caseStudy2-NutrientThreshold-phyloseq

Introduction

This document provides the detailed code required to replicate case study 2 discussed in Gao et al. (2023). Methods in Ecology and Evolution. DOI: 10.1111/2041-210X.14129

This replication study has been implemented with phyloseq. The TreeSE package has been since then upgraded to use the TreeSE data container.

For general instructions and examples on using the miaSim package tools, see the vignette. miaSim implements tools for microbiome data simulation based on different ecological modeling assumptions. These can be used to simulate species abundance matrices, including time series. For a detailed function documentation, see the function reference page

Case study 2: Nutrient concentration threshold

(Reference: Available energy fluxes drive a transition in the diversity, stability, and functional structure of microbial communities)

The aim of this case study is to design and demonstrate the existence of nutrient concentration threshold which limits the beta-diversity of communities.

To fulfill this aim, we designed a gradient of environments, as well as a gradient of communities.

Setup

Load dependencies

library(ggplot2)
library(vegan)
library(reshape2)
library(umap)
library(miaSim)
library(philentropy)
library(ape)
library(cluster)

(This batch of simulations is time-consuming. To reduce the calculation burden, we decreased the numbers of environments, resources, and communities from the original 10 to 5, and made other minor modifications.)

Set random seed

set.seed(42)

Set initial shared parameters

n_species <- 5
n_resources <- 5
E <- randomE(n_species, n_resources, mean_consumption = 1, mean_production = 3)
growth_rates <- runif(n_species)
monod_constant <- matrix(rbeta(n_species*n_resources, 10,10),nrow=n_species, ncol=n_resources)
t_store <- 50
n.instances <- 1 # no stochastic process: no need to repeat

Define generating function. This function generates a data frame, where each row is arranged in an increasing dissimilarity to the first row.

gradient.df.generator <- function(n_row, n_col, density_row, max_gradient, error_interval){
    list_initial <- list()
    dissimilarity.gradient <- seq(from = 0, to = max_gradient, length.out = n_row)
    for (i in seq_len(n_row)){
        print(i)
        if (i == 1){
            row_temp <- rbeta(n_col, 1, 1/n_col)
            col_to_remove <- sample(x = seq_len(n_col), size = n_col-n_col*density_row)
            row_temp[col_to_remove] <- 0
            list_initial[[i]] <- row_temp
        } else {
            while (length(list_initial) < i) {
                row_temp <- rbeta(n_col, 1, 1/n_col)
                col_to_remove <- sample(x = seq_len(n_col), size = n_col-n_col*density_row)
                row_temp[col_to_remove] <- 0
                diff_temp <- abs(vegdist(rbind(list_initial[[1]], row_temp), method = "bray") - dissimilarity.gradient[i])
                if (diff_temp < error_interval) {
                    list_initial[[i]] <- row_temp
                }
            }
        }
    }
    dataframe_to_return <- as.data.frame(t(matrix(unlist(list_initial), ncol = n_row)))
    return(dataframe_to_return)
}

Generate communities

n.community <- 5 # you can also try 20 or even 50.
density.community <- 0.8
set.seed(42)
community.initial.df <- gradient.df.generator(n_row = n.community, n_col = n_species, density_row = density.community, max_gradient = 0.7, error_interval = 0.1)

## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5

dist.community.initial.df <- vegdist(community.initial.df, method = "bray")

Load plotting functions

makePlot <- function(out_matrix, title = "abundance of species by time", obj = "species", y.label = "x.t"){
    df <- as.data.frame(out_matrix)
    dft <-  melt(df, id="time")
    names(dft)[2] = obj
    names(dft)[3] = y.label
    lgd = ncol(df)<= 20
    ggplot(dft, aes_string(names(dft)[1], names(dft)[3], col = names(dft)[2])) +
        geom_line(show.legend = lgd, lwd=0.5) +
        ggtitle(title) +
        theme_linedraw() +
        theme(plot.title = element_text(hjust = 0.5, size = 14))
}
makePlotRes <- function(out_matrix, title = "quantity of compounds by time"){
    df <- as.data.frame(out_matrix)
    dft <-  melt(df, id="time")
    names(dft)[2] = "resources"
    names(dft)[3] = "S.t"
    lgd = ncol(df)<= 20
    ggplot(dft, aes(time, S.t, col = resources)) +
        geom_line(show.legend = lgd, lwd=0.5) +
        ggtitle(title) +
        theme_linedraw() +
        theme(plot.title = element_text(hjust = 0.5, size = 14))
}
makeHeatmap <-function(matrix.A,
                       title = "Consumption/production matrix",
                       y.label = 'resources',
                       x.label = 'species',
                       midpoint_color = NULL,
                       lowColor = "red",
                       midColor = "white",
                       highColor = "blue"){
    df <- melt(t(matrix.A))
    if (is.null(midpoint_color)) {
        midpoint_color <- 0
    }
    names(df)<- c("x", "y", "strength")
    df$y <- factor(df$y, levels=rev(unique(sort(df$y))))
    fig <- ggplot(df, aes(x,y,fill=strength)) + geom_tile() + coord_equal() +
        theme(axis.title = element_blank()) +
        scale_fill_gradient2('strength', low = lowColor, mid = midColor, high = highColor, midpoint = midpoint_color)+
        theme_void() + ggtitle(title)

    if (ncol(matrix.A)<=10 & nrow(matrix.A)<=10){
        fig <- fig + geom_text(aes(label = round(strength, 2)))
    } else if (ncol(matrix.A)<=15 & nrow(matrix.A)<=15){
        fig <- fig + geom_text(aes(label = round(strength, 1)))
    } else {
        fig <- fig
    }

