iNEXT.link (INterpolation and EXTrapolation in Network diversity) is an R package, available in Github. Here we provide a quick introduction demonstrating how to run iNEXT.link. An online version of iNEXT.link Online is also available for users without an R background. Detailed information about all functions in iNEXT.link is provided in the iNEXT.link Manual in iNEXT.link_vignettes, which is also available from Anne Chao’s website.

iNEXT.link is an R package that extends the concepts of iNEXT.3D (Chao et al., 2021), iNEXT.4step (Chao et al., 2020) and iNEXT.beta3D (Chao et al., 2023) to ecological networks (Chiu et al., 2023). It is primarily designed to calculate and analyze various measures of diversity in ecological networks. Specifically, the package calculates three Hill numbers of order q (species richness, Shannon diversity, and Simpson diversity) in taxonomic diversity level, as well as phylogenetic and functional diversity levels.

For single ecological networks, iNEXT.link provides tools for analyzing diversity. The package provides two types of rarefaction and extrapolation (R/E) sampling curves to estimate diversity and confidence intervals for single ecological networks. These include sample-size-based (or size-based) R/E curves and coverage-based R/E curves.

Moreover, iNEXT.link offers dissimilarity-turnover curves for the coverage-based R/E curves for gamma, alpha, and beta diversity measures, which can be used to compare diversity patterns across different ecological networks.

• Required: R
• Suggested: RStudio IDE

The iNEXT.link package can be downloaded from Anne Chao’s iNEXT.link_github using the following commands. For a first-time installation, additional visualization extension packages (ggplot2) from CRAN and (iNEXT.3D), (iNEXT.4steps), and (iNEXT.beta3D) from Anne Chao’s github must be installed and loaded.

## install iNEXT.link package from CRAN
# install.packages("iNEXT.link")  # coming soon

## install the latest version from github
install.packages('devtools')
library(devtools)

# install_github('AnneChao/iNEXT.3D')
# install_github('AnneChao/iNEXT.4steps')
# install_github('AnneChao/iNEXT.beta3D')

install_github('AnneChao/iNEXT.link')

## import packages
library(iNEXT.link)

In this document, we provide a quick introduction demonstrating how to run the package iNEXT.link(iNterpolation and EXTrapolation in Network diversity). iNEXT.link has several main functions:

• iNEXT.link : Computes rarefaction/extrapolation taxonomic, phylogenetic, and functional diversity estimates and sample coverage estimates.

• DataInfo.link : exhibits basic data information

• estimateD.link : computes species diversity with a particular user-specified level of sample size or sample coverage.

• ObsAsy.link: compute asymptotic or empirical(observed) diversity of order q.

• Completeness.link : Calculates estimated sample completeness with order q.

• Spec.link : Computes standardized specialization estimation under specified sample coverage(or observed) with order q.

• iNEXTbeta.link : Computing standardized gamma, alpha, beta diversity, and four dissimilarity-turnover indices for three dimensions: taxonomic, phylogenetic and functional diversity at specified sample coverage.

• ggCompleteness.link : Visualizing the output from the function Completeness.link

• ggSpec.link : Visualizing the output from the function Spec.link

• ggObsAsy.link : Visualizing the output from the function ObsAsy.link

• ggiNEXT.link : Visualizing the output from the function iNEXT.link

• ggiNEXTbeta.link : Visualizing the output from the function iNEXTbeta.link

First, we load data from iNEXT.link:

We first describe the main function iNEXT.link() with default arguments:

iNEXT.link(data,diversity = "TD", q = c(0, 1, 2), size = NULL, nT = NULL,
           endpoint = NULL, knots = 40, conf = 0.95, nboot = 30, 
           row.tree = NULL, col.tree = NULL, PDtype = "meanPD", 
           row.distM = NULL, col.distM = NULL, FDtype = "AUC", FDtau = NULL)

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 diversity estimates of order q, the sample coverage estimates and related statistics for K (if knots = K) 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 diversity estimates will be calculated. By default, endpoint = double the reference sample size (total sample size for interaction data (so calles abundance data in iNEXT.3D)). For example, if endpoint = 10, knot = 4, diversity estimates will be computed for a sequence of samples with sizes (1, 4, 7, 10).

