7 Network topology information
Load R Package
library(tidyverse) # data manipulation / piping utilities
library(ggNetView) # graph builders + info-extraction helpersExample data
# Access built-in example datasets in ggNetView
# ---- Dataset 1: Relative abundance table of rarefied ASVs/OTUs ----
# Rows = ASVs/OTUs (features / variables), Columns = samples
data("otu_rare_relative")
dim(otu_rare_relative) # Check matrix dimensions: n_features x n_samples ## [1] 2859 18
otu_rare_relative[1:5, 1:5] # Preview first 5 rows x 5 cols to confirm data layout## KO1 KO2 KO3 KO4 KO5
## ASV_1 0.03306667 0.05453333 0.02013333 0.03613333 0.02686667
## ASV_2 0.05750000 0.03393333 0.06046667 0.05810000 0.07320000
## ASV_3 0.01733333 0.01296667 0.02290000 0.02336667 0.03106667
## ASV_4 0.04266667 0.01093333 0.01416667 0.01933333 0.03346667
## ASV_6 0.02646667 0.01856667 0.02110000 0.02353333 0.03806667
# ---- Dataset 2: Taxonomic annotation table for ASVs/OTUs ----
# Rows = ASVs/OTUs (row names should match the abundance table above)
# Columns = taxonomic ranks (Kingdom ~ Species, etc.)
data("tax_tab")
dim(tax_tab)## [1] 2859 8
tax_tab[1:5, 1:5]## # A tibble: 5 × 5
## OTUID Kingdom Phylum Class Order
## <chr> <chr> <chr> <chr> <chr>
## 1 ASV_2 Archaea Thaumarchaeota Unassigned Nitrososphaerales
## 2 ASV_3 Bacteria Verrucomicrobia Spartobacteria Unassigned
## 3 ASV_31 Bacteria Actinobacteria Actinobacteria Actinomycetales
## 4 ASV_27 Archaea Thaumarchaeota Unassigned Nitrososphaerales
## 5 ASV_9 Bacteria Unassigned Unassigned UnassignedBuild graph object
# ---- Build a co-occurrence network from an abundance matrix ----
# Internal pipeline: transform -> correlation -> p-value adjustment ->
# edge filtering -> community detection -> attach taxonomy.
graph_obj <- build_graph_from_mat(
mat = otu_rare_relative, # variables x samples numeric matrix
transfrom.method = "none", # input already relative abundance, no extra transform
method = "WGCNA", # correlation backend: WGCNA::corAndPvalue
proc = "bonferroni", # multiple-testing correction
r.threshold = 0.7, # |r| cutoff for keeping an edge
p.threshold = 0.05, # adjusted p-value cutoff
node_annotation = tax_tab, # taxonomy joined onto each node by name
top_modules = 15, # keep top-15 modules; rest -> "Others"
seed = 1115 # fix RNG for reproducibility
)
graph_obj # tbl_graph with Modularity / Degree / Strength + taxonomy columns## # A tbl_graph: 213 nodes and 844 edges
## #
## # An undirected simple graph with 29 components
## #
## # Node Data: 213 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_649 5 5 5 5 27 26.5 Bacter…
## 2 ASV_705 5 5 5 5 27 26.5 Bacter…
## 3 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 4 ASV_13… 5 5 5 5 27 26.5 Bacter…
## 5 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 6 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 7 ASV_24… 5 5 5 5 27 26.5 Bacter…
## 8 ASV_25… 5 5 5 5 27 26.4 Bacter…
## 9 ASV_28… 5 5 5 5 27 26.5 Bacter…
## 10 ASV_28… 5 5 5 5 27 26.5 Bacter…
## # ℹ 203 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 844 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 194 195 0.959 0.959 Positive
## 2 185 208 0.954 0.954 Positive
## 3 185 213 0.957 0.957 Positive
## # ℹ 841 more rows7.1 Get network topology information
when
mat = NULL
# ---- Compute network topology + robustness for a single graph ----
# When `mat = NULL`, the function still computes all *purely topological*
# metrics from the igraph object, but the following fields are returned as NA
# because they require the original abundance matrix:
#
# * Cohension_Positive - needs per-ASV mean abundance to weight positive r
# * Cohension_Negative - needs per-ASV mean abundance to weight negative r
# * Robustness_weight - abundance-weighted node-removal bootstrap (needs sp.ra)
# * Robustness_unweight - tied to the same `mat` branch in the code, so also NA
# * Stability - mean of the two Robustness_* fields, so also NA
# * out$Robustness - the whole 5%-100% removal curve is NA (mean/sd/se)
#
# All other fields (Node, Edge, Degree, Distance, Diameter, Density,
# Transitivity_global/local, Betweenness, Betweenness_edge, Closeness,
# Eigen_centrality, Modularity, K_core_mean/max/min, Network_efficiency,
# Network_info.centrality, Vulenrability) are computed normally from `graph_obj`.
topology_out <- get_network_topology(
graph_obj = graph_obj, # input tbl_graph (required)
mat = NULL, # raw abundance matrix; NULL -> skip cohesion + robustness
transfrom.method = "none", # pre-correlation transform (ignored when mat = NULL)
method = "WGCNA", # correlation backend used to rebuild network.raw from `mat`
proc = "bonferroni",# multiple-testing correction for p-values (used with `mat`)
r.threshold = 0.7, # |r| cutoff applied when rebuilding network.raw from `mat`
p.threshold = 0.05, # adjusted p-value cutoff applied when rebuilding network.raw
bootstrap = 100 # # of random ER networks for `Random_nerwork` column;
# also # of bootstrap iterations for robustness (only when mat != NULL)
)
class(topology_out)## [1] "list"
names(topology_out)## [1] "topology" "Robustness"
topology_out## $topology
## # A tibble: 24 × 3
## Topology Target_network Random_nerwork
## <chr> <dbl> <dbl>
## 1 Node 213 213
## 2 Edge 844 844
## 3 Degree 7.92 7.92
## 4 Distance 1.45 2.81
## 5 Diameter 3.83 5.04
## 6 Density 0.0374 0.0374
## 7 Transitivity_global 0.851 0.0374
## 8 Transitivity_local 0.783 0.0373
## 9 Betweenness 3.47 191.
## 10 Betweenness_edge 2.58 75.0
## # ℹ 14 more rows
##
## $Robustness
## Proportion.removed remain.mean remain.sd remain.se weighted
## 1 0.05 NA NA NA weighted
## 2 0.10 NA NA NA weighted
## 3 0.15 NA NA NA weighted
## 4 0.20 NA NA NA weighted
## 5 0.25 NA NA NA weighted
## 6 0.30 NA NA NA weighted
## 7 0.35 NA NA NA weighted
## 8 0.40 NA NA NA weighted
## 9 0.45 NA NA NA weighted
## 10 0.50 NA NA NA weighted
## 11 0.55 NA NA NA weighted
## 12 0.60 NA NA NA weighted
## 13 0.65 NA NA NA weighted
## 14 0.70 NA NA NA weighted
## 15 0.75 NA NA NA weighted
## 16 0.80 NA NA NA weighted
## 17 0.85 NA NA NA weighted
## 18 0.90 NA NA NA weighted
## 19 0.95 NA NA NA weighted
## 20 1.00 NA NA NA weighted
## 21 0.05 NA NA NA unweighted
## 22 0.10 NA NA NA unweighted
## 23 0.15 NA NA NA unweighted
## 24 0.20 NA NA NA unweighted
## 25 0.25 NA NA NA unweighted
## 26 0.30 NA NA NA unweighted
## 27 0.35 NA NA NA unweighted
## 28 0.40 NA NA NA unweighted
## 29 0.45 NA NA NA unweighted
## 30 0.50 NA NA NA unweighted
## 31 0.55 NA NA NA unweighted
## 32 0.60 NA NA NA unweighted
## 33 0.65 NA NA NA unweighted
## 34 0.70 NA NA NA unweighted
## 35 0.75 NA NA NA unweighted
## 36 0.80 NA NA NA unweighted
## 37 0.85 NA NA NA unweighted
## 38 0.90 NA NA NA unweighted
## 39 0.95 NA NA NA unweighted
## 40 1.00 NA NA NA unweighted7.2 Get network topology information with matrix
When a matrix is passed to
mat, all topology properties are computed.
# ---- Compute the FULL set of network topology + robustness metrics ----
# When `mat` is provided, the function recomputes the thresholded correlation
# matrix from `mat` (used as `network.raw`) and ALL topology fields are
# returned with real values - including the ones that are NA when mat = NULL:
# Cohension_Positive / Cohension_Negative
# Robustness_weight / Robustness_unweight
# Stability
# out$Robustness (the 5%-100% node-removal curve)
topology_with_mat <- get_network_topology(
graph_obj = graph_obj, # input tbl_graph (required)
mat = otu_rare_relative, # raw abundance matrix used to derive sp.ra and rebuild network.raw
transfrom.method = "none", # pre-correlation transform on `mat`; "none" = keep as-is
method = "WGCNA", # correlation backend: WGCNA::corAndPvalue
proc = "bonferroni", # multiple-testing correction
r.threshold = 0.7, # |r| cutoff for keeping an edge in network.raw
p.threshold = 0.05, # adjusted p-value cutoff for keeping an edge
bootstrap = 100 # # of bootstrap iterations for robustness AND # of random ER networks for the Random_nerwork column
)
