idopNetwork_vignette"

In idopNetwork: A Network Tool to Dissect Spatial Community Ecology

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  tidy = FALSE,
  cache = TRUE,
  collapse = TRUE,
  dev = "png",
  fig.width = 7, 
  fig.height = 3.5
)

library(idopNetwork)
backup_options <- options()
#load pre-computered results
test_result = idopNetwork:::test_result

About

idopNetwork is packed as a cartographic tool that performs power curve fitting, classification, variable selection, microbial abundance decomposition, and network visualization based on microbial 16S rRNA gene sequencing metadata.

For complete details on the use and execution of this protocol, please refer to Chen et al and Cao et al.

1. Input data

Before running idopNetwork, user need to provide datasets, and they should be cleaned and merged to exactly the same format of the example data.

1.1 gut microbe OTUs data

Microbe Operational taxonomic unit dataset must have first column as IDs for microbes.

data("gut_microbe")
View(gut_microbe)

knitr::kable(gut_microbe[1:10,1:5])

1.2 mustard microbe OTUs data

data("mustard_microbe")
View(mustard_microbe)

knitr::kable(mustard_microbe[1:10,1:5])
knitr::kable(mustard_microbe[1:10,89:93])

2. power curve fitting

The first major step in our idopNetwork reconstruction is to fit allometric growth curves to the data using the power function. This is easily done by using the related function power_fit. This function needs cleaned dataset as input and will return fitted OTUs for given dataset. Then the fitted output with original dataset can be transfer into function power_equation_plot for quick visualization

df = data_cleaning(gut_microbe)

result1 = power_equation_fit(df)

result1 = test_result$d1_power_fitting

power_equation_plot(result1)

3. Functional clustering

In this step we implement the power equation into functional clustering to detect different microbial modules. If after clustering there are still too many microbes within a certain module for network reconstruction, we can rerun functional clustering to further classify this module into distinct submodules.

3.1 mean curve

we fit mean vector of each cluster center by power equation(assume k=3)

matplot(t(power_equation(x = 1:30, matrix(c(2,1,3,0.2,0.5,-0.5),nrow = 3, ncol = 2))), 
        type = "l",
        xlab = "time", 
        ylab = "population")
legend("topright", 
       c("cluster 1", "cluster 2", "cluster 3"), 
       lty = c(1,2,3), 
       col = c(1,2,3), 
       box.lwd = 0)

3.2 covariance matrix

we fit covariance matrix of multivariate normal distribution with SAD1, it can be showed as

get_SAD1_covmatrix(c(2,0.5), n = 5)

3.3 initial parameters

we can check initial parameters (k=4)

get_par_int(X = log10(df+1), k = 4, times = as.numeric(log10(colSums(df)+1)))

#use kmeans to get initial centers
tmp = kmeans(log10(df+1),4)$centers
tmp2 = power_equation_fit(tmp, trans = NULL)
power_equation_plot(tmp2, label = NULL,n = 4)

3.4 functional clustering (power-equation,SAD1)

idopNetowrk already wrapped the mean curve modelling, covariance matrix modelling and likelihood ratio calculation into a function fun_clu().

options(max.print = 10)
fun_clu(result1$original_data, k = 3, iter.max = 5)

Usually we use multithread to calcuation k = 2-n and then to decide best k , fun_clu_BIC uses BIC to select best cluster number by default.

result2 = fun_clu_parallel(result1$original_data, start = 2, end = 5)

result2 = test_result$d1_cluster

best.k = which.min(sapply( result2 , "[[" , 'BIC' )) + 1 #skipped k = 1
best.k

fun_clu_BIC(result = result2)

#we can direct give other k value
fun_clu_plot(result = result2, best.k = best.k)

3.5 bi-functional clustering (power-equation,biSAD1)

In this part we select part of mustard data for demonstration purpose.

data("mustard_microbe")
df2 = data_cleaning(mustard_microbe, x = 160)

res_l = power_equation_fit(df2[,1:5]
res_r = power_equation_fit(df2[,89:95])
res1 = data_match(result1 = res_l, result2 = res_r)

res1 = test_result$d2_power_fitting

res2 = bifun_clu_parallel(data1 = res1$dataset1$original_data, 
                          data2 = res1$dataset2$original_data,
                          Time1 = res1$dataset1$Time, 
                          Time2 = res1$dataset2$Time,
                          start = 2, 
                          end = 10, 
                          thread = 9,
                          iter.max = 10)

res2 = test_result$d2_cluster

res2 = bifun_clu_parallel(data1 = res1$dataset1$original_data, 
                          data2 = res1$dataset2$original_data,
                          Time1 = res1$dataset1$Time, 
                          Time2 = res1$dataset2$Time,
                          start = 2, 
                          end = 10, 
                          thread = 9,
                          iter.max = 10)

res2 = test_result$d2_cluster

fun_clu_BIC(result = res2)

#we can set best.k directly
bifun_clu_plot(result = res2, best.k = 3, color1 = "#C060A1", color2 = "#59C1BD")

3.6 sub-clustering

Sometimes a module is still too large for network reconstruction, which is determined by Dunbar’s number, we can further cluster it into sub-modules.