Supported Data Types:

Individual-based interaction data : Input data matrix for each assemblage/site include samples species interactions in an empirical sample of n total interactions (“reference sample”). When dealing with N networks, the input data consists of N lists of species interaction matrix.

The data set (tree-beetles interaction data) is included in iNEXT.link package. The experiment took place in the Steigerwald forest in Germany, where deadwood objects from six tree species were exposed in open, net, and closed habitats. In each habitat, there are six plots (A, B, C, D, E, F). Saproxilic beetles were sampled using stem emergence traps and classified according to their functional traits. Data from four years were pooled for each plot and habitat, and pairwise distances were computed from the Gower distance. Here, the demonstration only uses data from plot A in each habitat. For these data, the following commands display the sample species interactions and run the iNEXT.link() function for three types of diversty ("TD", "PD", "FD" with specified threshold (default is dmean (quadratic entropy)), "AUC" which integrates FD from threshold 0 to 1).

Under taxonomic diversity dimension, iNEXT.link() function returns including: $DataInfo for summarizing data information; $iNextEst for showing diversity estimates along with related statistics for a series of rarefied and extrapolated samples; and $AsyEst for showing asymptotic diversity estimates along with related statistics. Result under phylogenetic diversity or functional diversity includes these three parts, too.

$DataInfo in TD example, as shown below, returns basic data information. It can also be presented using function DataInfo.link() to get the same result.

Because the three kinds of diversity output are similar, the demo shows TD only.

linkoutTD = iNEXT.link(data = beetles, diversity = 'TD', q = c(0,1,2), nboot = 30)
linkoutTD$DataInfo
NULL

Second part of output from function iNEXT.link is diversity estimates and related statistics computed for these 40 knots by default, which locates the reference sample size at the mid-point of the selected knots. The diversity can be based on sample-size-based and sample coverage-based. The first data frame of list $iNextEst (as shown below for ‘size_based’) includes the 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 order (Order.q), the diversity estimate of order q (qD in TD, qPD in PD, qFD in FD (under specified thresholds), qAUC in FD (area under curve)), the lower and upper confidence limits of diversity (qD.LCL and qD.UCL in TD, qPD.LCL and qPD.UCL in PD, qFD.LCL and qFD.UCL in FD (under specified thresholds), qAUC.LCL and qAUC.UCL in FD (area under curve)) conditioning on sample size, and the sample coverage estimate (SC) along with the lower and upper confidence limits of sample coverage (SC.LCL, SC.UCL). These sample coverage estimates with confidence intervals are used for plotting the sample completeness curve. It is time consuming for diversity = FD and FDtype = "AUC". If the argument nboot is greater than zero, then the bootstrap method is applied to obtain the confidence intervals for each diversity and sample coverage estimates.

Here only show first six rows:

head(linkoutTD$iNextEst$size_based)
NULL

The second data frame of list $iNextEst (as shown below for ‘coverage_based’) includes the sample coverage estimate (‘SC’), the 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 order (Order.q), the diversity estimate of order q (qD in TD, qPD in PD, qFD in FD (under specified thresholds), qAUC in FD (area under curve)), the lower and upper confidence limits of diversity (qD.LCL and qD.UCL in TD, qPD.LCL and qPD.UCL in PD, qFD.LCL and qFD.UCL in FD (under specified thresholds), qAUC.LCL and qAUC.UCL in FD (area under curve)) conditioning on sample coverage estimate.

Here only show first six rows:

head(linkoutTD$iNextEst$coverage_based)
NULL

The output $AsyEst lists the diversity labels (Diversity in TD, Phylogenetic Diversity in PD, Functional Diversity in FD), the observed diversity (Observed in TD, Phylogenetic Observed in PD, Functional Observed in FD), asymptotic diversity estimates (Estimator in TD, Phylogenetic Estimator in PD, Functional Estimator in FD), estimated bootstrap standard error (s.e.) and confidence intervals for diversity with q = 0, 1, and 2 (LCL, UCL). The estimated asymptotic and observed diversity can also be computed via the function ObsAsy.link(). The output are shown below:

Here only show first six rows:

head(linkoutTD$AsyEst)
NULL

The function ggiNEXT.link(), which extends ggplot2 with default arguments, is described as follows:

ggiNEXT.link(outcome, type = 1:3, facet.var = "Assemblage", color.var = "Order.q")  

Here outcome is the object of iNEXT.link()’s output. Three types of curves are allowed for different diversity dimensions:

1. Sample-size-based R/E curve (type = 1): This curve plots diversity estimates with confidence intervals as a function of sample size.