topology_with_mat## $topology
## # A tibble: 24 × 3
## Topology Target_network Random_nerwork
## <chr> <dbl> <dbl>
## 1 Node 213 213
## 2 Edge 844 844
## 3 Degree 7.92 7.92
## 4 Distance 1.45 2.81
## 5 Diameter 3.83 5.07
## 6 Density 0.0374 0.0374
## 7 Transitivity_global 0.851 0.0369
## 8 Transitivity_local 0.783 0.0369
## 9 Betweenness 3.47 191.
## 10 Betweenness_edge 2.58 75.0
## # ℹ 14 more rows
##
## $Robustness
## Proportion.removed remain.mean remain.sd remain.se weighted
## 1 0.05 0.93605634 0.007211109 0.0007211109 weighted
## 2 0.10 0.88028169 0.009795834 0.0009795834 weighted
## 3 0.15 0.82098592 0.010068306 0.0010068306 weighted
## 4 0.20 0.75812207 0.014099990 0.0014099990 weighted
## 5 0.25 0.70136150 0.014709199 0.0014709199 weighted
## 6 0.30 0.64497653 0.014509330 0.0014509330 weighted
## 7 0.35 0.58685446 0.016628903 0.0016628903 weighted
## 8 0.40 0.53352113 0.016501489 0.0016501489 weighted
## 9 0.45 0.47596244 0.015021992 0.0015021992 weighted
## 10 0.50 0.42164319 0.016598013 0.0016598013 weighted
## 11 0.55 0.36976526 0.017402457 0.0017402457 weighted
## 12 0.60 0.31342723 0.017882009 0.0017882009 weighted
## 13 0.65 0.26868545 0.016971541 0.0016971541 weighted
## 14 0.70 0.21671362 0.018246825 0.0018246825 weighted
## 15 0.75 0.16539906 0.017010851 0.0017010851 weighted
## 16 0.80 0.12633803 0.013887030 0.0013887030 weighted
## 17 0.85 0.08164319 0.015915997 0.0015915997 weighted
## 18 0.90 0.04460094 0.012313354 0.0012313354 weighted
## 19 0.95 0.01610329 0.009721802 0.0009721802 weighted
## 20 1.00 0.00000000 0.000000000 0.0000000000 weighted
## 21 0.05 0.93671362 0.007709494 0.0007709494 unweighted
## 22 0.10 0.88164319 0.009396664 0.0009396664 unweighted
## 23 0.15 0.81835681 0.012795630 0.0012795630 unweighted
## 24 0.20 0.76169014 0.013146217 0.0013146217 unweighted
## 25 0.25 0.70309859 0.013163142 0.0013163142 unweighted
## 26 0.30 0.64441315 0.013669288 0.0013669288 unweighted
## 27 0.35 0.58643192 0.015622327 0.0015622327 unweighted
## 28 0.40 0.53389671 0.013950773 0.0013950773 unweighted
## 29 0.45 0.47577465 0.015780078 0.0015780078 unweighted
## 30 0.50 0.42441315 0.017169071 0.0017169071 unweighted
## 31 0.55 0.36943662 0.017358583 0.0017358583 unweighted
## 32 0.60 0.31089202 0.015939550 0.0015939550 unweighted
## 33 0.65 0.26976526 0.017057446 0.0017057446 unweighted
## 34 0.70 0.21596244 0.019154967 0.0019154967 unweighted
## 35 0.75 0.16741784 0.017708100 0.0017708100 unweighted
## 36 0.80 0.12718310 0.016630175 0.0016630175 unweighted
## 37 0.85 0.08309859 0.014241705 0.0014241705 unweighted
## 38 0.90 0.04394366 0.013169906 0.0013169906 unweighted
## 39 0.95 0.01507042 0.010170393 0.0010170393 unweighted
## 40 1.00 0.00000000 0.000000000 0.0000000000 unweighted7.3 Get network topology information from sample
# ---- Per-sample subgraph topology -------------------------------------------
# Step 1: split `graph_obj` into per-sample subgraphs by the abundance matrix
# (an OTU is "present" in a sample when its abundance > min_abundance).
# Step 2: run the full `get_network_topology()` pipeline on EACH sample subgraph.
# When `mat` is supplied, every topology field (including cohesion, robustness,
# stability) is computed for each sample.
t3_group <- system.time(
topology_from_sample <- get_sample_subgraph_topology(
graph_obj = graph_obj, # input tbl_graph (the full network)
mat = otu_rare_relative, # abundance matrix used for both presence-call AND cohesion/robustness
transfrom.method = "none", # pre-correlation transform on `mat`; "none" = keep as-is
method = "WGCNA", # correlation backend: WGCNA::corAndPvalue
cor.method = "pearson", # Pearson correlation
proc = "bonferroni", # multiple-testing correction
bootstrap = 100 # # of bootstrap iterations for robustness; also # of random ER nets for reference
)
)
topology_from_sample # one topology table per sample, plus per-sample robustness curves## $subgraph_list
## $subgraph_list$KO1
## # A tbl_graph: 113 nodes and 161 edges
## #
## # An undirected simple graph with 35 components
## #
## # Node Data: 113 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 3 ASV_913 5 5 5 5 26 25.2 Bacter…
## 4 ASV_767 5 5 5 5 22 21.1 Bacter…
## 5 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 6 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 9 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 10 ASV_25… 5 5 5 5 12 11.3 Bacter…
## # ℹ 103 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 161 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 100 101 0.959 0.959 Positive
## 2 90 92 0.969 0.969 Positive
## 3 87 89 0.943 0.943 Positive
## # ℹ 158 more rows
##
## $subgraph_list$KO2
## # A tbl_graph: 122 nodes and 164 edges
## #
## # An undirected simple graph with 37 components
## #
## # Node Data: 122 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_767 5 5 5 5 22 21.1 Bacter…
## 4 ASV_996 5 5 5 5 19 18.3 Bacter…
## 5 ASV_322 5 5 5 5 18 17.2 Bacter…
## 6 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 7 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 8 ASV_244 5 5 5 5 3 2.87 Bacter…
## 9 ASV_367 5 5 5 5 2 1.89 Bacter…
## 10 ASV_277 5 5 5 5 1 0.950 Bacter…
## # ℹ 112 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 164 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 108 109 0.959 0.959 Positive
## 2 104 122 0.957 0.957 Positive
## 3 91 93 0.969 0.969 Positive
## # ℹ 161 more rows
##
## $subgraph_list$KO3
## # A tbl_graph: 102 nodes and 379 edges
## #
## # An undirected simple graph with 36 components
## #
## # Node Data: 102 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_649 5 5 5 5 27 26.5 Bacter…
## 2 ASV_705 5 5 5 5 27 26.5 Bacter…
## 3 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 4 ASV_13… 5 5 5 5 27 26.5 Bacter…
## 5 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 6 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 7 ASV_24… 5 5 5 5 27 26.5 Bacter…
## 8 ASV_25… 5 5 5 5 27 26.4 Bacter…
## 9 ASV_28… 5 5 5 5 27 26.5 Bacter…
## 10 ASV_28… 5 5 5 5 27 26.5 Bacter…
## # ℹ 92 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 379 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.996 0.996 Positive
## 2 1 3 0.997 0.997 Positive
## 3 2 3 0.994 0.994 Positive
## # ℹ 376 more rows
##
## $subgraph_list$KO4
## # A tbl_graph: 94 nodes and 107 edges
## #
## # An undirected simple graph with 36 components
## #
## # Node Data: 94 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_913 5 5 5 5 26 25.2 Bacter…
## 2 ASV_767 5 5 5 5 22 21.1 Bacter…
## 3 ASV_996 5 5 5 5 19 18.3 Bacter…
## 4 ASV_322 5 5 5 5 18 17.2 Bacter…
## 5 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 6 ASV_244 5 5 5 5 3 2.87 Bacter…
## 7 ASV_367 5 5 5 5 2 1.89 Bacter…
## 8 ASV_277 5 5 5 5 1 0.950 Bacter…
## 9 ASV_671 2 2 2 2 18 17.5 Bacter…
## 10 ASV_568 2 2 2 2 16 15.6 Bacter…
## # ℹ 84 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 107 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.967 0.967 Positive
## 2 1 3 0.947 0.947 Positive
## 3 1 4 0.954 0.954 Positive
## # ℹ 104 more rows
##
## $subgraph_list$KO5
## # A tbl_graph: 71 nodes and 63 edges
## #
## # An undirected simple graph with 32 components
## #
## # Node Data: 71 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_913 5 5 5 5 26 25.2 Bacter…
## 2 ASV_819 5 5 5 5 26 25.5 Bacter…
## 3 ASV_767 5 5 5 5 22 21.1 Bacter…
## 4 ASV_996 5 5 5 5 19 18.3 Bacter…
## 5 ASV_322 5 5 5 5 18 17.2 Bacter…
## 6 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 7 ASV_244 5 5 5 5 3 2.87 Bacter…
## 8 ASV_367 5 5 5 5 2 1.89 Bacter…
## 9 ASV_277 5 5 5 5 1 0.950 Bacter…
## 10 ASV_24… 2 2 2 2 15 14.5 Bacter…
## # ℹ 61 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 63 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.974 0.974 Positive
## 2 1 3 0.967 0.967 Positive
## 3 2 3 0.969 0.969 Positive
## # ℹ 60 more rows
##
## $subgraph_list$KO6
## # A tbl_graph: 97 nodes and 119 edges
## #
## # An undirected simple graph with 35 components
## #
## # Node Data: 97 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_25… 5 5 5 5 25 24.4 Bacter…
## 2 ASV_28… 5 5 5 5 23 22.5 Bacter…
## 3 ASV_767 5 5 5 5 22 21.1 Bacter…
## 4 ASV_26… 5 5 5 5 21 20.4 Bacter…
## 5 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 6 ASV_996 5 5 5 5 19 18.3 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 9 ASV_244 5 5 5 5 3 2.87 Bacter…
## 10 ASV_367 5 5 5 5 2 1.89 Bacter…
## # ℹ 87 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 119 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.989 0.989 Positive
## 2 1 3 0.949 0.949 Positive
## 3 2 3 0.943 0.943 Positive
## # ℹ 116 more rows
##
## $subgraph_list$OE1
## # A tbl_graph: 138 nodes and 308 edges
## #
## # An undirected simple graph with 34 components
## #
## # Node Data: 138 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_819 5 5 5 5 26 25.5 Bacter…
## 4 ASV_767 5 5 5 5 22 21.1 Bacter…
## 5 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 6 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 7 ASV_996 5 5 5 5 19 18.3 Bacter…
## 8 ASV_322 5 5 5 5 18 17.2 Bacter…
## 9 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 10 ASV_23… 5 5 5 5 18 17.3 Bacter…
## # ℹ 128 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 308 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 125 126 0.959 0.959 Positive
## 2 113 115 0.969 0.969 Positive
## 3 111 112 0.943 0.943 Positive
## # ℹ 305 more rows
##
## $subgraph_list$OE2
## # A tbl_graph: 135 nodes and 230 edges
## #
## # An undirected simple graph with 41 components
## #
## # Node Data: 135 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_649 5 5 5 5 27 26.5 Bacter…
## 2 ASV_705 5 5 5 5 27 26.5 Bacter…
## 3 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 4 ASV_913 5 5 5 5 26 25.2 Bacter…
## 5 ASV_819 5 5 5 5 26 25.5 Bacter…
## 6 ASV_17… 5 5 5 5 24 23.5 Bacter…
## 7 ASV_767 5 5 5 5 22 21.1 Bacter…
## 8 ASV_26… 5 5 5 5 21 20.4 Bacter…
## 9 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 10 ASV_28… 5 5 5 5 20 19.1 Bacter…
## # ℹ 125 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 230 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 120 121 0.959 0.959 Positive
## 2 114 135 0.957 0.957 Positive
## 3 105 107 0.969 0.969 Positive
## # ℹ 227 more rows
##
## $subgraph_list$OE3
## # A tbl_graph: 119 nodes and 160 edges
## #
## # An undirected simple graph with 33 components
## #
## # Node Data: 119 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 3 ASV_913 5 5 5 5 26 25.2 Bacter…
## 4 ASV_767 5 5 5 5 22 21.1 Bacter…
## 5 ASV_996 5 5 5 5 19 18.3 Bacter…
## 6 ASV_322 5 5 5 5 18 17.2 Bacter…
## 7 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 8 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 9 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 10 ASV_25… 5 5 5 5 12 11.3 Bacter…
## # ℹ 109 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 160 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 106 107 0.959 0.959 Positive
## 2 101 119 0.954 0.954 Positive
## 3 91 93 0.969 0.969 Positive
## # ℹ 157 more rows
##
## $subgraph_list$OE4
## # A tbl_graph: 118 nodes and 171 edges
## #
## # An undirected simple graph with 34 components
## #
## # Node Data: 118 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_819 5 5 5 5 26 25.5 Bacter…
## 3 ASV_28… 5 5 5 5 25 24.5 Bacter…
## 4 ASV_24… 5 5 5 5 23 22.6 Bacter…
## 5 ASV_767 5 5 5 5 22 21.1 Bacter…
## 6 ASV_996 5 5 5 5 19 18.3 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 9 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 10 ASV_244 5 5 5 5 3 2.87 Bacter…
## # ℹ 108 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 171 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 107 108 0.959 0.959 Positive
## 2 103 116 0.954 0.954 Positive
## 3 94 96 0.969 0.969 Positive
## # ℹ 168 more rows
##
## $subgraph_list$OE5
## # A tbl_graph: 111 nodes and 165 edges
## #
## # An undirected simple graph with 29 components
## #
## # Node Data: 111 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_819 5 5 5 5 26 25.5 Bacter…
## 4 ASV_17… 5 5 5 5 24 23.5 Bacter…
## 5 ASV_767 5 5 5 5 22 21.1 Bacter…
## 6 ASV_26… 5 5 5 5 21 20.4 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 9 ASV_25… 5 5 5 5 12 11.3 Bacter…
## 10 ASV_244 5 5 5 5 3 2.87 Bacter…
## # ℹ 101 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 165 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 101 102 0.959 0.959 Positive
## 2 91 93 0.969 0.969 Positive
## 3 87 89 0.943 0.943 Positive
## # ℹ 162 more rows
##
## $subgraph_list$OE6
## # A tbl_graph: 140 nodes and 234 edges
## #
## # An undirected simple graph with 36 components
## #
## # Node Data: 140 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 3 ASV_913 5 5 5 5 26 25.2 Bacter…
## 4 ASV_819 5 5 5 5 26 25.5 Bacter…
## 5 ASV_25… 5 5 5 5 25 24.4 Bacter…
## 6 ASV_17… 5 5 5 5 24 23.5 Bacter…
## 7 ASV_767 5 5 5 5 22 21.1 Bacter…
## 8 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 9 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 10 ASV_996 5 5 5 5 19 18.3 Bacter…
## # ℹ 130 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 234 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 125 126 0.959 0.959 Positive
## 2 119 138 0.954 0.954 Positive
## 3 108 110 0.969 0.969 Positive
## # ℹ 231 more rows
##
## $subgraph_list$WT1
## # A tbl_graph: 105 nodes and 130 edges
## #
## # An undirected simple graph with 37 components
## #
## # Node Data: 105 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_25… 5 5 5 5 27 26.4 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_819 5 5 5 5 26 25.5 Bacter…
## 4 ASV_28… 5 5 5 5 23 22.5 Bacter…
## 5 ASV_767 5 5 5 5 22 21.1 Bacter…
## 6 ASV_26… 5 5 5 5 21 20.4 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 9 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 10 ASV_25… 5 5 5 5 12 11.3 Bacter…
## # ℹ 95 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 130 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.976 0.976 Positive
## 2 1 3 0.990 0.990 Positive
## 3 2 3 0.974 0.974 Positive
## # ℹ 127 more rows
##
## $subgraph_list$WT2
## # A tbl_graph: 83 nodes and 59 edges
## #
## # An undirected simple graph with 41 components
## #
## # Node Data: 83 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_913 5 5 5 5 26 25.2 Bacter…
## 2 ASV_819 5 5 5 5 26 25.5 Bacter…
## 3 ASV_767 5 5 5 5 22 21.1 Bacter…
## 4 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 5 ASV_996 5 5 5 5 19 18.3 Bacter…
## 6 ASV_322 5 5 5 5 18 17.2 Bacter…
## 7 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 8 ASV_244 5 5 5 5 3 2.87 Bacter…
## 9 ASV_367 5 5 5 5 2 1.89 Bacter…
## 10 ASV_277 5 5 5 5 1 0.950 Bacter…
## # ℹ 73 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 59 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.974 0.974 Positive
## 2 1 3 0.967 0.967 Positive
## 3 2 3 0.969 0.969 Positive
## # ℹ 56 more rows
##
## $subgraph_list$WT3
## # A tbl_graph: 117 nodes and 171 edges
## #
## # An undirected simple graph with 38 components
## #
## # Node Data: 117 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 2 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 3 ASV_913 5 5 5 5 26 25.2 Bacter…
## 4 ASV_24… 5 5 5 5 23 22.6 Bacter…
## 5 ASV_28… 5 5 5 5 23 22.5 Bacter…
## 6 ASV_767 5 5 5 5 22 21.1 Bacter…
## 7 ASV_996 5 5 5 5 19 18.3 Bacter…
## 8 ASV_322 5 5 5 5 18 17.2 Bacter…
## 9 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 10 ASV_18… 5 5 5 5 17 16.3 Bacter…
## # ℹ 107 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 171 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 106 107 0.959 0.959 Positive
## 2 95 97 0.969 0.969 Positive
## 3 92 93 0.943 0.943 Positive
## # ℹ 168 more rows
##
## $subgraph_list$WT4
## # A tbl_graph: 111 nodes and 222 edges
## #
## # An undirected simple graph with 34 components
## #
## # Node Data: 111 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_819 5 5 5 5 26 25.5 Bacter…
## 4 ASV_767 5 5 5 5 22 21.1 Bacter…
## 5 ASV_996 5 5 5 5 19 18.3 Bacter…
## 6 ASV_322 5 5 5 5 18 17.2 Bacter…
## 7 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 8 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 9 ASV_25… 5 5 5 5 12 11.3 Bacter…
## 10 ASV_244 5 5 5 5 3 2.87 Bacter…
## # ℹ 101 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 222 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 102 103 0.959 0.959 Positive
## 2 92 94 0.969 0.969 Positive
## 3 88 90 0.943 0.943 Positive
## # ℹ 219 more rows
##
## $subgraph_list$WT5
## # A tbl_graph: 90 nodes and 103 edges
## #
## # An undirected simple graph with 32 components
## #
## # Node Data: 90 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_819 5 5 5 5 26 25.5 Bacter…
## 2 ASV_767 5 5 5 5 22 21.1 Bacter…
## 3 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 4 ASV_996 5 5 5 5 19 18.3 Bacter…
## 5 ASV_322 5 5 5 5 18 17.2 Bacter…
## 6 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 7 ASV_18… 5 5 5 5 17 16.3 Bacter…
## 8 ASV_25… 5 5 5 5 12 11.3 Bacter…
## 9 ASV_367 5 5 5 5 2 1.89 Bacter…
## 10 ASV_277 5 5 5 5 1 0.950 Bacter…
## # ℹ 80 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 103 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 1 2 0.969 0.969 Positive
