upper_cloud Estimated 0.98
19 1.4 0.939 0.001415 0.936 0.941 Upper_cloud Estimated 0.98
20 1.6 0.965 0.000767 0.963 0.966 Upper_cloud Estimated 0.98
21 1.8 0.981 0.000413 0.980 0.982 Upper_cloud Estimated 0.98
22 2.0 0.990 0.000226 0.990 0.991 Upper_cloud Estimated 0.98
The following commands plot the evenness profiles for five classes,
along with their confidence intervals.
ggEvenness(Even_out2_est)
License
The iNEXT.4steps package is licensed under the GPLv3. To help refine
iNEXT.4steps, your comments or feedback would be welcome
(please send them to Anne Chao or report an issue on the iNEXT.4steps
github iNEXT.4steps_github.
References
Chao, A., Gotelli, N. G., Hsieh, T. C., Sander, E. L., Ma, K. H.,
Colwell, R. K. and Ellison, A. M. (2014). Rarefaction and extrapolation
with Hill numbers: a framework for sampling and estimation in species
biodiversity studies. Ecological Monographs 84, 45-67.
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., Kubota, Y., Zelený, D., Chiu, C.-H., Li, C.-F.,
Kusumoto, B., Yasuhara, M., Thorn, S., Wei, C.-L., Costello, M. J. and
Colwell, R. K. (2020). Quantifying sample completeness and comparing
diversities among assemblages. Ecological Research, 35,
292-314.
Chao, A. and Ricotta, C. (2019). Quantifying evenness and linking
it to diversity, beta diversity, and similarity. Ecology, 100(12),
e02852.
Chao, A., Thorn, S., Chiu, C.-H., Moyes, F., Hu, K.-H., Chazdon,
R. L., Wu, J., Magnago, L. F. S., Dornelas, M., Zelený, D., Colwell, R.
K., and Magurran, A. E. (2023). Rarefaction and extrapolation with beta
diversity under a framework of Hill numbers: the iNEXT.beta3D
standardization. Ecological Monographs e1588.