2. Sample completeness curve (type = 2): This curve plots the sample coverage with respect to sample size.

3. 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" or facet.var = "Assemblage" is used to create a separate plot for each value of the specified variable. For example, the following code displays a separate plot of the diversity order q. The ggiNEXT.link() function is a wrapper with package ggplot2 to create a R/E curve in a single line of code. The figure object is of class "ggplot", so can be manipulated by using the ggplot2 tools.

When facet.var = "Assemblage" in ggiNEXT.link function, it creates a separate plot for each network and the different color lines represent each diversity order. Sample-size-based R/E curve (type = 1) as below:

# Sample-size-based R/E curves, separating by "assemblage""
ggiNEXT.link(linkoutTD, type = 1, facet.var = "Assemblage")
[[1]]

When facet.var = "Order.q" in ggiNEXT.link function, it creates a separate plot for each diversity order and the different color lines represent each network. Sample-size-based R/E curve (type = 1) as below:

# Sample-size-based R/E curves, separating by "Order.q"
ggiNEXT.link(linkoutTD, type = 1, facet.var = "Order.q")
[[1]]

The following command return the sample completeness (sample coverage) curve (type = 2) in which different colors are used for the three networks.

ggiNEXT.link(linkoutTD, type = 2, facet.var = "Order.q", color.var = "Assemblage")
[[1]]

The following commands return the coverage-based R/E sampling curves in which different colors are used for the three assemblages (facet.var = "Assemblage") and for three diversity orders (facet.var = "Order.q").

ggiNEXT.link(linkoutTD, type = 3, facet.var = "Assemblage")
[[1]]

ggiNEXT.link(linkoutTD, type = 3, facet.var = "Order.q")
[[1]]

DataInfo.link(data, diversity = "TD", row.tree = NULL, 
              col.tree = NULL, row.distM = NULL, col.distM = NULL) 

Here provide the function DataInfo.link to compute three diversity dimensions (‘TD’, ‘PD’, ‘FD’) data information, which including sample size, observed species richness, sample coverage estimate, and the first ten interaction frequency counts when diversity = TD. And so on for PD, FD.

DataInfo.link(beetles, diversity = 'TD')
  Networks    n S.obs(row) S.obs(col) Links.obs Connectance  Coverage  f1 f2 f3 f4 f5 f6 f7 f8 f9 f10
1   Closed  816          6         83       178      0.3574 0.8799951  98 31 15  3  3  5  0  2  2   1
2     Open 1932          6         88       206      0.3902 0.9430819 110 33 15  8  7  5  3  2  3   2
DataInfo.link(beetles, diversity = 'PD', col.tree = beetles_col_tree)
  Networks    n S.obs(row) S.obs(col) Links.obs Connectance f1* f2*       g1       g2 PD.obs mean_T
1   Closed  816          6         83       178      0.3574 171  76 11508.99 3873.052    924    285
2     Open 1932          6         88       206      0.3902 190  76 13918.45 5172.410   1014    285
DataInfo.link(beetles, diversity = 'FD', col.distM = beetles_col_distM)
  Networks    n S.obs(row) S.obs(col) Links.obs Connectance  f1 f2 a1' a2' threshold
1   Closed  816          6         83       178      0.3574  98 31   0   0  8.930741
2     Open 1932          6         88       206      0.3902 110 33   0   0  8.021019

estimateD.link(data, diversity = "TD", q = c(0, 1, 2),  
               base = "coverage", level = NULL, nboot = 50, conf = 0.95, 
               PDtype = "meanPD", row.tree = NULL, col.tree = NULL, row.distM = NULL, 
               col.distM = NULL, FDtype = "AUC", FDtau = NULL) 

estimateD.link is used to compute three diversity dimensions (TD, PD, FD) estimates with q = 0, 1, 2 under any specified level of sample size (when base = "size") or sample coverage (when base = "coverage"). If level = NULL, this function computes the diversity estimates for the minimum sample size among all samples extrapolated to double reference sizes (when base = "size") or the minimum sample coverage among all samples extrapolated to double reference sizes (when base = "coverage").