## 2 1 3 0.955 0.955 Positive
## 3 2 3 0.953 0.953 Positive
## # ℹ 100 more rows
##
## $subgraph_list$WT6
## # A tbl_graph: 111 nodes and 162 edges
## #
## # An undirected simple graph with 36 components
## #
## # Node Data: 111 × 14 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_705 5 5 5 5 27 26.5 Bacter…
## 2 ASV_913 5 5 5 5 26 25.2 Bacter…
## 3 ASV_819 5 5 5 5 26 25.5 Bacter…
## 4 ASV_17… 5 5 5 5 24 23.5 Bacter…
## 5 ASV_767 5 5 5 5 22 21.1 Bacter…
## 6 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 7 ASV_322 5 5 5 5 18 17.2 Bacter…
## 8 ASV_15… 5 5 5 5 18 17.1 Bacter…
## 9 ASV_23… 5 5 5 5 18 17.3 Bacter…
## 10 ASV_18… 5 5 5 5 17 16.3 Bacter…
## # ℹ 101 more rows
## # ℹ 6 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>
## #
## # Edge Data: 162 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 103 104 0.959 0.959 Positive
## 2 88 90 0.969 0.969 Positive
## 3 84 86 0.943 0.943 Positive
## # ℹ 159 more rows
##
##
## $topology
## # A tibble: 432 × 4
## Sample Topology Target_network Random_nerwork
## * <chr> <chr> <dbl> <dbl>
## 1 KO1 Node 113 113
## 2 KO1 Edge 161 161
## 3 KO1 Degree 2.85 2.85
## 4 KO1 Distance 1.43 4.37
## 5 KO1 Diameter 2.88 9.87
## 6 KO1 Density 0.0254 0.0254
## 7 KO1 Transitivity_global 0.741 0.0245
## 8 KO1 Transitivity_local 0.702 0.0243
## 9 KO1 Betweenness 1.24 165.
## 10 KO1 Betweenness_edge 2.61 150.
## # ℹ 422 more rows
##
## $Robustness
## Sample Proportion.removed remain.mean remain.sd remain.se
## KO1.1 KO1 0.05 0.948148148 0.006580269 0.0006580269
## KO1.2 KO1 0.10 0.887222222 0.009153909 0.0009153909
## KO1.3 KO1 0.15 0.831944444 0.010559230 0.0010559230
## KO1.4 KO1 0.20 0.772314815 0.012422251 0.0012422251
## KO1.5 KO1 0.25 0.719444444 0.012240008 0.0012240008
## KO1.6 KO1 0.30 0.669351852 0.013568445 0.0013568445
## KO1.7 KO1 0.35 0.608611111 0.014347703 0.0014347703
## KO1.8 KO1 0.40 0.556018519 0.015312386 0.0015312386
## KO1.9 KO1 0.45 0.493796296 0.016545419 0.0016545419
## KO1.10 KO1 0.50 0.449629630 0.017275932 0.0017275932
## KO1.11 KO1 0.55 0.392037037 0.017119832 0.0017119832
## KO1.12 KO1 0.60 0.333425926 0.018401002 0.0018401002
## KO1.13 KO1 0.65 0.282037037 0.018724074 0.0018724074
## KO1.14 KO1 0.70 0.225370370 0.018575483 0.0018575483
## KO1.15 KO1 0.75 0.171759259 0.020907245 0.0020907245
## KO1.16 KO1 0.80 0.133333333 0.020217602 0.0020217602
## KO1.17 KO1 0.85 0.076944444 0.021812177 0.0021812177
## KO1.18 KO1 0.90 0.041574074 0.017631929 0.0017631929
## KO1.19 KO1 0.95 0.007222222 0.009633298 0.0009633298
## KO1.20 KO1 1.00 0.000000000 0.000000000 0.0000000000
## KO1.21 KO1 0.05 0.948796296 0.006373696 0.0006373696
## KO1.22 KO1 0.10 0.885740741 0.009043502 0.0009043502
## KO1.23 KO1 0.15 0.835648148 0.011196130 0.0011196130
## KO1.24 KO1 0.20 0.771111111 0.012559870 0.0012559870
## KO1.25 KO1 0.25 0.721296296 0.013388867 0.0013388867
## KO1.26 KO1 0.30 0.665740741 0.013127595 0.0013127595
## KO1.27 KO1 0.35 0.608240741 0.015939742 0.0015939742
## KO1.28 KO1 0.40 0.555833333 0.016670563 0.0016670563
## KO1.29 KO1 0.45 0.492129630 0.017378639 0.0017378639
## KO1.30 KO1 0.50 0.443333333 0.018531608 0.0018531608
## KO1.31 KO1 0.55 0.395833333 0.019625315 0.0019625315
## KO1.32 KO1 0.60 0.332592593 0.020501736 0.0020501736
## KO1.33 KO1 0.65 0.279629630 0.019740807 0.0019740807
## KO1.34 KO1 0.70 0.225462963 0.021195209 0.0021195209
## KO1.35 KO1 0.75 0.179351852 0.022436884 0.0022436884
## KO1.36 KO1 0.80 0.135092593 0.020349741 0.0020349741
## KO1.37 KO1 0.85 0.079259259 0.019622887 0.0019622887
## KO1.38 KO1 0.90 0.043518519 0.017384867 0.0017384867
## KO1.39 KO1 0.95 0.010185185 0.011282811 0.0011282811
## KO1.40 KO1 1.00 0.000000000 0.000000000 0.0000000000
## KO2.1 KO2 0.05 0.943949580 0.006326384 0.0006326384
## KO2.2 KO2 0.10 0.886638655 0.009739686 0.0009739686
## KO2.3 KO2 0.15 0.830252101 0.009921446 0.0009921446
## KO2.4 KO2 0.20 0.773781513 0.010527010 0.0010527010
## KO2.5 KO2 0.25 0.716638655 0.011017021 0.0011017021
## KO2.6 KO2 0.30 0.663865546 0.013138419 0.0013138419
## KO2.7 KO2 0.35 0.605630252 0.013420687 0.0013420687
## KO2.8 KO2 0.40 0.550000000 0.013532894 0.0013532894
## KO2.9 KO2 0.45 0.498823529 0.016701137 0.0016701137
## KO2.10 KO2 0.50 0.442100840 0.017055079 0.0017055079
## KO2.11 KO2 0.55 0.395714286 0.018545756 0.0018545756
## KO2.12 KO2 0.60 0.339075630 0.018049897 0.0018049897
## KO2.13 KO2 0.65 0.285630252 0.018941533 0.0018941533
## KO2.14 KO2 0.70 0.231344538 0.020599709 0.0020599709
## KO2.15 KO2 0.75 0.183949580 0.020889913 0.0020889913
## KO2.16 KO2 0.80 0.132268908 0.019245071 0.0019245071
## KO2.17 KO2 0.85 0.085714286 0.021828489 0.0021828489
## KO2.18 KO2 0.90 0.042100840 0.017695497 0.0017695497
## KO2.19 KO2 0.95 0.009915966 0.010161545 0.0010161545
## KO2.20 KO2 1.00 0.000000000 0.000000000 0.0000000000
## KO2.21 KO2 0.05 0.943865546 0.005713187 0.0005713187
## KO2.22 KO2 0.10 0.886890756 0.009284121 0.0009284121
## KO2.23 KO2 0.15 0.831428571 0.009616232 0.0009616232
## KO2.24 KO2 0.20 0.771932773 0.012181727 0.0012181727
## KO2.25 KO2 0.25 0.720420168 0.011754698 0.0011754698
## KO2.26 KO2 0.30 0.661680672 0.013909525 0.0013909525
## KO2.27 KO2 0.35 0.607478992 0.013633718 0.0013633718
## KO2.28 KO2 0.40 0.552941176 0.015618830 0.0015618830
## KO2.29 KO2 0.45 0.495546218 0.015639596 0.0015639596
## KO2.30 KO2 0.50 0.439411765 0.018164923 0.0018164923
## KO2.31 KO2 0.55 0.394117647 0.017896109 0.0017896109
## KO2.32 KO2 0.60 0.339327731 0.016712238 0.0016712238
## KO2.33 KO2 0.65 0.286806723 0.020537286 0.0020537286
## KO2.34 KO2 0.70 0.235042017 0.018674540 0.0018674540
## KO2.35 KO2 0.75 0.181680672 0.020191396 0.0020191396
## KO2.36 KO2 0.80 0.126974790 0.020124695 0.0020124695
## KO2.37 KO2 0.85 0.085630252 0.017903879 0.0017903879
## KO2.38 KO2 0.90 0.040336134 0.017184449 0.0017184449
## KO2.39 KO2 0.95 0.010756303 0.012359606 0.0012359606
## KO2.40 KO2 1.00 0.000000000 0.000000000 0.0000000000
## KO3.1 KO3 0.05 0.941919192 0.008893780 0.0008893780
## KO3.2 KO3 0.10 0.882929293 0.010161537 0.0010161537
## KO3.3 KO3 0.15 0.827171717 0.014704139 0.0014704139
## KO3.4 KO3 0.20 0.770808081 0.014619789 0.0014619789
## KO3.5 KO3 0.25 0.712424242 0.017255538 0.0017255538
## KO3.6 KO3 0.30 0.655151515 0.018554380 0.0018554380
## KO3.7 KO3 0.35 0.597676768 0.019424641 0.0019424641
## KO3.8 KO3 0.40 0.542828283 0.019401548 0.0019401548
## KO3.9 KO3 0.45 0.486666667 0.019964939 0.0019964939
## KO3.10 KO3 0.50 0.428989899 0.019604204 0.0019604204
## KO3.11 KO3 0.55 0.383737374 0.020022414 0.0020022414
## KO3.12 KO3 0.60 0.331212121 0.019543127 0.0019543127
## KO3.13 KO3 0.65 0.280000000 0.023019525 0.0023019525
## KO3.14 KO3 0.70 0.221414141 0.025869616 0.0025869616
## KO3.15 KO3 0.75 0.178080808 0.020688710 0.0020688710
## KO3.16 KO3 0.80 0.132424242 0.022236826 0.0022236826
## KO3.17 KO3 0.85 0.088383838 0.018518519 0.0018518519
## KO3.18 KO3 0.90 0.045858586 0.019811551 0.0019811551
## KO3.19 KO3 0.95 0.016666667 0.013030465 0.0013030465
## KO3.20 KO3 1.00 0.000000000 0.000000000 0.0000000000
## KO3.21 KO3 0.05 0.941212121 0.007648361 0.0007648361
## KO3.22 KO3 0.10 0.883030303 0.011229669 0.0011229669
## KO3.23 KO3 0.15 0.824242424 0.012679715 0.0012679715
## KO3.24 KO3 0.20 0.770000000 0.013908840 0.0013908840
## KO3.25 KO3 0.25 0.713030303 0.016312364 0.0016312364
## KO3.26 KO3 0.30 0.653636364 0.017424335 0.0017424335
## KO3.27 KO3 0.35 0.598080808 0.017305635 0.0017305635
## KO3.28 KO3 0.40 0.542727273 0.019782138 0.0019782138
## KO3.29 KO3 0.45 0.484141414 0.021355451 0.0021355451
## KO3.30 KO3 0.50 0.431919192 0.021348935 0.0021348935
## KO3.31 KO3 0.55 0.384545455 0.022160687 0.0022160687
## KO3.32 KO3 0.60 0.326969697 0.021945716 0.0021945716
## KO3.33 KO3 0.65 0.274141414 0.021631880 0.0021631880
## KO3.34 KO3 0.70 0.229191919 0.021182950 0.0021182950
## KO3.35 KO3 0.75 0.180505051 0.022456354 0.0022456354
## KO3.36 KO3 0.80 0.132828283 0.022671939 0.0022671939
## KO3.37 KO3 0.85 0.089393939 0.020118950 0.0020118950
## KO3.38 KO3 0.90 0.050808081 0.018015256 0.0018015256
## KO3.39 KO3 0.95 0.015454545 0.013804714 0.0013804714
## KO3.40 KO3 1.00 0.000000000 0.000000000 0.0000000000
## KO4.1 KO4 0.05 0.947303371 0.008554813 0.0008554813
## KO4.2 KO4 0.10 0.880449438 0.012006280 0.0012006280
## KO4.3 KO4 0.15 0.828876404 0.016275004 0.0016275004
## KO4.4 KO4 0.20 0.765168539 0.016325464 0.0016325464
## KO4.5 KO4 0.25 0.713258427 0.016861875 0.0016861875
## KO4.6 KO4 0.30 0.647078652 0.018285231 0.0018285231
## KO4.7 KO4 0.35 0.592471910 0.017556571 0.0017556571
## KO4.8 KO4 0.40 0.527865169 0.020882383 0.0020882383
## KO4.9 KO4 0.45 0.482808989 0.021865324 0.0021865324
## KO4.10 KO4 0.50 0.431910112 0.023050103 0.0023050103
## KO4.11 KO4 0.55 0.366292135 0.023307581 0.0023307581
## KO4.12 KO4 0.60 0.322247191 0.022914716 0.0022914716
## KO4.13 KO4 0.65 0.256629213 0.028466211 0.0028466211
## KO4.14 KO4 0.70 0.213820225 0.028319569 0.0028319569
## KO4.15 KO4 0.75 0.159550562 0.022753877 0.0022753877
## KO4.16 KO4 0.80 0.116516854 0.025233502 0.0025233502
## KO4.17 KO4 0.85 0.065842697 0.024325967 0.0024325967
## KO4.18 KO4 0.90 0.032359551 0.019512288 0.0019512288
## KO4.19 KO4 0.95 0.005280899 0.010767087 0.0010767087
## KO4.20 KO4 1.00 0.000000000 0.000000000 0.0000000000
## KO4.21 KO4 0.05 0.946292135 0.008386959 0.0008386959
## KO4.22 KO4 0.10 0.882134831 0.011896914 0.0011896914
## KO4.23 KO4 0.15 0.827640449 0.015169065 0.0015169065
## KO4.24 KO4 0.20 0.763595506 0.015311312 0.0015311312
## KO4.25 KO4 0.25 0.710337079 0.016641111 0.0016641111
## KO4.26 KO4 0.30 0.646629213 0.017521672 0.0017521672
## KO4.27 KO4 0.35 0.596629213 0.019197352 0.0019197352
## KO4.28 KO4 0.40 0.533370787 0.019458296 0.0019458296
## KO4.29 KO4 0.45 0.482471910 0.020872610 0.0020872610
## KO4.30 KO4 0.50 0.432921348 0.022835276 0.0022835276
## KO4.31 KO4 0.55 0.372359551 0.026532469 0.0026532469
## KO4.32 KO4 0.60 0.323258427 0.027189285 0.0027189285
## KO4.33 KO4 0.65 0.266067416 0.028961838 0.0028961838
## KO4.34 KO4 0.70 0.213932584 0.025796517 0.0025796517
## KO4.35 KO4 0.75 0.158314607 0.024590570 0.0024590570
## KO4.36 KO4 0.80 0.119550562 0.025277179 0.0025277179
## KO4.37 KO4 0.85 0.065730337 0.022997763 0.0022997763
## KO4.38 KO4 0.90 0.035955056 0.019689251 0.0019689251
## KO4.39 KO4 0.95 0.007303371 0.011557647 0.0011557647
## KO4.40 KO4 1.00 0.000000000 0.000000000 0.0000000000
## KO5.1 KO5 0.05 0.947910448 0.008615862 0.0008615862
## KO5.2 KO5 0.10 0.878955224 0.012709825 0.0012709825
## KO5.3 KO5 0.15 0.827313433 0.013459611 0.0013459611
## KO5.4 KO5 0.20 0.778208955 0.016973853 0.0016973853
## KO5.5 KO5 0.25 0.706417910 0.020131518 0.0020131518
## KO5.6 KO5 0.30 0.650895522 0.019080223 0.0019080223
## KO5.7 KO5 0.35 0.602686567 0.021190653 0.0021190653
## KO5.8 KO5 0.40 0.535223881 0.021843212 0.0021843212
## KO5.9 KO5 0.45 0.482089552 0.022198808 0.0022198808
## KO5.10 KO5 0.50 0.418955224 0.022275207 0.0022275207
## KO5.11 KO5 0.55 