res3 = bifun_clu_convert(res2, best.k = 3)
large.module = order(sapply(res3$a$Module.all,nrow))[5]

res_suba = fun_clu_select(result_fit = res1$dataset1, result_funclu = res3$a, i = large.module)
res_subb = fun_clu_select(result_fit = res1$dataset2, result_funclu = res3$b, i = large.module)
dfsuba_l = power_equation_fit(res_suba$original_data)
dfsubb_r = power_equation_fit(res_subb$original_data)
ressub1 = data_match(result1 = dfsuba_l, result2 = dfsubb_r)
ressub2 = bifun_clu_parallel(data1 = ressub1$dataset1$original_data, 
                             data2 = ressub1$dataset2$original_data,
                             Time1 = ressub1$dataset1$Time, 
                             Time2 = ressub1$dataset2$Time, 
                             start = 2, 
                             end = 5, 
                             iter.max = 3)

ressub2 = test_result$d2_subcluster

fun_clu_BIC(result = ressub2)
bifun_clu_plot(result = ressub2, best.k = 2, color1 = "#C060A1", color2 = "#59C1BD", degree = 1)

4. LASSO-based variable selection

idopNetwork implements a LASSO-based procedure to choose a small set of the most significant microbes/module that links with a given microbes/modules. get_interaction()return a compound list contain the target microbe/module name, the most relevant Modules/microbes names and the coefficients.

4.1 For Modules

result3 = fun_clu_convert(result2,best.k = best.k)
df.module = result3$original_data
get_interaction(df.module,1)

4.2 For Microbes

#we can the microbial relationship in Module1
df.M1 = result3$Module.all$`1`
get_interaction(df.M1,1)

5 qdODE solving

qdODE system is build based on variable selection results, it has unique ability to decompose the observed module/microbe abundance level into its independent component and dependent component, which can be used for inferring idopNetwork.

5.1 solving qdODE between modules

options(max.print = 10)
# first we test solving a qdODE
module.relationship = lapply(1:best.k, function(c)get_interaction(df.module,c))
ode.test = qdODE_all(result = result3, relationship = module.relationship, 1, maxit = 100)
# we can view the result
qdODE_plot_base(ode.test)

# then we solve all qdODEs
ode.module = qdODE_parallel(result3) 

ode.module = test_result$d1_module

qdODE_plot_all(ode.module)

5.2 solving qdODE within a module

result_m1 = fun_clu_select(result_fit = result1, result_funclu = result3, i = 1)
ode.M1 = qdODE_parallel(result_m1)

ode.M1 = test_result$d1_M1

qdODE_plot_all(ode.M1)

6 idopNetwork reconstruction

The final step of this guide is to visualization the multilayer network, and our package provide network_plot function to easily draw our idopNetwork. We can simply plug previous qdODE results into network_conversion function, and it will convert qdODE result for network visualization

6.1 network between modules

net_module = lapply(ode.module$ode_result, network_conversion)
network_plot(net_module, title = "Module Network")

6.2 network within a module

net_m1 = lapply(ode.M1$ode_result, network_conversion)
network_plot(net_m1, title = "M1 Network")

6.3 network comparison

mustard_module_a = qdODE_parallel(res3$a) 
mustard_module_b = qdODE_parallel(res3$b) 

res_m1a = fun_clu_select(result_fit = res1$dataset1, result_funclu = res3$a, i = 3)
res_m1b = fun_clu_select(result_fit = res1$dataset2, result_funclu = res3$b, i = 3)
mustard_M1a = qdODE_parallel(res_m1a)
mustard_M1b = qdODE_parallel(res_m1b)

mustard_module_a = test_result$d2_module[[1]]
mustard_module_b = test_result$d2_module[[2]]

mustard_m_a <- lapply(mustard_module_a$ode_result, network_conversion)
mustard_m_b <- lapply(mustard_module_b$ode_result, network_conversion)

#set seed to make same random layout
layout(matrix(c(1,2),1,2,byrow=TRUE))
set.seed(1)
network_plot(mustard_m_a, title = "Module Network a")
set.seed(1)
network_plot(mustard_m_b, title = "Module Network b")

result_m1a = fun_clu_select(result_fit = res1$dataset1, result_funclu = res3$a, i = 1)
result_m1b = fun_clu_select(result_fit = res1$dataset2, result_funclu = res3$b, i = 1)
ode.m1a = qdODE_parallel(result_m1a, thread = 16)
ode.m1b = qdODE_parallel(result_m1b, thread = 16)

ode.m1a = test_result$d2_m1[[1]]
ode.m1b = test_result$d2_m1[[2]]

net_m1a = lapply(ode.m1a$ode_result, network_conversion)
net_m1b = lapply(ode.m1b$ode_result, network_conversion)

#set seed to make same random layout
layout(matrix(c(1,2),1,2,byrow=TRUE))
set.seed(1)
network_plot(net_m1a, title = "Module1 a")
set.seed(1)
network_plot(net_m1b, title = "Module1 b")

options(backup_options)

Troubleshooting

object "LL.next" not found\ This happens when parameters optimization failure, try rerun cluster.

plot failure when using fun_clu_plot() or bifun_clu_plot()\ This often happens when bad initial parameters is given and some cluster is lost, try rerun cluster or use a smaller k.

Session info

sessionInfo()

idopNetwork documentation built on April 18, 2023, 9:09 a.m.