For example, the following command returns the taxonomic diversity (‘TD’) with a specified level of sample coverage of 95% for the tree-beetles interaction data. For some networks, this coverage value corresponds to the rarefaction part whereas the others correspond to extrapolation, as indicated in the method of the output.

estimateD.link(beetles, diversity = 'TD', q = c(0, 1, 2), base = "coverage", level = 0.95)
  Assemblage Order.q   SC        m        Method        qTD       s.e.    qTD.LCL    qTD.UCL
1     Closed       0 0.95 1944.292 Extrapolation 268.252103 19.4789617 230.074040 306.430166
2     Closed       1 0.95 1944.292 Extrapolation  74.577021  3.6666959  67.390429  81.763613
3     Closed       2 0.95 1944.292 Extrapolation  33.378889  1.8831205  29.688040  37.069737
4       Open       0 0.95 2349.132 Extrapolation 228.271774 20.1609372 188.757063 267.786485
5       Open       1 0.95 2349.132 Extrapolation  23.704215  1.3613738  21.035971  26.372458
6       Open       2 0.95 2349.132 Extrapolation   8.065214  0.3508078   7.377643   8.752784

ObsAsy.link(data, diversity = "TD", q = seq(0, 2, 0.2),  nboot = 30, 
            conf = 0.95, method = c("Asymptotic", "Observed"), 
            row.tree = NULL, col.tree = NULL, PDtype = "meanPD", row.distM = NULL, 
            col.distM = NULL, FDtype = "AUC", FDtau = NULL)

The function ObsAsy.link() compute three diversity dimensions (TD, PD, FD) for empirical (observed) diversity and estimated asymptotic diversity with any diversity order. For example, the following commands returns empirical and asymptotic taxonomic diversity (‘TD’) for dunes data, along with its confidence interval at diversity order q from 0 to 2. Here only show the first ten rows.

out1 <- ObsAsy.link(beetles, diversity = 'TD', q = seq(0, 2, 0.2), method = c("Asymptotic", "Observed"),
                nboot = 5,conf = 0.95)