0.369253731 0.025066657 0.0025066657
## KO5.12 KO5 0.60 0.316865672 0.026821664 0.0026821664
## KO5.13 KO5 0.65 0.254626866 0.026138887 0.0026138887
## KO5.14 KO5 0.70 0.207611940 0.026757828 0.0026757828
## KO5.15 KO5 0.75 0.167910448 0.031205140 0.0031205140
## KO5.16 KO5 0.80 0.103283582 0.029293763 0.0029293763
## KO5.17 KO5 0.85 0.067761194 0.026531924 0.0026531924
## KO5.18 KO5 0.90 0.034029851 0.022358390 0.0022358390
## KO5.19 KO5 0.95 0.005820896 0.012167113 0.0012167113
## KO5.20 KO5 1.00 0.000000000 0.000000000 0.0000000000
## KO5.21 KO5 0.05 0.948805970 0.008009515 0.0008009515
## KO5.22 KO5 0.10 0.878656716 0.012843672 0.0012843672
## KO5.23 KO5 0.15 0.827014925 0.016169328 0.0016169328
## KO5.24 KO5 0.20 0.774328358 0.016333404 0.0016333404
## KO5.25 KO5 0.25 0.706119403 0.019407623 0.0019407623
## KO5.26 KO5 0.30 0.655074627 0.019430798 0.0019430798
## KO5.27 KO5 0.35 0.603880597 0.021573711 0.0021573711
## KO5.28 KO5 0.40 0.532985075 0.020380352 0.0020380352
## KO5.29 KO5 0.45 0.485671642 0.024133666 0.0024133666
## KO5.30 KO5 0.50 0.424626866 0.024222544 0.0024222544
## KO5.31 KO5 0.55 0.366567164 0.025748590 0.0025748590
## KO5.32 KO5 0.60 0.322089552 0.023829661 0.0023829661
## KO5.33 KO5 0.65 0.252985075 0.027771308 0.0027771308
## KO5.34 KO5 0.70 0.209701493 0.025753396 0.0025753396
## KO5.35 KO5 0.75 0.166119403 0.032977710 0.0032977710
## KO5.36 KO5 0.80 0.110895522 0.028323274 0.0028323274
## KO5.37 KO5 0.85 0.068507463 0.028310560 0.0028310560
## KO5.38 KO5 0.90 0.036865672 0.021990541 0.0021990541
## KO5.39 KO5 0.95 0.006567164 0.012427857 0.0012427857
## KO5.40 KO5 1.00 0.000000000 0.000000000 0.0000000000
## KO6.1 KO6 0.05 0.939354839 0.007567888 0.0007567888
## KO6.2 KO6 0.10 0.893010753 0.008423112 0.0008423112
## KO6.3 KO6 0.15 0.832688172 0.011469534 0.0011469534
## KO6.4 KO6 0.20 0.772580645 0.013786688 0.0013786688
## KO6.5 KO6 0.25 0.727096774 0.012674929 0.0012674929
## KO6.6 KO6 0.30 0.666451613 0.014972862 0.0014972862
## KO6.7 KO6 0.35 0.604408602 0.014919336 0.0014919336
## KO6.8 KO6 0.40 0.559462366 0.017787380 0.0017787380
## KO6.9 KO6 0.45 0.499892473 0.017324375 0.0017324375
## KO6.10 KO6 0.50 0.453225806 0.014925598 0.0014925598
## KO6.11 KO6 0.55 0.390967742 0.020760422 0.0020760422
## KO6.12 KO6 0.60 0.332150538 0.019565786 0.0019565786
## KO6.13 KO6 0.65 0.287634409 0.022272355 0.0022272355
## KO6.14 KO6 0.70 0.232365591 0.023323544 0.0023323544
## KO6.15 KO6 0.75 0.178172043 0.024128837 0.0024128837
## KO6.16 KO6 0.80 0.134731183 0.021421308 0.0021421308
## KO6.17 KO6 0.85 0.087634409 0.021197701 0.0021197701
## KO6.18 KO6 0.90 0.039247312 0.018107535 0.0018107535
## KO6.19 KO6 0.95 0.011935484 0.013488674 0.0013488674
## KO6.20 KO6 1.00 0.000000000 0.000000000 0.0000000000
## KO6.21 KO6 0.05 0.939784946 0.008087112 0.0008087112
## KO6.22 KO6 0.10 0.892365591 0.008439734 0.0008439734
## KO6.23 KO6 0.15 0.832903226 0.010852152 0.0010852152
## KO6.24 KO6 0.20 0.776881720 0.012070346 0.0012070346
## KO6.25 KO6 0.25 0.725483871 0.012736972 0.0012736972
## KO6.26 KO6 0.30 0.664731183 0.013616641 0.0013616641
## KO6.27 KO6 0.35 0.606236559 0.017208374 0.0017208374
## KO6.28 KO6 0.40 0.558172043 0.017229738 0.0017229738
## KO6.29 KO6 0.45 0.498279570 0.016117805 0.0016117805
## KO6.30 KO6 0.50 0.451827957 0.017289622 0.0017289622
## KO6.31 KO6 0.55 0.394946237 0.020496311 0.0020496311
## KO6.32 KO6 0.60 0.335591398 0.019649175 0.0019649175
## KO6.33 KO6 0.65 0.291935484 0.019474846 0.0019474846
## KO6.34 KO6 0.70 0.229892473 0.020377735 0.0020377735
## KO6.35 KO6 0.75 0.175591398 0.022044666 0.0022044666
## KO6.36 KO6 0.80 0.133978495 0.023991225 0.0023991225
## KO6.37 KO6 0.85 0.083225806 0.020195818 0.0020195818
## KO6.38 KO6 0.90 0.042688172 0.018177058 0.0018177058
## KO6.39 KO6 0.95 0.013333333 0.012979032 0.0012979032
## KO6.40 KO6 1.00 0.000000000 0.000000000 0.0000000000
## OE1.1 OE1 0.05 0.942000000 0.006579637 0.0006579637
## OE1.2 OE1 0.10 0.882592593 0.008512742 0.0008512742
## OE1.3 OE1 0.15 0.833037037 0.009500122 0.0009500122
## OE1.4 OE1 0.20 0.774814815 0.011723964 0.0011723964
## OE1.5 OE1 0.25 0.719111111 0.009398062 0.0009398062
## OE1.6 OE1 0.30 0.669777778 0.011779615 0.0011779615
## OE1.7 OE1 0.35 0.612888889 0.012078822 0.0012078822
## OE1.8 OE1 0.40 0.557777778 0.013503507 0.0013503507
## OE1.9 OE1 0.45 0.502962963 0.014066393 0.0014066393
## OE1.10 OE1 0.50 0.445925926 0.014007166 0.0014007166
## OE1.11 OE1 0.55 0.398518519 0.016845489 0.0016845489
## OE1.12 OE1 0.60 0.342370370 0.017190061 0.0017190061
## OE1.13 OE1 0.65 0.290814815 0.017510777 0.0017510777
## OE1.14 OE1 0.70 0.236222222 0.017200214 0.0017200214
## OE1.15 OE1 0.75 0.190296296 0.017857875 0.0017857875
## OE1.16 OE1 0.80 0.142592593 0.017053945 0.0017053945
## OE1.17 OE1 0.85 0.095629630 0.017651849 0.0017651849
## OE1.18 OE1 0.90 0.052000000 0.016679506 0.0016679506
## OE1.19 OE1 0.95 0.015851852 0.011865873 0.0011865873
## OE1.20 OE1 1.00 0.000000000 0.000000000 0.0000000000
## OE1.21 OE1 0.05 0.941481481 0.006002129 0.0006002129
## OE1.22 OE1 0.10 0.881555556 0.009087139 0.0009087139
## OE1.23 OE1 0.15 0.833481481 0.010069936 0.0010069936
## OE1.24 OE1 0.20 0.776444444 0.011011148 0.0011011148
## OE1.25 OE1 0.25 0.719111111 0.011756066 0.0011756066
## OE1.26 OE1 0.30 0.668740741 0.012191177 0.0012191177
## OE1.27 OE1 0.35 0.612740741 0.013649654 0.0013649654
## OE1.28 OE1 0.40 0.558296296 0.013468780 0.0013468780
## OE1.29 OE1 0.45 0.501185185 0.014748073 0.0014748073
## OE1.30 OE1 0.50 0.444814815 0.014488551 0.0014488551
## OE1.31 OE1 0.55 0.396296296 0.016729938 0.0016729938
## OE1.32 OE1 0.60 0.343481481 0.015674814 0.0015674814
## OE1.33 OE1 0.65 0.292074074 0.018121597 0.0018121597
## OE1.34 OE1 0.70 0.238518519 0.017522801 0.0017522801
## OE1.35 OE1 0.75 0.194518519 0.018102166 0.0018102166
## OE1.36 OE1 0.80 0.143851852 0.016917062 0.0016917062
## OE1.37 OE1 0.85 0.092592593 0.016829030 0.0016829030
## OE1.38 OE1 0.90 0.048222222 0.013212866 0.0013212866
## OE1.39 OE1 0.95 0.015185185 0.012518432 0.0012518432
## OE1.40 OE1 1.00 0.000000000 0.000000000 0.0000000000
## OE2.1 OE2 0.05 0.941503759 0.005909687 0.0005909687
## OE2.2 OE2 0.10 0.890526316 0.007505114 0.0007505114
## OE2.3 OE2 0.15 0.833082707 0.009677266 0.0009677266
## OE2.4 OE2 0.20 0.773984962 0.011199187 0.0011199187
## OE2.5 OE2 0.25 0.723007519 0.012632085 0.0012632085
## OE2.6 OE2 0.30 0.666090226 0.013437078 0.0013437078
## OE2.7 OE2 0.35 0.607067669 0.012536795 0.0012536795
## OE2.8 OE2 0.40 0.558195489 0.013897710 0.0013897710
## OE2.9 OE2 0.45 0.501278195 0.012419414 0.0012419414
## OE2.10 OE2 0.50 0.454210526 0.015416173 0.0015416173
## OE2.11 OE2 0.55 0.394060150 0.017334130 0.0017334130
## OE2.12 OE2 0.60 0.339248120 0.018113337 0.0018113337
## OE2.13 OE2 0.65 0.295263158 0.020496707 0.0020496707
## OE2.14 OE2 0.70 0.235112782 0.020635536 0.0020635536
## OE2.15 OE2 0.75 0.186466165 0.018755175 0.0018755175
## OE2.16 OE2 0.80 0.140375940 0.017820140 0.0017820140
## OE2.17 OE2 0.85 0.088270677 0.019402270 0.0019402270
## OE2.18 OE2 0.90 0.043383459 0.015444299 0.0015444299
## OE2.19 OE2 0.95 0.016015038 0.010774823 0.0010774823
## OE2.20 OE2 1.00 0.000000000 0.000000000 0.0000000000
## OE2.21 OE2 0.05 0.941654135 0.006056665 0.0006056665
## OE2.22 OE2 0.10 0.889849624 0.008165057 0.0008165057
## OE2.23 OE2 0.15 0.831278195 0.009754845 0.0009754845
## OE2.24 OE2 0.20 0.774661654 0.010974364 0.0010974364
## OE2.25 OE2 0.25 0.722631579 0.010681141 0.0010681141
## OE2.26 OE2 0.30 0.663233083 0.013986792 0.0013986792
## OE2.27 OE2 0.35 0.608872180 0.013933001 0.0013933001
## OE2.28 OE2 0.40 0.560601504 0.015163143 0.0015163143
## OE2.29 OE2 0.45 0.505563910 0.014182412 0.0014182412
## OE2.30 OE2 0.50 0.452706767 0.017763653 0.0017763653
## OE2.31 OE2 0.55 0.399699248 0.016302816 0.0016302816
## OE2.32 OE2 0.60 0.340225564 0.017734054 0.0017734054
## OE2.33 OE2 0.65 0.293984962 0.018921891 0.0018921891
## OE2.34 OE2 0.70 0.236992481 0.020035310 0.0020035310
## OE2.35 OE2 0.75 0.184887218 0.015890414 0.0015890414
## OE2.36 OE2 0.80 0.139849624 0.018663611 0.0018663611
## OE2.37 OE2 0.85 0.089548872 0.017949132 0.0017949132
## OE2.38 OE2 0.90 0.042180451 0.014570673 0.0014570673
## OE2.39 OE2 0.95 0.014436090 0.012263252 0.0012263252
## OE2.40 OE2 1.00 0.000000000 0.000000000 0.0000000000
## OE3.1 OE3 0.05 0.942222222 0.006667132 0.0006667132
## OE3.2 OE3 0.10 0.883760684 0.009642326 0.0009642326
## OE3.3 OE3 0.15 0.824700855 0.012238660 0.0012238660
## OE3.4 OE3 0.20 0.776068376 0.013027481 0.0013027481
## OE3.5 OE3 0.25 0.718803419 0.013168323 0.0013168323
## OE3.6 OE3 0.30 0.663504274 0.016008668 0.0016008668
## OE3.7 OE3 0.35 0.605299145 0.015480244 0.0015480244
## OE3.8 OE3 0.40 0.549487179 0.014843427 0.0014843427
## OE3.9 OE3 0.45 0.492478632 0.017041272 0.0017041272
## OE3.10 OE3 0.50 0.443760684 0.018649745 0.0018649745
## OE3.11 OE3 0.55 0.385982906 0.018965187 0.0018965187
## OE3.12 OE3 0.60 0.327948718 0.021651570 0.0021651570
## OE3.13 OE3 0.65 0.276153846 0.020280382 0.0020280382
## OE3.14 OE3 0.70 0.222307692 0.021128596 0.0021128596
## OE3.15 OE3 0.75 0.171794872 0.021578002 0.0021578002
## OE3.16 OE3 0.80 0.117948718 0.021076320 0.0021076320
## OE3.17 OE3 0.85 0.081623932 0.020232297 0.0020232297
## OE3.18 OE3 0.90 0.040683761 0.015324063 0.0015324063
## OE3.19 OE3 0.95 0.009829060 0.010334889 0.0010334889
## OE3.20 OE3 1.00 0.000000000 0.000000000 0.0000000000
## OE3.21 OE3 0.05 0.940854701 0.006944685 0.0006944685
## OE3.22 OE3 0.10 0.883333333 0.011025778 0.0011025778
## OE3.23 OE3 0.15 0.827777778 0.011420267 0.0011420267
## OE3.24 OE3 0.20 0.775811966 0.011515496 0.0011515496
## OE3.25 OE3 0.25 0.718974359 0.012641123 0.0012641123
## OE3.26 OE3 0.30 0.661794872 0.013154587 0.0013154587
## OE3.27 OE3 0.35 0.605042735 0.015040959 0.0015040959
## OE3.28 OE3 0.40 0.550085470 0.014854608 0.0014854608
## OE3.29 OE3 0.45 0.493076923 0.016102423 0.0016102423
## OE3.30 OE3 0.50 0.444273504 0.019360265 0.0019360265
## OE3.31 OE3 0.55 0.391709402 0.018425843 0.0018425843
## OE3.32 OE3 0.60 0.330341880 0.019864239 0.0019864239
## OE3.33 OE3 0.65 0.277435897 0.020233938 0.0020233938
## OE3.34 OE3 0.70 0.221623932 0.018869035 0.0018869035
## OE3.35 OE3 0.75 0.165299145 0.021840403 0.0021840403
## OE3.36 OE3 0.80 0.115042735 0.024095712 0.0024095712
## OE3.37 OE3 0.85 0.077435897 0.022328226 0.0022328226
## OE3.38 OE3 0.90 0.040256410 0.018475435 0.0018475435
## OE3.39 OE3 0.95 0.008717949 0.010932020 0.0010932020
## OE3.40 OE3 1.00 0.000000000 0.000000000 0.0000000000
## OE4.1 OE4 0.05 0.940775862 0.007418328 0.0007418328
## OE4.2 OE4 0.10 0.885258621 0.010081327 0.0010081327
## OE4.3 OE4 0.15 0.835086207 0.012414507 0.0012414507
## OE4.4 OE4 0.20 0.778620690 0.012060255 0.0012060255
## OE4.5 OE4 0.25 0.720517241 0.013263745 0.0013263745
## OE4.6 OE4 0.30 0.665431034 0.015337938 0.0015337938
## OE4.7 OE4 0.35 0.610603448 0.015109141 0.0015109141