out1
   Network Order.q        qTD       s.e.    qTD.LCL    qTD.UCL     Method
1   Closed     0.0 332.713393 60.7494794 248.807295 388.150139 Asymptotic
2   Closed     0.2 265.977501 40.0782717 210.483668 304.674929 Asymptotic
3   Closed     0.4 203.167245 23.0455368 171.395956 226.923193 Asymptotic
4   Closed     0.6 149.540048 11.1877823 134.610344 161.910172 Asymptotic
5   Closed     0.8 108.592546  4.7257148 103.413490 114.136074 Asymptotic
6   Closed     1.0  80.316088  2.5887035  77.135131  83.272186 Asymptotic
7   Closed     1.2  61.983531  2.3287095  59.172274  64.715248 Asymptotic
8   Closed     1.4  50.295815  2.1913699  47.830763  52.895399 Asymptotic
9   Closed     1.6  42.699384  1.9902762  40.563109  45.119820 Asymptotic
10  Closed     1.8  37.568079  1.7887645  35.732154  39.803041 Asymptotic
11  Closed     2.0  33.944467  1.6174707  32.375699  36.001151 Asymptotic
12    Open     0.0 389.238440 25.0436417 351.956315 411.302136 Asymptotic
13    Open     0.2 263.223968 16.6619512 239.923045 281.351119 Asymptotic
14    Open     0.4 159.174040 10.5518258 146.956595 171.822803 Asymptotic
15    Open     0.6  86.647814  6.4185253  79.429038  93.640386 Asymptotic
16    Open     0.8  45.571274  3.7189968  40.476046  49.255856 Asymptotic
17    Open     1.0  25.911799  2.1349317  22.779659  27.982319 Asymptotic
18    Open     1.2  16.963237  1.2985247  15.021985  18.161496 Asymptotic
19    Open     1.4  12.643810  0.8629161  11.349884  13.412179 Asymptotic
20    Open     1.6  10.333946  0.6238429   9.397577  10.866772 Asymptotic
21    Open     1.8   8.967960  0.4825937   8.242270   9.361798 Asymptotic
22    Open     2.0   8.089554  0.3928921   7.497158   8.395495 Asymptotic
23  Closed     0.0 178.000000 14.5705182 163.000000 195.000000   Observed
24  Closed     0.2 149.140436 12.9906767 135.699274 164.058644   Observed
25  Closed     0.4 122.284123 11.1339416 110.785042 134.787250   Observed
26  Closed     0.6  98.784711  9.1630339  89.408484 108.761439   Observed
27  Closed     0.8  79.539008  7.2927705  72.198747  87.535873   Observed
28  Closed     1.0  64.690053  5.6997735  59.081390  71.255242   Observed
29  Closed     1.2  53.711702  4.4581426  49.439587  59.094022   Observed
30  Closed     1.4  45.761569  3.5471212  42.454094  50.222956   Observed
31  Closed     1.6  40.008527  2.8997899  37.370939  43.775855   Observed
32  Closed     1.8  35.788959  2.4443288  33.608940  39.038698   Observed
33  Closed     2.0  32.627205  2.1223556  30.759029  35.489163   Observed
34    Open     0.0 206.000000  6.6858059 198.500000 214.600000   Observed
35    Open     0.2 147.911160  4.7333977 142.653699 153.717494   Observed
36    Open     0.4  98.276240  3.0741560  94.997952 101.634857   Observed
37    Open     0.6  60.906771  1.8905086  59.104208  63.299753   Observed
38    Open     0.8  36.832763  1.1698536  35.761650  38.478061   Observed
39    Open     1.0  23.311453  0.7590379  22.496702  24.386806   Observed
40    Open     1.2  16.195155  0.5259785  15.581739  16.917882   Observed
41    Open     1.4  12.394607  0.3925491  11.915707  12.918305   Observed
42    Open     1.6  10.237828  0.3139364   9.841360  10.644900   Observed
43    Open     1.8   8.920980  0.2654315   8.578456   9.257250   Observed
44    Open     2.0   8.059978  0.2338830   7.754363   8.352926   Observed

ggObsAsy.link(outcome)

ggObsAsy.link() plots q-profile based on ggplot2. Here outcome is the object from the function ObsAsy.link.

# q profile curve
ggObsAsy.link(out1)

Function Completeness.link() provides a easy way to compute estimated sample completeness with order q. The arguments is below:

Completeness.link(data, q = seq(0, 2, 0.2), nboot = 30, conf = 0.95) 

We also provides a realized function ggCompleteness.link to plot the output from Completeness.link():

ggCompleteness.link(output)

Use data beetles to calculate sample completeness and plot it.

out1 <- Completeness.link(data = beetles)
ggCompleteness.link(out1)

The main function Spec.link() with default arguments:

Spec.link(data, q = seq(0, 2, 0.2), method = "Estimated",
         nboot = 30, conf = 0.95, E.class = c(1:5), C = NULL) 

The function ggSpec.link() is provided to plot the output from Spec.link().

ggSpec.link(output)

There is an example for function Spec.link and function ggSpec.link.

out1 <- Spec.link(data = beetles)
ggSpec.link(out1)

iNEXTbeta.link(data, diversity = "TD", level = seq(0.5, 1, 0.05), 
               q = c(0, 1, 2), nboot = 20, conf = 0.95, 
               PDtype = "meanPD", row.tree = NULL, col.tree = NULL, row.distM = NULL, 
               col.distM = NULL, FDtype = "AUC", FDtau = NULL, FDcut_number = 30) 

The arguments of this function are briefly described below, and will be explained in more details by illustrative examples in later text. This main function computes gamma, alpha and beta diversity estimates of order q at specified sample coverage and measures of dissimilarity. By default of base = “coverage” and level = NULL, then this function computes the gamma, alpha, beta diversity, and four dissimilarity-turnover indices estimates up to one (for q = 1, 2) or up to the coverage of double the reference sample size (for q = 0).

the iNEXTbeta.link() function returns the "iNEXTbeta.link" object including seven data frames for each datasets:

• gamma
• alpha
• beta
• C ( Sorensen-type non-overlap )
• U ( Jaccard-type non-overlap )
• V ( Sorensen-type turnover )
• S ( Jaccard-type turnover )

Here only show the first six rows in each table output:

# Taxonomic diversity
Abundance_TD = iNEXTbeta.link(data = beetles, diversity = 'TD', level = NULL, q = c(0, 1, 2))
Abundance_TD

$gamma
    Dataset Order.q    SC   Size  Gamma      Method  s.e.    LCL    UCL Diversity
1 Dataset_1       0 0.500 20.941 13.978 Rarefaction 1.058 11.905 16.052        TD
2 Dataset_1       0 0.525 25.102 16.017 Rarefaction 1.222 13.622 18.411        TD
3 Dataset_1       0 0.550 30.426 18.489 Rarefaction 1.397 15.752 21.226        TD
4 Dataset_1       0 0.575 37.171 21.450 Rarefaction 1.574 18.365 24.535        TD
5 Dataset_1       0 0.600 45.591 24.932 Rarefaction 1.751 21.500 28.363        TD
6 Dataset_1       0 0.625 56.005 28.975 Rarefaction 1.932 25.189 32.762        TD

$alpha
    Dataset Order.q    SC   Size  Alpha      Method  s.e.    LCL    UCL Diversity
1 Dataset_1       0 0.500 25.949  8.432 Rarefaction 0.411  7.626  9.238        TD
2 Dataset_1       0 0.525 32.249  9.972 Rarefaction 0.477  9.037 10.907        TD
3 Dataset_1       0 0.550 40.247 11.826 Rarefaction 0.541 10.765 12.887        TD
4 Dataset_1       0 0.575 50.044 13.974 Rarefaction 0.606 12.786 15.161        TD
5 Dataset_1       0 0.600 61.802 16.403 Rarefaction 0.677 15.076 17.730        TD
6 Dataset_1       0 0.625 75.870 19.132 Rarefaction 0.760 17.643 20.621        TD

$beta
    Dataset Order.q    SC   Size  Beta      Method  s.e.   LCL   UCL Diversity
1 Dataset_1       0 0.500 25.949 1.658 Rarefaction 0.028 1.602 1.714        TD
2 Dataset_1       0 0.525 32.249 1.606 Rarefaction 0.029 1.550 1.662        TD
3 Dataset_1       0 0.550 40.247 1.563 Rarefaction 0.028 1.509 1.617        TD
4 Dataset_1       0 0.575 50.044 1.535 Rarefaction 0.026 1.484 1.586        TD
5 Dataset_1       0 0.600 61.802 1.520 Rarefaction 0.025 1.472 1.568        TD
6 Dataset_1       0 0.625 75.870 1.514 Rarefaction 0.023 1.469 1.560        TD

$`1-C`
    Dataset Order.q    SC   Size Dissimilarity      Method  s.e.   LCL   UCL Diversity
1 Dataset_1       0 0.500 25.949         0.658 Rarefaction 0.028 0.602 0.714        TD
2 Dataset_1       0 0.525 32.249         0.606 Rarefaction 0.029 0.550 0.662        TD
3 Dataset_1       0 0.550 40.247         0.563 Rarefaction 0.028 0.509 0.617        TD
4 Dataset_1       0 0.575 50.044         0.535 Rarefaction 0.026 0.484 0.586        TD
5 Dataset_1       0 0.600 61.802         0.520 Rarefaction 0.025 0.472 0.568        TD
6 Dataset_1       0 0.625 75.870         0.514 Rarefaction 0.023 0.469 0.560        TD

$`1-U`
    Dataset Order.q    SC   Size Dissimilarity      Method  s.e.   LCL   UCL Diversity
1 Dataset_1       0 0.500 25.949         0.794 Rarefaction 0.020 0.754 0.834        TD
2 Dataset_1       0 0.525 32.249         0.755 Rarefaction 0.022 0.712 0.798        TD
3 Dataset_1       0 0.550 40.247         0.721 Rarefaction 0.022 0.677 0.764        TD
4 Dataset_1       0 0.575 50.044         0.697 Rarefaction 0.022 0.654 0.740        TD
5 Dataset_1       0 0.600 61.802         0.684 Rarefaction 0.021 0.643 0.726        TD
6 Dataset_1       0 0.625 75.870         0.679 Rarefaction 0.020 0.640 0.719        TD