## OE4.8 OE4 0.40 0.560603448 0.014828305 0.0014828305
## OE4.9 OE4 0.45 0.505775862 0.017156487 0.0017156487
## OE4.10 OE4 0.50 0.447586207 0.017096219 0.0017096219
## OE4.11 OE4 0.55 0.389741379 0.018553964 0.0018553964
## OE4.12 OE4 0.60 0.336551724 0.019409174 0.0019409174
## OE4.13 OE4 0.65 0.289482759 0.018750563 0.0018750563
## OE4.14 OE4 0.70 0.237844828 0.018946311 0.0018946311
## OE4.15 OE4 0.75 0.183103448 0.022630440 0.0022630440
## OE4.16 OE4 0.80 0.132241379 0.020437774 0.0020437774
## OE4.17 OE4 0.85 0.084482759 0.021952901 0.0021952901
## OE4.18 OE4 0.90 0.047586207 0.017818620 0.0017818620
## OE4.19 OE4 0.95 0.011810345 0.011601835 0.0011601835
## OE4.20 OE4 1.00 0.000000000 0.000000000 0.0000000000
## OE4.21 OE4 0.05 0.942844828 0.006084038 0.0006084038
## OE4.22 OE4 0.10 0.882931034 0.010117376 0.0010117376
## OE4.23 OE4 0.15 0.837844828 0.011342718 0.0011342718
## OE4.24 OE4 0.20 0.777844828 0.013470128 0.0013470128
## OE4.25 OE4 0.25 0.721206897 0.014248196 0.0014248196
## OE4.26 OE4 0.30 0.666293103 0.015021444 0.0015021444
## OE4.27 OE4 0.35 0.606982759 0.015980309 0.0015980309
## OE4.28 OE4 0.40 0.563103448 0.014543338 0.0014543338
## OE4.29 OE4 0.45 0.504655172 0.016458178 0.0016458178
## OE4.30 OE4 0.50 0.449827586 0.017982170 0.0017982170
## OE4.31 OE4 0.55 0.391465517 0.018946311 0.0018946311
## OE4.32 OE4 0.60 0.337327586 0.017356590 0.0017356590
## OE4.33 OE4 0.65 0.290948276 0.018996958 0.0018996958
## OE4.34 OE4 0.70 0.238965517 0.018585697 0.0018585697
## OE4.35 OE4 0.75 0.180517241 0.019826261 0.0019826261
## OE4.36 OE4 0.80 0.128706897 0.022501870 0.0022501870
## OE4.37 OE4 0.85 0.077931034 0.018859939 0.0018859939
## OE4.38 OE4 0.90 0.046724138 0.019068150 0.0019068150
## OE4.39 OE4 0.95 0.010689655 0.011103602 0.0011103602
## OE4.40 OE4 1.00 0.000000000 0.000000000 0.0000000000
## OE5.1 OE5 0.05 0.947570093 0.005774137 0.0005774137
## OE5.2 OE5 0.10 0.884112150 0.008608714 0.0008608714
## OE5.3 OE5 0.15 0.834672897 0.008679648 0.0008679648
## OE5.4 OE5 0.20 0.782149533 0.011783850 0.0011783850
## OE5.5 OE5 0.25 0.718971963 0.011446599 0.0011446599
## OE5.6 OE5 0.30 0.669345794 0.012656357 0.0012656357
## OE5.7 OE5 0.35 0.617570093 0.015977833 0.0015977833
## OE5.8 OE5 0.40 0.555140187 0.013740594 0.0013740594
## OE5.9 OE5 0.45 0.505233645 0.016949914 0.0016949914
## OE5.10 OE5 0.50 0.446915888 0.017389764 0.0017389764
## OE5.11 OE5 0.55 0.395420561 0.017657359 0.0017657359
## OE5.12 OE5 0.60 0.347943925 0.017962511 0.0017962511
## OE5.13 OE5 0.65 0.284112150 0.018644328 0.0018644328
## OE5.14 OE5 0.70 0.239532710 0.019687210 0.0019687210
## OE5.15 OE5 0.75 0.190280374 0.018526601 0.0018526601
## OE5.16 OE5 0.80 0.132990654 0.016951736 0.0016951736
## OE5.17 OE5 0.85 0.088411215 0.019541699 0.0019541699
## OE5.18 OE5 0.90 0.044766355 0.019626168 0.0019626168
## OE5.19 OE5 0.95 0.012336449 0.014299402 0.0014299402
## OE5.20 OE5 1.00 0.000000000 0.000000000 0.0000000000
## OE5.21 OE5 0.05 0.947196262 0.007199504 0.0007199504
## OE5.22 OE5 0.10 0.885046729 0.009806451 0.0009806451
## OE5.23 OE5 0.15 0.833271028 0.011011721 0.0011011721
## OE5.24 OE5 0.20 0.782897196 0.010779733 0.0010779733
## OE5.25 OE5 0.25 0.717570093 0.014646865 0.0014646865
## OE5.26 OE5 0.30 0.670186916 0.013303113 0.0013303113
## OE5.27 OE5 0.35 0.615607477 0.015414338 0.0015414338
## OE5.28 OE5 0.40 0.559439252 0.014308037 0.0014308037
## OE5.29 OE5 0.45 0.504766355 0.014641745 0.0014641745
## OE5.30 OE5 0.50 0.447663551 0.016985272 0.0016985272
## OE5.31 OE5 0.55 0.396261682 0.016105429 0.0016105429
## OE5.32 OE5 0.60 0.346448598 0.015562441 0.0015562441
## OE5.33 OE5 0.65 0.284579439 0.019221002 0.0019221002
## OE5.34 OE5 0.70 0.235700935 0.017041278 0.0017041278
## OE5.35 OE5 0.75 0.192056075 0.019358215 0.0019358215
## OE5.36 OE5 0.80 0.131962617 0.020201456 0.0020201456
## OE5.37 OE5 0.85 0.089532710 0.019073785 0.0019073785
## OE5.38 OE5 0.90 0.047943925 0.018341621 0.0018341621
## OE5.39 OE5 0.95 0.012056075 0.011216133 0.0011216133
## OE5.40 OE5 1.00 0.000000000 0.000000000 0.0000000000
## OE6.1 OE6 0.05 0.945072464 0.005563665 0.0005563665
## OE6.2 OE6 0.10 0.888695652 0.007247841 0.0007247841
## OE6.3 OE6 0.15 0.832971014 0.008822514 0.0008822514
## OE6.4 OE6 0.20 0.776014493 0.009275031 0.0009275031
## OE6.5 OE6 0.25 0.728043478 0.010824579 0.0010824579
## OE6.6 OE6 0.30 0.674057971 0.010899048 0.0010899048
## OE6.7 OE6 0.35 0.618115942 0.013837477 0.0013837477
## OE6.8 OE6 0.40 0.565144928 0.013760409 0.0013760409
## OE6.9 OE6 0.45 0.507463768 0.015430605 0.0015430605
## OE6.10 OE6 0.50 0.450507246 0.016090227 0.0016090227
## OE6.11 OE6 0.55 0.397028986 0.013829617 0.0013829617
## OE6.12 OE6 0.60 0.341811594 0.016956922 0.0016956922
## OE6.13 OE6 0.65 0.288985507 0.017457056 0.0017457056
## OE6.14 OE6 0.70 0.237753623 0.017039300 0.0017039300
## OE6.15 OE6 0.75 0.180652174 0.017425885 0.0017425885
## OE6.16 OE6 0.80 0.137898551 0.017553258 0.0017553258
## OE6.17 OE6 0.85 0.089710145 0.017743350 0.0017743350
## OE6.18 OE6 0.90 0.046956522 0.015397054 0.0015397054
## OE6.19 OE6 0.95 0.012608696 0.011074772 0.0011074772
## OE6.20 OE6 1.00 0.000000000 0.000000000 0.0000000000
## OE6.21 OE6 0.05 0.944275362 0.005612547 0.0005612547
## OE6.22 OE6 0.10 0.889057971 0.007333324 0.0007333324
## OE6.23 OE6 0.15 0.835072464 0.009161392 0.0009161392
## OE6.24 OE6 0.20 0.777608696 0.011030382 0.0011030382
## OE6.25 OE6 0.25 0.727101449 0.011662622 0.0011662622
## OE6.26 OE6 0.30 0.673405797 0.011294575 0.0011294575
## OE6.27 OE6 0.35 0.619710145 0.012759810 0.0012759810
## OE6.28 OE6 0.40 0.563188406 0.013031273 0.0013031273
## OE6.29 OE6 0.45 0.506304348 0.015540211 0.0015540211
## OE6.30 OE6 0.50 0.454565217 0.016825035 0.0016825035
## OE6.31 OE6 0.55 0.397028986 0.015765212 0.0015765212
## OE6.32 OE6 0.60 0.340942029 0.016587555 0.0016587555
## OE6.33 OE6 0.65 0.288695652 0.015913390 0.0015913390
## OE6.34 OE6 0.70 0.233333333 0.020624836 0.0020624836
## OE6.35 OE6 0.75 0.180000000 0.019315984 0.0019315984
## OE6.36 OE6 0.80 0.136666667 0.019731640 0.0019731640
## OE6.37 OE6 0.85 0.087318841 0.019001905 0.0019001905
## OE6.38 OE6 0.90 0.046594203 0.016162586 0.0016162586
## OE6.39 OE6 0.95 0.013985507 0.011434590 0.0011434590
## OE6.40 OE6 1.00 0.000000000 0.000000000 0.0000000000
## WT1.1 WT1 0.05 0.943030303 0.007109228 0.0007109228
## WT1.2 WT1 0.10 0.885555556 0.009199098 0.0009199098
## WT1.3 WT1 0.15 0.829090909 0.012406931 0.0012406931
## WT1.4 WT1 0.20 0.770505051 0.014290756 0.0014290756
## WT1.5 WT1 0.25 0.716363636 0.013671557 0.0013671557
## WT1.6 WT1 0.30 0.660202020 0.015296723 0.0015296723
## WT1.7 WT1 0.35 0.602626263 0.015343813 0.0015343813
## WT1.8 WT1 0.40 0.551515152 0.017465984 0.0017465984
## WT1.9 WT1 0.45 0.490303030 0.019915321 0.0019915321
## WT1.10 WT1 0.50 0.437070707 0.018766188 0.0018766188
## WT1.11 WT1 0.55 0.398787879 0.021172487 0.0021172487
## WT1.12 WT1 0.60 0.339191919 0.020312929 0.0020312929
## WT1.13 WT1 0.65 0.285252525 0.018392593 0.0018392593
## WT1.14 WT1 0.70 0.231212121 0.019148911 0.0019148911
## WT1.15 WT1 0.75 0.179292929 0.022853046 0.0022853046
## WT1.16 WT1 0.80 0.125555556 0.022020726 0.0022020726
## WT1.17 WT1 0.85 0.082525253 0.019318236 0.0019318236
## WT1.18 WT1 0.90 0.042929293 0.020170110 0.0020170110
## WT1.19 WT1 0.95 0.009595960 0.011958142 0.0011958142
## WT1.20 WT1 1.00 0.000000000 0.000000000 0.0000000000
## WT1.21 WT1 0.05 0.943838384 0.006629119 0.0006629119
## WT1.22 WT1 0.10 0.883434343 0.011251673 0.0011251673
## WT1.23 WT1 0.15 0.827676768 0.013300148 0.0013300148
## WT1.24 WT1 0.20 0.770909091 0.014491278 0.0014491278
## WT1.25 WT1 0.25 0.716060606 0.016108921 0.0016108921
## WT1.26 WT1 0.30 0.660000000 0.016001400 0.0016001400
## WT1.27 WT1 0.35 0.602828283 0.016611929 0.0016611929
## WT1.28 WT1 0.40 0.548282828 0.016992226 0.0016992226
## WT1.29 WT1 0.45 0.493535354 0.017408062 0.0017408062
## WT1.30 WT1 0.50 0.437777778 0.017654963 0.0017654963
## WT1.31 WT1 0.55 0.392626263 0.020638834 0.0020638834
## WT1.32 WT1 0.60 0.340202020 0.020449459 0.0020449459
## WT1.33 WT1 0.65 0.286363636 0.020624848 0.0020624848
## WT1.34 WT1 0.70 0.234343434 0.019208291 0.0019208291
## WT1.35 WT1 0.75 0.181414141 0.023631035 0.0023631035
## WT1.36 WT1 0.80 0.131111111 0.026355076 0.0026355076
## WT1.37 WT1 0.85 0.085151515 0.021690639 0.0021690639
## WT1.38 WT1 0.90 0.043535354 0.019245544 0.0019245544
## WT1.39 WT1 0.95 0.008888889 0.011688357 0.0011688357
## WT1.40 WT1 1.00 0.000000000 0.000000000 0.0000000000
## WT2.1 WT2 0.05 0.941012658 0.011267410 0.0011267410
## WT2.2 WT2 0.10 0.883037975 0.012863695 0.0012863695
## WT2.3 WT2 0.15 0.822278481 0.014827541 0.0014827541
## WT2.4 WT2 0.20 0.764936709 0.017651514 0.0017651514
## WT2.5 WT2 0.25 0.708734177 0.018997568 0.0018997568
## WT2.6 WT2 0.30 0.649493671 0.020410383 0.0020410383
## WT2.7 WT2 0.35 0.592025316 0.020263950 0.0020263950
## WT2.8 WT2 0.40 0.528734177 0.024328970 0.0024328970
## WT2.9 WT2 0.45 0.473037975 0.026359721 0.0026359721
## WT2.10 WT2 0.50 0.420379747 0.022920436 0.0022920436
## WT2.11 WT2 0.55 0.375822785 0.023089287 0.0023089287
## WT2.12 WT2 0.60 0.321645570 0.023395681 0.0023395681
## WT2.13 WT2 0.65 0.266455696 0.028067795 0.0028067795
## WT2.14 WT2 0.70 0.211392405 0.030717763 0.0030717763
## WT2.15 WT2 0.75 0.164303797 0.028785470 0.0028785470
## WT2.16 WT2 0.80 0.115696203 0.026988632 0.0026988632
## WT2.17 WT2 0.85 0.071139241 0.022599368 0.0022599368
## WT2.18 WT2 0.90 0.033670886 0.019971510 0.0019971510
## WT2.19 WT2 0.95 0.007974684 0.013055398 0.0013055398
## WT2.20 WT2 1.00 0.000000000 0.000000000 0.0000000000
## WT2.21 WT2 0.05 0.941898734 0.009190708 0.0009190708
## WT2.22 WT2 0.10 0.880379747 0.013266915 0.0013266915
## WT2.23 WT2 0.15 0.820886076 0.016817596 0.0016817596
## WT2.24 WT2 0.20 0.761012658 0.018460491 0.0018460491
## WT2.25 WT2 0.25 0.707974684 0.021683823 0.0021683823
## WT2.26 WT2 0.30 0.647468354 0.016721081 0.0016721081
## WT2.27 WT2 0.35 0.590126582 0.024056352 0.0024056352
## WT2.28 WT2 0.40 0.531518987 0.022721858 0.0022721858
## WT2.29 WT2 0.45 0.470253165 0.024029089 0.0024029089
## WT2.30 WT2 0.50 0.418860759 0.026812648 0.0026812648
## WT2.31 WT2 0.55 0.374556962 0.025703158 0.0025703158
## WT2.32 WT2 0.60 0.319367089 0.024790274 0.0024790274
## WT2.33 WT2 0.65 0.262151899 0.028063181 0.0028063181
## WT2.34 WT2 0.70 0.215063291 0.026594453 0.0026594453
## WT2.35 WT2 0.75 0.157088608 0.030057049 0.0030057049
## WT2.36 WT2 0.80 0.113544304 0.025976251 0.0025976251
## WT2.37 WT2 0.85 0.067215190 0.029436789 0.0029436789
## WT2.38 WT2 0.90 0.032911392 0.021961573 0.0021961573
## WT2.39 WT2 0.95 0.007594937 0.012721998 0.0012721998
## WT2.40 WT2 1.00 0.000000000 0.000000000 0.0000000000
## WT3.1 WT3 0.05 0.941810345 0.006863273 0.0006863273
## WT3.2 WT3 0.10 0.882413793 0.009292848 0.0009292848
## WT3.3 WT3 0.15 0.835689655 0.009864928 0.0009864928
## WT3.4 WT3 0.20 0.778275862 0.011301944 0.0011301944
## WT3.5 WT3 0.25 0.719913793 0.013505747 0.0013505747
## WT3.6 WT3 0.30 0.662241379 0.014517507 0.0014517507
## WT3.7 WT3 0.35 0.601724138 0.015106408 0.0015106408
## WT3.8 WT3 0.40 0.557931034 0.015979605 0.0015979605
## WT3.9 WT3 0.45 0.500000000 0.016530086 0.0016530086
## WT3.10 WT3 0.50 0.446637931 0.016008469 0.0016008469
## WT3.11 WT3 0.55 0.390086207 0.019193517 0.0019193517
## WT3.12 WT3 0.60 0.332155172 0.022441741 0.0022441741
## WT3.13 WT3 0.65 0.287672414 0.018649202 0.0018649202
## WT3.14 WT3 0.70 0.235862069 0.022841747 0.0022841747
## WT3.15 WT3 0.75 0.180086207 0.020204124 0.0020204124
## WT3.16 WT3 0.80 0.130000000 0.018119405 0.0018119405
## WT3.17 WT3 0.85 0.080862069 0.020421606 0.0020421606
## WT3.18 WT3 0.90 0.046810345 0.018266914 0.0018266914
## WT3.19 WT3 0.95 0.012844828 0.010786393 0.0010786393
## WT3.20 WT3 1.00 0.000000000 0.000000000 0.0000000000
## WT3.21 WT3 0.05 0.942758621 0.006987385 0.0006987385
## WT3.22 WT3 0.10 0.884396552 0.009577281 0.0009577281
## WT3.23 WT3 0.15 0.836206897 0.010890629 0.0010890629
## WT3.24 WT3 0.20 0.778879310 0.013609839 0.0013609839
## WT3.25 WT3 0.25 0.719655172 0.012995023 0.0012995023
## WT3.26 WT3 0.30 0.661982759 0.015021444 0.0015021444
## WT3.27 WT3 0.35 0.601551724 0.015135202 0.0015135202
## WT3.28 WT3 0.40 0.555258621 0.017928447 0.0017928447
## WT3.29 WT3 0.45 0.496379310 0.016171062 0.0016171062
## WT3.30 WT3 0.50 0.442931034 0.018694431 0.0018694431
## WT3.31 WT3 0.55 0.386034483 0.018646183 0.0018646183
## WT3.32 WT3 0.60 0.330000000 0.021012230 0.0021012230
## WT3.33 WT3 0.65 0.287241379 0.019407627 0.0019407627
## WT3.34 WT3 0.70 0.231206897 0.023195904 0.0023195904
## WT3.35 WT3 0.75 0.181465517 0.018394682 0.0018394682
## WT3.36 WT3 0.80 0.127758621 0.020807599 0.0020807599
## WT3.37 WT3 0.85 0.080775862 0.017656743 0.0017656743
## WT3.38 WT3 0.90 0.046034483 0.017638240 0.0017638240
## WT3.39 WT3 0.95 0.012327586 0.012748626 0.0012748626
## WT3.40 WT3 1.00 0.000000000 0.000000000 0.0000000000
## WT4.1 WT4 0.05 0.947247706 0.006696797 0.0006696797
## WT4.2 WT4 0.10 0.884678899 0.009952622 0.0009952622
## WT4.3 WT4 0.15 0.835137615 0.010305155 0.0010305155
## WT4.4 WT4 0.20 0.770000000 0.012524658 0.0012524658
## WT4.5 WT4 0.25 0.721376147 0.012346907 0.0012346907
## WT4.6 WT4 0.30 0.660183486 0.015258237 0.0015258237
## WT4.7 WT4 0.35 0.608807339 0.015998085 0.0015998085
## WT4.8 WT4 0.40 0.547706422 0.016260583 0.0016260583
## WT4.9 WT4 0.45 0.499357798 0.018498829 0.0018498829
## WT4.10 WT4 0.50 0.447798165 0.017721418 0.0017721418
## WT4.11 WT4 0.55 0.388807339 0.020525986 0.0020525986
## WT4.12 WT4 0.60 0.338348624 0.018864042 0.0018864042
## WT4.13 WT4 0.65 0.281284404 0.020419676 0.0020419676
## WT4.14 WT4 0.70 0.233119266 0.020744964 0.0020744964
## WT4.15 WT4 0.75 0.180825688 0.022140604 0.0022140604
## WT4.16 WT4 0.80 0.130275229 0.021347071 0.0021347071
## WT4.17 WT4 0.85 0.084495413 0.019133212 0.0019133212
## WT4.18 WT4 0.90 0.045321101 0.016014020 0.0016014020
## WT4.19 WT4 0.95 0.011467890 0.011762954 0.0011762954
## WT4.20 WT4 1.00 0.000000000 0.000000000 0.0000000000
## WT4.21 WT4 0.05 0.946513761 0.007497034 0.0007497034
## WT4.22 WT4 0.10 0.885137615 0.010307217 0.0010307217
## WT4.23 WT4 0.15 0.834128440 0.010073614 0.0010073614
## WT4.24 WT4 0.20 0.771009174 0.011730022 0.0011730022
## WT4.25 WT4 0.25 0.718715596 0.014415909 0.0014415909
## WT4.26 WT4 0.30 0.661651376 0.013817266 0.0013817266
## WT4.27 WT4 0.35 0.607798165 0.014774443 0.0014774443
## WT4.28 WT4 0.40 0.549541284 0.015456425 0.0015456425
## WT4.29 WT4 0.45 0.501559633 0.017738681 0.0017738681
## WT4.30 WT4 0.50 0.448899083 0.018127431 0.0018127431
## WT4.31 WT4 0.55 0.386880734 0.017690688 0.0017690688
## WT4.32 WT4 0.60 0.342568807 0.020750086 0.0020750086
## WT4.33 WT4 0.65 0.276697248 0.018748311 0.0018748311
## WT4.34 WT4 0.70 0.236880734 0.021202409 0.0021202409
## WT4.35 WT4 0.75 0.181559633 0.019221876 0.0019221876
## WT4.36 WT4 0.80 0.132201835 0.021029885 0.0021029885
## WT4.37 WT4 0.85 0.082844037 0.020178220 0.0020178220
## WT4.38 WT4 0.90 0.047706422 0.015917103 0.0015917103
## WT4.39 WT4 0.95 0.010825688 0.011906986 0.0011906986
## WT4.40 WT4 1.00 0.000000000 0.000000000 0.0000000000
## WT5.1 WT5 0.05 0.947325581 0.008173024 0.0008173024
## WT5.2 WT5 0.10 0.882325581 0.011835128 0.0011835128
## WT5.3 WT5 0.15 0.828139535 0.011869697 0.0011869697
## WT5.4 WT5 0.20 0.773953488 0.014719407 0.0014719407
## WT5.5 WT5 0.25 0.706511628 0.015948522 0.0015948522
## WT5.6 WT5 0.30 0.654186047 0.017303894 0.0017303894
## WT5.7 WT5 0.35 0.600348837 0.019600924 0.0019600924
## WT5.8 WT5 0.40 0.547790698 0.019547897 0.0019547897
## WT5.9 WT5 0.45 0.479069767 0.019555232 0.0019555232
## WT5.10 WT5 0.50 0.423720930 0.019647204 0.0019647204
## WT5.11 WT5 0.55 0.374883721 0.021301486 0.0021301486
## WT5.12 WT5 0.60 0.309302326 0.025603808 0.0025603808
## WT5.13 WT5 0.65 0.269069767 0.023020895 0.0023020895
## WT5.14 WT5 0.70 0.217674419 0.023954731 0.0023954731
## WT5.15 WT5 0.75 0.163139535 0.025998427 0.0025998427
## WT5.16 WT5 0.80 0.116627907 0.023689577 0.0023689577
## WT5.17 WT5 0.85 0.075348837 0.025469034 0.0025469034
## WT5.18 WT5 0.90 0.036976744 0.020401539 0.0020401539
## WT5.19 WT5 0.95 0.005813953 0.010517838 0.0010517838
## WT5.20 WT5 1.00 0.000000000 0.000000000 0.0000000000
## WT5.21 WT5 0.05 0.947558140 0.007838662 0.0007838662
## WT5.22 WT5 0.10 0.880465116 0.010198761 0.0010198761
## WT5.23 WT5 0.15 0.826627907 0.012704990 0.0012704990
## WT5.24 WT5 0.20 0.770581395 0.014676198 0.0014676198
## WT5.25 WT5 0.25 0.709534884 0.015850598 0.0015850598
## WT5.26 WT5 0.30 0.652674419 0.015384938 0.0015384938
## WT5.27 WT5 0.35 0.601395349 0.018994046 0.0018994046
## WT5.28 WT5 0.40 0.549767442 0.019560818 0.0019560818
## WT5.29 WT5 0.45 0.477558140 0.020987250 0.0020987250
## WT5.30 WT5 0.50 0.428255814 0.024848834 0.0024848834
## WT5.31 WT5 0.55 0.375348837 0.023142784 0.0023142784
## WT5.32 WT5 0.60 0.314186047 0.021420408 0.0021420408
## WT5.33 WT5 0.65 0.265116279 0.022540078 0.0022540078
## WT5.34 WT5 0.70 0.211046512 0.024645744 0.0024645744
## WT5.35 WT5 0.75 0.155116279 0.025508684 0.0025508684
## WT5.36 WT5 0.80 0.111046512 0.027024605 0.0027024605
## WT5.37 WT5 0.85 0.071976744 0.023875637 0.0023875637
## WT5.38 WT5 0.90 0.041279070 0.023742557 0.0023742557
## WT5.39 WT5 0.95 0.009069767 0.012649508 0.0012649508
## WT5.40 WT5 1.00 0.000000000 0.000000000 0.0000000000
## WT6.1 WT6 0.05 0.948095238 0.005307814 0.0005307814
## WT6.2 WT6 0.10 0.898285714 0.007879158 0.0007879158
## WT6.3 WT6 0.15 0.837809524 0.008609823 0.0008609823
## WT6.4 WT6 0.20 0.784761905 0.010309132 0.0010309132
## WT6.5 WT6 0.25 0.734285714 0.011365869 0.0011365869
## WT6.6 WT6 0.30 0.669428571 0.014660469 0.0014660469
## WT6.7 WT6 0.35 0.616000000 0.013595984 0.0013595984
## WT6.8 WT6 0.40 0.568761905 0.014394646 0.0014394646
## WT6.9 WT6 0.45 0.516761905 0.015822141 0.0015822141
## WT6.10 WT6 0.50 0.460761905 0.014565482 0.0014565482
## WT6.11 WT6 0.55 0.398571429 0.020231374 0.0020231374
## WT6.12 WT6 0.60 0.347523810 0.022468028 0.0022468028
## WT6.13 WT6 0.65 0.293047619 0.020478036 0.0020478036
## WT6.14 WT6 0.70 0.231904762 0.019304426 0.0019304426
## WT6.15 WT6 0.75 0.182095238 0.018375840 0.0018375840
## WT6.16 WT6 0.80 0.131904762 0.022422311 0.0022422311
## WT6.17 WT6 0.85 0.087333333 0.020576229 0.0020576229
## WT6.18 WT6 0.90 0.038095238 0.017855940 0.0017855940
## WT6.19 WT6 0.95 0.007904762 0.011001729 0.0011001729
## WT6.20 WT6 1.00 0.000000000 0.000000000 0.0000000000
## WT6.21 WT6 0.05 0.948571429 0.006768277 0.0006768277
## WT6.22 WT6 0.10 0.898761905 0.006988717 0.0006988717
## WT6.23 WT6 0.15 0.835142857 0.010192494 0.0010192494
## WT6.24 WT6 0.20 0.783619048 0.010579317 0.0010579317
## WT6.25 WT6 0.25 0.734190476 0.009956041 0.0009956041
## WT6.26 WT6 0.30 0.670095238 0.012221941 0.0012221941
## WT6.27 WT6 0.35 0.617428571 0.014005918 0.0014005918
## WT6.28 WT6 0.40 0.569047619 0.014602861 0.0014602861
## WT6.29 WT6 0.45 0.516000000 0.014790195 0.0014790195
## WT6.30 WT6 0.50 0.462190476 0.015101298 0.0015101298
## WT6.31 WT6 0.55 0.397809524 0.015835743 0.0015835743
## WT6.32 WT6 0.60 0.346380952 0.020780042 0.0020780042
## WT6.33 WT6 0.65 0.291047619 0.021115288 0.0021115288
## WT6.34 WT6 0.70 0.235142857 0.019366972 0.0019366972
## WT6.35 WT6 0.75 0.185714286 0.017519250 0.0017519250
## WT6.36 WT6 0.80 0.128380952 0.022262590 0.0022262590
## WT6.37 WT6 0.85 0.088285714 0.019562779 0.0019562779
## WT6.38 WT6 0.90 0.039142857 0.016181420 0.0016181420
## WT6.39 WT6 0.95 0.010000000 0.011355789 0.0011355789
## WT6.40 WT6 1.00 0.000000000 0.000000000 0.0000000000
## weighted
## KO1.1 weighted
## KO1.2 weighted
## KO1.3 weighted
## KO1.4 weighted
## KO1.5 weighted
## KO1.6 weighted
## KO1.7 weighted
## KO1.8 weighted
## KO1.9 weighted
## KO1.10 weighted
## KO1.11 weighted
## KO1.12 weighted
## KO1.13 weighted
## KO1.14 weighted
## KO1.15 weighted
## KO1.16 weighted
## KO1.17 weighted
## KO1.18 weighted
## KO1.19 weighted
## KO1.20 weighted
## KO1.21 unweighted
## KO1.22 unweighted
## KO1.23 unweighted
## KO1.24 unweighted
## KO1.25 unweighted
## KO1.26 unweighted
## KO1.27 unweighted
## KO1.28 unweighted
## KO1.29 unweighted
## KO1.30 unweighted
## KO1.31 unweighted
## KO1.32 unweighted
## KO1.33 unweighted
## KO1.34 unweighted
## KO1.35 unweighted
## KO1.36 unweighted
## KO1.37 unweighted
## KO1.38 unweighted
## KO1.39 unweighted
## KO1.40 unweighted
## KO2.1 weighted
## KO2.2 weighted
## KO2.3 weighted
## KO2.4 weighted
## KO2.5 weighted
## KO2.6 weighted
## KO2.7 weighted
## KO2.8 weighted
## KO2.9 weighted
## KO2.10 weighted
## KO2.11 weighted
## KO2.12 weighted
## KO2.13 weighted
## KO2.14 weighted
## KO2.15 weighted
## KO2.16 weighted
## KO2.17 weighted
## KO2.18 weighted
## KO2.19 weighted
## KO2.20 weighted
## KO2.21 unweighted
## KO2.22 unweighted
## KO2.23 unweighted
## KO2.24 unweighted
## KO2.25 unweighted
## KO2.26 unweighted
## KO2.27 unweighted
## KO2.28 unweighted
## KO2.29 unweighted
## KO2.30 unweighted
## KO2.31 unweighted
## KO2.32 unweighted
## KO2.33 unweighted
## KO2.34 unweighted
## KO2.35 unweighted
## KO2.36 unweighted
## KO2.37 unweighted
## KO2.38 unweighted
## KO2.39 unweighted
## KO2.40 unweighted
## KO3.1 weighted
## KO3.2 weighted
## KO3.3 weighted
## KO3.4 weighted
## KO3.5 weighted
## KO3.6 weighted
## KO3.7 weighted
## KO3.8 weighted
## KO3.9 weighted
## KO3.10 weighted
## KO3.11 weighted
## KO3.12 weighted
## KO3.13 weighted
## KO3.14 weighted
## KO3.15 weighted
## KO3.16 weighted
## KO3.17 weighted
## KO3.18 weighted
## KO3.19 weighted
## KO3.20 weighted
## KO3.21 unweighted
## KO3.22 unweighted
## KO3.23 unweighted
## KO3.24 unweighted
## KO3.25 unweighted
## KO3.26 unweighted
## KO3.27 unweighted
## KO3.28 unweighted
## KO3.29 unweighted
## KO3.30 unweighted
## KO3.31 unweighted
## KO3.32 unweighted
## KO3.33 unweighted
## KO3.34 