$`1-V`
    Dataset Order.q    SC   Size Dissimilarity      Method  s.e.   LCL   UCL Diversity
1 Dataset_1       0 0.500 25.949         0.658 Rarefaction 0.028 0.602 0.714        TD
2 Dataset_1       0 0.525 32.249         0.606 Rarefaction 0.029 0.550 0.662        TD
3 Dataset_1       0 0.550 40.247         0.563 Rarefaction 0.028 0.509 0.617        TD
4 Dataset_1       0 0.575 50.044         0.535 Rarefaction 0.026 0.484 0.586        TD
5 Dataset_1       0 0.600 61.802         0.520 Rarefaction 0.025 0.472 0.568        TD
6 Dataset_1       0 0.625 75.870         0.514 Rarefaction 0.023 0.469 0.560        TD

$`1-S`
    Dataset Order.q    SC   Size Dissimilarity      Method  s.e.   LCL   UCL Diversity
1 Dataset_1       0 0.500 25.949         0.794 Rarefaction 0.020 0.754 0.834        TD
2 Dataset_1       0 0.525 32.249         0.755 Rarefaction 0.022 0.712 0.798        TD
3 Dataset_1       0 0.550 40.247         0.721 Rarefaction 0.022 0.677 0.764        TD
4 Dataset_1       0 0.575 50.044         0.697 Rarefaction 0.022 0.654 0.740        TD
5 Dataset_1       0 0.600 61.802         0.684 Rarefaction 0.021 0.643 0.726        TD
6 Dataset_1       0 0.625 75.870         0.679 Rarefaction 0.020 0.640 0.719        TD

The output contains seven data frames: gamma, alpha, beta, C, U, V, S. For each data frame, it includes the diversity estimate (Estimate), the diversity order (Order.q), Method (Rarefaction, Observed, or Extrapolation, depending on whether the size m is less than, equal to, or greater than the reference sample size), the sample coverage estimate (SC), the sample size (Size), the standard error from bootstrap replications (s.e.), the lower and upper confidence limits of diversity (LCL, UCL), and the name of dataset (Dataset). These diversity estimates with confidence intervals are used for plotting the diversity curve.

The function ggiNEXTbeta.link(), which extends ggplot2 to the "iNEXT.link" object with default arguments, is described as follows:

The ggiNEXTbeta.link() function is a wrapper around the ggplot2 package to create a R/E curve using a single line of code. The resulting object is of class "ggplot", so it can be manipulated using the ggplot2 tools. Users can visualize the output of beta diversity or four dissimilarities by setting the parameter type:

ggiNEXTbeta.link(Abundance_TD, type = 'B')

ggiNEXTbeta.link(Abundance_TD, type = 'D')

If you publish your work based on the results from the iNEXT.link package, you should make references to the following methodology paper:

• Chiu, C-H., Chao, A., Vogel, S., Kriegel, P. and Thorn, S. (2023). Quantifying and estimating ecological network diversity based on incomplete sampling data. Philosophical Transactions of the Royal Society B, 378: 20220183. https://doi.org/10.1098/rstb.2022.0183

The iNEXT.link package is licensed under the GPLv3. To help refine iNEXT.link, your comments or feedback would be welcome (please send them to Anne Chao or report an issue on the iNEXT.link github iNEXT.link_github.

• 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. & Jost, L. (2012) Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology, 93, 2533�M2547

• Chao, A., Y. Kubota, D. Zelen??, C.-H. Chiu, C.-F. Li, B. Kusumoto, M. Yasuhara, S. Thorn, C.-L. Wei, M. J. Costello, and R. K. Colwell (2020). Quantifying sample completeness and comparing diversities among assemblages. Ecological Research, 35, 292-314.

• Chiu, C-H., Chao, A., Vogel, S., Kriegel, P. and Thorn, S. (2023). Quantifying and estimating ecological network diversity based on incomplete sampling data. Philosophical Transactions of the Royal Society B, 378: 20220183. https://doi.org/10.1098/rstb.2022.0183