unweighted
## KO3.35 unweighted
## KO3.36 unweighted
## KO3.37 unweighted
## KO3.38 unweighted
## KO3.39 unweighted
## KO3.40 unweighted
## KO4.1 weighted
## KO4.2 weighted
## KO4.3 weighted
## KO4.4 weighted
## KO4.5 weighted
## KO4.6 weighted
## KO4.7 weighted
## KO4.8 weighted
## KO4.9 weighted
## KO4.10 weighted
## KO4.11 weighted
## KO4.12 weighted
## KO4.13 weighted
## KO4.14 weighted
## KO4.15 weighted
## KO4.16 weighted
## KO4.17 weighted
## KO4.18 weighted
## KO4.19 weighted
## KO4.20 weighted
## KO4.21 unweighted
## KO4.22 unweighted
## KO4.23 unweighted
## KO4.24 unweighted
## KO4.25 unweighted
## KO4.26 unweighted
## KO4.27 unweighted
## KO4.28 unweighted
## KO4.29 unweighted
## KO4.30 unweighted
## KO4.31 unweighted
## KO4.32 unweighted
## KO4.33 unweighted
## KO4.34 unweighted
## KO4.35 unweighted
## KO4.36 unweighted
## KO4.37 unweighted
## KO4.38 unweighted
## KO4.39 unweighted
## KO4.40 unweighted
## KO5.1 weighted
## KO5.2 weighted
## KO5.3 weighted
## KO5.4 weighted
## KO5.5 weighted
## KO5.6 weighted
## KO5.7 weighted
## KO5.8 weighted
## KO5.9 weighted
## KO5.10 weighted
## KO5.11 weighted
## KO5.12 weighted
## KO5.13 weighted
## KO5.14 weighted
## KO5.15 weighted
## KO5.16 weighted
## KO5.17 weighted
## KO5.18 weighted
## KO5.19 weighted
## KO5.20 weighted
## KO5.21 unweighted
## KO5.22 unweighted
## KO5.23 unweighted
## KO5.24 unweighted
## KO5.25 unweighted
## KO5.26 unweighted
## KO5.27 unweighted
## KO5.28 unweighted
## KO5.29 unweighted
## KO5.30 unweighted
## KO5.31 unweighted
## KO5.32 unweighted
## KO5.33 unweighted
## KO5.34 unweighted
## KO5.35 unweighted
## KO5.36 unweighted
## KO5.37 unweighted
## KO5.38 unweighted
## KO5.39 unweighted
## KO5.40 unweighted
## KO6.1 weighted
## KO6.2 weighted
## KO6.3 weighted
## KO6.4 weighted
## KO6.5 weighted
## KO6.6 weighted
## KO6.7 weighted
## KO6.8 weighted
## KO6.9 weighted
## KO6.10 weighted
## KO6.11 weighted
## KO6.12 weighted
## KO6.13 weighted
## KO6.14 weighted
## KO6.15 weighted
## KO6.16 weighted
## KO6.17 weighted
## KO6.18 weighted
## KO6.19 weighted
## KO6.20 weighted
## KO6.21 unweighted
## KO6.22 unweighted
## KO6.23 unweighted
## KO6.24 unweighted
## KO6.25 unweighted
## KO6.26 unweighted
## KO6.27 unweighted
## KO6.28 unweighted
## KO6.29 unweighted
## KO6.30 unweighted
## KO6.31 unweighted
## KO6.32 unweighted
## KO6.33 unweighted
## KO6.34 unweighted
## KO6.35 unweighted
## KO6.36 unweighted
## KO6.37 unweighted
## KO6.38 unweighted
## KO6.39 unweighted
## KO6.40 unweighted
## OE1.1 weighted
## OE1.2 weighted
## OE1.3 weighted
## OE1.4 weighted
## OE1.5 weighted
## OE1.6 weighted
## OE1.7 weighted
## OE1.8 weighted
## OE1.9 weighted
## OE1.10 weighted
## OE1.11 weighted
## OE1.12 weighted
## OE1.13 weighted
## OE1.14 weighted
## OE1.15 weighted
## OE1.16 weighted
## OE1.17 weighted
## OE1.18 weighted
## OE1.19 weighted
## OE1.20 weighted
## OE1.21 unweighted
## OE1.22 unweighted
## OE1.23 unweighted
## OE1.24 unweighted
## OE1.25 unweighted
## OE1.26 unweighted
## OE1.27 unweighted
## OE1.28 unweighted
## OE1.29 unweighted
## OE1.30 unweighted
## OE1.31 unweighted
## OE1.32 unweighted
## OE1.33 unweighted
## OE1.34 unweighted
## OE1.35 unweighted
## OE1.36 unweighted
## OE1.37 unweighted
## OE1.38 unweighted
## OE1.39 unweighted
## OE1.40 unweighted
## OE2.1 weighted
## OE2.2 weighted
## OE2.3 weighted
## OE2.4 weighted
## OE2.5 weighted
## OE2.6 weighted
## OE2.7 weighted
## OE2.8 weighted
## OE2.9 weighted
## OE2.10 weighted
## OE2.11 weighted
## OE2.12 weighted
## OE2.13 weighted
## OE2.14 weighted
## OE2.15 weighted
## OE2.16 weighted
## OE2.17 weighted
## OE2.18 weighted
## OE2.19 weighted
## OE2.20 weighted
## OE2.21 unweighted
## OE2.22 unweighted
## OE2.23 unweighted
## OE2.24 unweighted
## OE2.25 unweighted
## OE2.26 unweighted
## OE2.27 unweighted
## OE2.28 unweighted
## OE2.29 unweighted
## OE2.30 unweighted
## OE2.31 unweighted
## OE2.32 unweighted
## OE2.33 unweighted
## OE2.34 unweighted
## OE2.35 unweighted
## OE2.36 unweighted
## OE2.37 unweighted
## OE2.38 unweighted
## OE2.39 unweighted
## OE2.40 unweighted
## OE3.1 weighted
## OE3.2 weighted
## OE3.3 weighted
## OE3.4 weighted
## OE3.5 weighted
## OE3.6 weighted
## OE3.7 weighted
## OE3.8 weighted
## OE3.9 weighted
## OE3.10 weighted
## OE3.11 weighted
## OE3.12 weighted
## OE3.13 weighted
## OE3.14 weighted
## OE3.15 weighted
## OE3.16 weighted
## OE3.17 weighted
## OE3.18 weighted
## OE3.19 weighted
## OE3.20 weighted
## OE3.21 unweighted
## OE3.22 unweighted
## OE3.23 unweighted
## OE3.24 unweighted
## OE3.25 unweighted
## OE3.26 unweighted
## OE3.27 unweighted
## OE3.28 unweighted
## OE3.29 unweighted
## OE3.30 unweighted
## OE3.31 unweighted
## OE3.32 unweighted
## OE3.33 unweighted
## OE3.34 unweighted
## OE3.35 unweighted
## OE3.36 unweighted
## OE3.37 unweighted
## OE3.38 unweighted
## OE3.39 unweighted
## OE3.40 unweighted
## OE4.1 weighted
## OE4.2 weighted
## OE4.3 weighted
## OE4.4 weighted
## OE4.5 weighted
## OE4.6 weighted
## OE4.7 weighted
## OE4.8 weighted
## OE4.9 weighted
## OE4.10 weighted
## OE4.11 weighted
## OE4.12 weighted
## OE4.13 weighted
## OE4.14 weighted
## OE4.15 weighted
## OE4.16 weighted
## OE4.17 weighted
## OE4.18 weighted
## OE4.19 weighted
## OE4.20 weighted
## OE4.21 unweighted
## OE4.22 unweighted
## OE4.23 unweighted
## OE4.24 unweighted
## OE4.25 unweighted
## OE4.26 unweighted
## OE4.27 unweighted
## OE4.28 unweighted
## OE4.29 unweighted
## OE4.30 unweighted
## OE4.31 unweighted
## OE4.32 unweighted
## OE4.33 unweighted
## OE4.34 unweighted
## OE4.35 unweighted
## OE4.36 unweighted
## OE4.37 unweighted
## OE4.38 unweighted
## OE4.39 unweighted
## OE4.40 unweighted
## OE5.1 weighted
## OE5.2 weighted
## OE5.3 weighted
## OE5.4 weighted
## OE5.5 weighted
## OE5.6 weighted
## OE5.7 weighted
## OE5.8 weighted
## OE5.9 weighted
## OE5.10 weighted
## OE5.11 weighted
## OE5.12 weighted
## OE5.13 weighted
## OE5.14 weighted
## OE5.15 weighted
## OE5.16 weighted
## OE5.17 weighted
## OE5.18 weighted
## OE5.19 weighted
## OE5.20 weighted
## OE5.21 unweighted
## OE5.22 unweighted
## OE5.23 unweighted
## OE5.24 unweighted
## OE5.25 unweighted
## OE5.26 unweighted
## OE5.27 unweighted
## OE5.28 unweighted
## OE5.29 unweighted
## OE5.30 unweighted
## OE5.31 unweighted
## OE5.32 unweighted
## OE5.33 unweighted
## OE5.34 unweighted
## OE5.35 unweighted
## OE5.36 unweighted
## OE5.37 unweighted
## OE5.38 unweighted
## OE5.39 unweighted
## OE5.40 unweighted
## OE6.1 weighted
## OE6.2 weighted
## OE6.3 weighted
## OE6.4 weighted
## OE6.5 weighted
## OE6.6 weighted
## OE6.7 weighted
## OE6.8 weighted
## OE6.9 weighted
## OE6.10 weighted
## OE6.11 weighted
## OE6.12 weighted
## OE6.13 weighted
## OE6.14 weighted
## OE6.15 weighted
## OE6.16 weighted
## OE6.17 weighted
## OE6.18 weighted
## OE6.19 weighted
## OE6.20 weighted
## OE6.21 unweighted
## OE6.22 unweighted
## OE6.23 unweighted
## OE6.24 unweighted
## OE6.25 unweighted
## OE6.26 unweighted
## OE6.27 unweighted
## OE6.28 unweighted
## OE6.29 unweighted
## OE6.30 unweighted
## OE6.31 unweighted
## OE6.32 unweighted
## OE6.33 unweighted
## OE6.34 unweighted
## OE6.35 unweighted
## OE6.36 unweighted
## OE6.37 unweighted
## OE6.38 unweighted
## OE6.39 unweighted
## OE6.40 unweighted
## WT1.1 weighted
## WT1.2 weighted
## WT1.3 weighted
## WT1.4 weighted
## WT1.5 weighted
## WT1.6 weighted
## WT1.7 weighted
## WT1.8 weighted
## WT1.9 weighted
## WT1.10 weighted
## WT1.11 weighted
## WT1.12 weighted
## WT1.13 weighted
## WT1.14 weighted
## WT1.15 weighted
## WT1.16 weighted
## WT1.17 weighted
## WT1.18 weighted
## WT1.19 weighted
## WT1.20 weighted
## WT1.21 unweighted
## WT1.22 unweighted
## WT1.23 unweighted
## WT1.24 unweighted
## WT1.25 unweighted
## WT1.26 unweighted
## WT1.27 unweighted
## WT1.28 unweighted
## WT1.29 unweighted
## WT1.30 unweighted
## WT1.31 unweighted
## WT1.32 unweighted
## WT1.33 unweighted
## WT1.34 unweighted
## WT1.35 unweighted
## WT1.36 unweighted
## WT1.37 unweighted
## WT1.38 unweighted
## WT1.39 unweighted
## WT1.40 unweighted
## WT2.1 weighted
## WT2.2 weighted
## WT2.3 weighted
## WT2.4 weighted
## WT2.5 weighted
## WT2.6 weighted
## WT2.7 weighted
## WT2.8 weighted
## WT2.9 weighted
## WT2.10 weighted
## WT2.11 weighted
## WT2.12 weighted
## WT2.13 weighted
## WT2.14 weighted
## WT2.15 weighted
## WT2.16 weighted
## WT2.17 weighted
## WT2.18 weighted
## WT2.19 weighted
## WT2.20 weighted
## WT2.21 unweighted
## WT2.22 unweighted
## WT2.23 unweighted
## WT2.24 unweighted
## WT2.25 unweighted
## WT2.26 unweighted
## WT2.27 unweighted
## WT2.28 unweighted
## WT2.29 unweighted
## WT2.30 unweighted
## WT2.31 unweighted
## WT2.32 unweighted
## WT2.33 unweighted
## WT2.34 unweighted
## WT2.35 unweighted
## WT2.36 unweighted
## WT2.37 unweighted
## WT2.38 unweighted
## WT2.39 unweighted
## WT2.40 unweighted
## WT3.1 weighted
## WT3.2 weighted
## WT3.3 weighted
## WT3.4 weighted
## WT3.5 weighted
## WT3.6 weighted
## WT3.7 weighted
## WT3.8 weighted
## WT3.9 weighted
## WT3.10 weighted
## WT3.11 weighted
## WT3.12 weighted
## WT3.13 weighted
## WT3.14 weighted
## WT3.15 weighted
## WT3.16 weighted
## WT3.17 weighted
## WT3.18 weighted
## WT3.19 weighted
## WT3.20 weighted
## WT3.21 unweighted
## WT3.22 unweighted
## WT3.23 unweighted
## WT3.24 unweighted
## WT3.25 unweighted
## WT3.26 unweighted
## WT3.27 unweighted
## WT3.28 unweighted
## WT3.29 unweighted
## WT3.30 unweighted
## WT3.31 unweighted
## WT3.32 unweighted
## WT3.33 unweighted
## WT3.34 unweighted
## WT3.35 unweighted
## WT3.36 unweighted
## WT3.37 unweighted
## WT3.38 unweighted
## WT3.39 unweighted
## WT3.40 unweighted
## WT4.1 weighted
## WT4.2 weighted
## WT4.3 weighted
## WT4.4 weighted
## WT4.5 weighted
## WT4.6 weighted
## WT4.7 weighted
## WT4.8 weighted
## WT4.9 weighted
## WT4.10 weighted
## WT4.11 weighted
## WT4.12 weighted
## WT4.13 weighted
## WT4.14 weighted
## WT4.15 weighted
## WT4.16 weighted
## WT4.17 weighted
## WT4.18 weighted
## WT4.19 weighted
## WT4.20 weighted
## WT4.21 unweighted
## WT4.22 unweighted
## WT4.23 unweighted
## WT4.24 unweighted
## WT4.25 unweighted
## WT4.26 unweighted
## WT4.27 unweighted
## WT4.28 unweighted
## WT4.29 unweighted
## WT4.30 unweighted
## WT4.31 unweighted
## WT4.32 unweighted
## WT4.33 unweighted
## WT4.34 unweighted
## WT4.35 unweighted
## WT4.36 unweighted
## WT4.37 unweighted
## WT4.38 unweighted
## WT4.39 unweighted
## WT4.40 unweighted
## WT5.1 weighted
## WT5.2 weighted
## WT5.3 weighted
## WT5.4 weighted
## WT5.5 weighted
## WT5.6 weighted
## WT5.7 weighted
## WT5.8 weighted
## WT5.9 weighted
## WT5.10 weighted
## WT5.11 weighted
## WT5.12 weighted
## WT5.13 weighted
## WT5.14 weighted
## WT5.15 weighted
## WT5.16 weighted
## WT5.17 weighted
## WT5.18 weighted
## WT5.19 weighted
## WT5.20 weighted
## WT5.21 unweighted
## WT5.22 unweighted
## WT5.23 unweighted
## WT5.24 unweighted
## WT5.25 unweighted
## WT5.26 unweighted
## WT5.27 unweighted
## WT5.28 unweighted
## WT5.29 unweighted
## WT5.30 unweighted
## WT5.31 unweighted
## WT5.32 unweighted
## WT5.33 unweighted
## WT5.34 unweighted
## WT5.35 unweighted
## WT5.36 unweighted
## WT5.37 unweighted
## WT5.38 unweighted
## WT5.39 unweighted
## WT5.40 unweighted
## WT6.1 weighted
## WT6.2 weighted
## WT6.3 weighted
## WT6.4 weighted
## WT6.5 weighted
## WT6.6 weighted
## WT6.7 weighted
## WT6.8 weighted
## WT6.9 weighted
## WT6.10 weighted
## WT6.11 weighted
## WT6.12 weighted
## WT6.13 weighted
## WT6.14 weighted
## WT6.15 weighted
## WT6.16 weighted
## WT6.17 weighted
## WT6.18 weighted
## WT6.19 weighted
## WT6.20 weighted
## WT6.21 unweighted
## WT6.22 unweighted
## WT6.23 unweighted
## WT6.24 unweighted
## WT6.25 unweighted
## WT6.26 unweighted
## WT6.27 unweighted
## WT6.28 unweighted
## WT6.29 unweighted
## WT6.30 unweighted
## WT6.31 unweighted
## WT6.32 unweighted
## WT6.33 unweighted
## WT6.34 unweighted
## WT6.35 unweighted
## WT6.36 unweighted
## WT6.37 unweighted
## WT6.38 unweighted
## WT6.39 unweighted
## WT6.40 unweighted
##
## $sample_stat
## Sample Node Edge Status
## KO1 KO1 113 161 OK
## KO2 KO2 122 164 OK
## KO3 KO3 102 379 OK
## KO4 KO4 94 107 OK
## KO5 KO5 71 63 OK
## KO6 KO6 97 119 OK
## OE1 OE1 138 308 OK
## OE2 OE2 135 230 OK
## OE3 OE3 119 160 OK
## OE4 OE4 118 171 OK
## OE5 OE5 111 165 OK
## OE6 OE6 140 234 OK
## WT1 WT1 105 130 OK
## WT2 WT2 83 59 OK
## WT3 WT3 117 171 OK
## WT4 WT4 111 222 OK
## WT5 WT5 90 103 OK
## WT6 WT6 111 162 OK7.4 Get network topology information by parallel
# ---- Same as get_network_topology(), but with parallel execution ------------
# Useful when `bootstrap` is large (the random-ER-network reference loop is
# the main bottleneck) or when running on `graph_obj_list` of many networks.
# With `mat = NULL`, cohesion / robustness / stability fields are NA - see
# get_network_topology() docs for the full list of skipped metrics.
t4 <- system.time(
topology_parallel <- get_network_topology_parallel(
graph_obj = graph_obj,
mat = NULL, # no abundance matrix -> cohesion + robustness = NA
transfrom.method = "none", # ignored when mat = NULL
method = "WGCNA", # ignored when mat = NULL (no correlation rebuild)
cor.method = "pearson", # ignored when mat = NULL
proc = "bonferroni", # ignored when mat = NULL
bootstrap = 100, # # of random ER networks for the Random_nerwork column
parallel = TRUE, # enable parallel backend
n_workers = 2 # # of parallel workers (keep <= cores; 2 is safe under R CMD check)
)
)## Number of parallel workers: 2## Warning: package ‘future’ was built under R version 4.5.2
## Warning: package ‘future’ was built under R version 4.5.2
topology_parallel## $topology
## # A tibble: 24 × 3
## Topology Target_network Random_nerwork
## <chr> <dbl> <dbl>
## 1 Node 213 213
## 2 Edge 844 844
## 3 Degree 7.92 7.92
## 4 Distance 1.45 2.81
## 5 Diameter 3.83 5.08
## 6 Density 0.0374 0.0374
## 7 Transitivity_global 0.851 0.0369
## 8 Transitivity_local 0.783 0.0369
## 9 Betweenness 3.47 191.
## 10 Betweenness_edge 2.58 75.1
## # ℹ 14 more rows
##
## $Robustness
## Proportion.removed remain.mean remain.sd remain.se weighted
## 1 0.05 NA NA NA weighted
## 2 0.10 NA NA NA weighted
## 3 0.15 NA NA NA weighted
## 4 0.20 NA NA NA weighted
## 5 0.25 NA NA NA weighted
## 6 0.30 NA NA NA weighted
## 7 0.35 NA NA NA weighted
## 8 0.40 NA NA NA weighted
## 9 0.45 NA NA NA weighted
## 10 0.50 NA NA NA weighted
## 11 0.55 NA NA NA weighted
## 12 0.60 NA NA NA weighted
## 13 0.65 NA NA NA weighted
## 14 0.70 NA NA NA weighted
## 15 0.75 NA NA NA weighted
## 16 0.80 NA NA NA weighted
## 17 0.85 NA NA NA weighted
## 18 0.90 NA NA NA weighted
## 19 0.95 NA NA NA weighted
## 20 1.00 NA NA NA weighted
## 21 0.05 NA NA NA unweighted
## 22 0.10 NA NA NA unweighted
## 23 0.15 NA NA NA unweighted
## 24 0.20 NA NA NA unweighted
## 25 0.25 NA NA NA unweighted
## 26 0.30 NA NA NA unweighted
## 27 0.35 NA NA NA unweighted
## 28 0.40 NA NA NA unweighted
## 29 0.45 NA NA NA unweighted
## 30 0.50 NA NA NA unweighted
## 31 0.55 NA NA NA unweighted
## 32 0.60 NA NA NA unweighted
## 33 0.65 NA NA NA unweighted
## 34 0.70 NA NA NA unweighted
## 35 0.75 NA NA NA unweighted
## 36 0.80 NA NA NA unweighted
## 37 0.85 NA NA NA unweighted
## 38 0.90 NA NA NA unweighted
## 39 0.95 NA NA NA unweighted
## 40 1.00 NA NA NA unweighted7.5 Get network topology information with matrix by parallel
# ---- Parallel + abundance matrix -> FULL topology panel ---------------------
# Same as above, but `mat` is now provided, so every topology field gets a
# real value (cohesion, robustness, stability included).
t5 <- system.time(
topology_parallel_with_mat <- get_network_topology_parallel(
graph_obj = graph_obj,
mat = otu_rare_relative, # abundance matrix -> enables cohesion + robustness
transfrom.method = "none", # pre-correlation transform on `mat`
method = "WGCNA", # correlation backend used to rebuild network.raw from `mat`
cor.method = "pearson", # Pearson correlation
proc = "bonferroni", # multiple-testing correction
bootstrap = 100, # bootstrap iterations for robustness + # of random ER reference nets
parallel = TRUE, # enable parallel backend
n_workers = 2 # # of parallel workers
)
)## Number of parallel workers: 2## Warning: package ‘future’ was built under R version 4.5.2
## Warning: package ‘future’ was built under R version 4.5.2
topology_parallel_with_mat## $topology
## # A tibble: 24 × 3
## Topology Target_network Random_nerwork
## <chr> <dbl> <dbl>
## 1 Node 213 213
## 2 Edge 844 844
## 3 Degree 7.92 7.92
## 4 Distance 1.45 2.81
## 5 Diameter 3.83 5.07
## 6 Density 0.0374 0.0374
## 7 Transitivity_global 0.851 0.0369
## 8 Transitivity_local 0.783 0.0372
## 9 Betweenness 3.47 191.
## 10 Betweenness_edge 2.58 75.0
## # ℹ 14 more rows
##
## $Robustness
## Proportion.removed remain.mean remain.sd remain.se weighted
## 1 0.05 0.93765258 0.006506724 0.0006506724 weighted
## 2 0.10 0.88042254 0.009907812 0.0009907812 weighted
## 3 0.15 0.81859155 0.012057928 0.0012057928 weighted
## 4 0.20 0.75816901 0.013453813 0.0013453813 weighted
## 5 0.25 0.70455399 0.012630308 0.0012630308 weighted
## 6 0.30 0.64333333 0.016021401 0.0016021401 weighted
## 7 0.35 0.58652582 0.016937398 0.0016937398 weighted
## 8 0.40 0.53028169 0.016859929 0.0016859929 weighted
## 9 0.45 0.47309859 0.018089169 0.0018089169 weighted
## 10 0.50 0.42140845 0.015919144 0.0015919144 weighted
## 11 0.55 0.37046948 0.018756744 0.0018756744 weighted
## 12 0.60 0.31450704 0.015513637 0.0015513637 weighted
## 13 0.65 0.26737089 0.019720511 0.0019720511 weighted
## 14 0.70 0.21652582 0.017859085 0.0017859085 weighted
## 15 0.75 0.17023474 0.016271873 0.0016271873 weighted
## 16 0.80 0.12455399 0.016887373 0.0016887373 weighted
## 17 0.85 0.08291080 0.015878534 0.0015878534 weighted
## 18 0.90 0.04262911 0.013423744 0.0013423744 weighted
## 19 0.95 0.01413146 0.009998184 0.0009998184 weighted
## 20 1.00 0.00000000 0.000000000 0.0000000000 weighted
## 21 0.05 0.93666667 0.006347900 0.0006347900 unweighted
## 22 0.10 0.88004695 0.009586197 0.0009586197 unweighted
## 23 0.15 0.81882629 0.011087843 0.0011087843 unweighted
## 24 0.20 0.75755869 0.014084823 0.0014084823 unweighted
## 25 0.25 0.70258216 0.013923536 0.0013923536 unweighted
## 26 0.30 0.64220657 0.014112853 0.0014112853 unweighted
## 27 0.35 0.58239437 0.013335467 0.0013335467 unweighted
## 28 0.40 0.53103286 0.016600696 0.0016600696 unweighted
## 29 0.45 0.47755869 0.015290812 0.0015290812 unweighted
## 30 0.50 0.42812207 0.015401290 0.0015401290 unweighted
## 31 0.55 0.36694836 0.016218423 0.0016218423 unweighted
## 32 0.60 0.31892019 0.018094092 0.0018094092 unweighted
## 33 0.65 0.26699531 0.017332399 0.0017332399 unweighted
## 34 0.70 0.21441315 0.017260315 0.0017260315 unweighted
## 35 0.75 0.16938967 0.018751817 0.0018751817 unweighted
## 36 0.80 0.12624413 0.017219505 0.0017219505 unweighted
## 37 0.85 0.07910798 0.015222150 0.0015222150 unweighted
## 38 0.90 0.04286385 0.012864348 0.0012864348 unweighted
## 39 0.95 0.01413146 0.009519073 0.0009519073 unweighted
## 40 1.00 0.00000000 0.000000000 0.0000000000 unweighted7.6 Integrated Value of Influence (IVI)
# ---- Compute IVI (Salavaty et al. 2020) per node ----------------------------
# IVI integrates 6 centrality measures across 3 scales (local / semi-local /
# global) into a single robust influence score. Thin wrapper over
# influential::ivi() — that package must be installed.
obj_aug <- get_node_ivi(
graph_obj = graph_obj, # input tbl_graph
weights = NULL, # NULL = unweighted IVI; pass "weight" to use the graph's `weight` edge attribute
mode = "all", # edge mode; "all" is the right choice for undirected graphs
directed = FALSE, # treat the graph as undirected
d = 3, # search radius for the collective-influence component (paper recommends 3)
scale = "z-scale", # "range" [1,100] for single-network view, "z-scale" for cross-network / thresholding (z > 1.645), "none" for raw
ncores = 1 # parallel cores for the cluster-rank step; 1 is the safe default
)
obj_aug # tbl_graph with one extra node column: IVI## # A tbl_graph: 213 nodes and 844 edges
## #
## # An undirected simple graph with 29 components
## #
## # Node Data: 213 × 15 (active)
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_649 5 5 5 5 27 26.5 Bacter…
## 2 ASV_705 5 5 5 5 27 26.5 Bacter…
## 3 ASV_12… 5 5 5 5 27 26.5 Bacter…
## 4 ASV_13… 5 5 5 5 27 26.5 Bacter…
## 5 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 6 ASV_14… 5 5 5 5 27 26.5 Bacter…
## 7 ASV_24… 5 5 5 5 27 26.5 Bacter…
## 8 ASV_25… 5 5 5 5 27 26.4 Bacter…
## 9 ASV_28… 5 5 5 5 27 26.5 Bacter…
## 10 ASV_28… 5 5 5 5 27 26.5 Bacter…
## # ℹ 203 more rows
## # ℹ 7 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>, IVI <dbl>
## #
## # Edge Data: 844 × 5
## from to weight correlation corr_direction
## <int> <int> <dbl> <dbl> <chr>
## 1 194 195 0.959 0.959 Positive
## 2 185 208 0.954 0.954 Positive
## 3 185 213 0.957 0.957 Positive
## # ℹ 841 more rows
class(obj_aug) # still a tbl_graph - all other vertex/edge columns are preserved## [1] "tbl_graph" "igraph"
# ---- Top-10 most influential nodes ------------------------------------------
# Activate the node table, convert to tibble, sort by IVI descending, take 10.
obj_aug %>%
tidygraph::activate(nodes) %>%
tidygraph::as_tibble() %>%
dplyr::arrange(desc(IVI)) %>%
dplyr::slice_head(n = 10)## # A tibble: 10 × 15
## name modularity modularity2 modularity3 Modularity Degree Strength Kingdom
## <chr> <fct> <ord> <chr> <ord> <dbl> <dbl> <chr>
## 1 ASV_913 5 5 5 5 26 25.2 Bacter…
## 2 ASV_25… 5 5 5 5 27 26.4 Bacter…
## 3 ASV_11… 5 5 5 5 20 19.1 Bacter…
## 4 ASV_28… 5 5 5 5 23 22.5 Bacter…
## 5 ASV_26… 5 5 5 5 21 20.4 Bacter…
## 6 ASV_24… 5 5 5 5 23 22.6 Bacter…
## 7 ASV_996 5 5 5 5 19 18.3 Bacter…
## 8 ASV_28… 5 5 5 5 20 19.1 Bacter…
## 9 ASV_767 5 5 5 5 22 21.1 Bacter…
## 10 ASV_802 8 8 8 8 18 17.5 Bacter…
## # ℹ 7 more variables: Phylum <chr>, Class <chr>, Order <chr>, Family <chr>,
## # Genus <chr>, Species <chr>, IVI <dbl>