    fig <- fig + labs(x = x.label, y = y.label)+
        theme_linedraw() +
        theme(plot.title = element_text(hjust = 0.5, size = 14), axis.text.x = element_text(
            angle = 90))

    if (nrow(matrix.A) >= 20){
        # too many species
        fig <- fig + theme(
            axis.title.y=element_blank(),
            axis.text.y=element_blank(),
            axis.ticks.y=element_blank(),
        )
    }
    if (ncol(matrix.A) >= 20){
        # too many resources
        fig <- fig + theme(
            axis.title.x=element_blank(),
            axis.text.x=element_blank(),
            axis.ticks.x=element_blank()
        )
    }
    fig
}
makeUMAP <- function(matrix, n_neighbors=10, min_dist=0.1, gradient=NULL, gradient_title = 'gradient', group=NULL, group2=NULL){
    custom.config = umap.defaults
    custom.config$n_neighbors = n_neighbors
    custom.config$min_dist = min_dist

    df <- as.data.frame(umap(matrix,config = custom.config)$layout)
    df$gradient <- gradient

    if (is.null(gradient)){
        df$gradient <- 1

    }
    colnames(df) = c('UMAP_2', 'UMAP_1', gradient_title)
    if (is.null(group)){
        ggplot(df, aes_string('UMAP_2', 'UMAP_1', color=gradient_title)) +
            geom_point() +
            scale_color_gradient(low="blue", high="red")
    } else {
        if (is.null(group2)){
            ggplot(df, aes_string('UMAP_2', 'UMAP_1', color=gradient_title)) +
                geom_point(aes(color = group)) + theme_bw()
        } else {
            ggplot(df, aes_string('UMAP_2', 'UMAP_1', color=gradient_title)) +
                geom_point(aes(color = group, shape = group2)) + theme_bw()
        }
    }
}

makeHeatmap(as.matrix(dist.community.initial.df),
            title = "dissimilarity matrix",
            x.label = "community.1",
            y.label = "community.2")

makeUMAP(matrix = community.initial.df,
         n_neighbors = 5,
         group = factor(seq_len(n.community)),
         gradient_title = "community")

Initialize shared parameters

crm_params <- list(
    n_species = n_species,
    n_resources = n_resources,
    x0 = NULL,
    E = E,
    resources = rep(1,n_resources),
    monod_constant = monod_constant,
    migration_p = 0,
    stochastic = FALSE,
    t_start = 0,
    t_end = 50,
    t_step = 1,
    t_store = t_store,
    growth_rates = growth_rates,
    norm=FALSE)

Generate resource gradients

resourceConcentration <- 10^seq(0,4,1) # 1 to 10000
n.medium <- 5
density.medium <- 0.8
set.seed(42)
resource.initial.df <- gradient.df.generator(n_row = n.medium, n_col = n_resources, density_row = density.medium, max_gradient = 0.7, error_interval = 0.1)

## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5

test one run

crmExample <- simulateConsumerResource(
    n_species = n_species,
    n_resources = n_resources,
    E = E,
    x0 = as.numeric(community.initial.df[1,]),
    resources = as.numeric(resourceConcentration[3]*resource.initial.df[1,]),
    growth_rates = growth_rates,
    monod_constant = monod_constant,
    stochastic = FALSE,
    t_end = 50,
    t_step = 1,
    t_store = 50,
    norm = FALSE)
makePlot(crmExample$matrix)
makePlotRes(crmExample$resources)

Generate simulations and store the final community in community.simulation. In this step, the final relative abundance table is basisComposition_prop

set.seed(42)
library(miaSim)
community.simulation <- list()
counter_i <- 1
for (resConc in resourceConcentration) {
    for (medium in seq_len(n.medium)){
        crm_params$resources <- as.numeric(resource.initial.df[medium,]*resConc)
        paramx0 <- as.list(as.data.frame(t(community.initial.df)))
        crm_param_iter <- list(x0 = paramx0)
        print(paste("resConc", resConc, "medium", medium))
        crmMoments <- generateSimulations(model = "simulateConsumerResource",
                                          params_list = crm_params,
                                          param_iter = crm_param_iter,
                                          n_instances = n.instances,
                                          t_end = 50)
        community.simulation[[counter_i]] <- as.data.frame(do.call(rbind, lapply(crmMoments, getCommunity)))
        counter_i <- counter_i +1
    }
}
basisComposition <- do.call(rbind.data.frame, community.simulation)
rm(counter_i, community.simulation)
basisComposition_prop <- basisComposition / rowSums(basisComposition)

Visualization

Make UMAP plots.

In this step, plot result is stored in umap_CRM_gradient_plot, and this is visualized in different facets.

concentration <- as.factor(rep(resourceConcentration, each = n.medium*n.community))
medium <- as.factor(rep(seq_len(n.medium), each = n.community ,times = length(resourceConcentration) ))
community <- as.factor(rep(seq_len(n.community), times = length(resourceConcentration)*n.medium))

#plot the result in a UMAP space
makeUMAP(basisComposition, group = medium, group2 = concentration, gradient_title = 'Medium')
umap_CRM_gradient <- umap(basisComposition_prop)
# umap_CRM_gradient <- umap(basisComposition)
umap_CRM_coor <- as.data.frame(umap_CRM_gradient$layout)
colnames(umap_CRM_coor) <- c("UMAP_1", "UMAP_2")
umap_CRM_coor <- cbind(umap_CRM_coor, concentration, medium, community)
umap_CRM_gradient_plot <- ggplot(umap_CRM_coor,
                                 aes(UMAP_1, UMAP_2,
                                     # alpha = concentration,
                                     color = medium,
                                     shape = community)) +
    geom_point() +
    # scale_shape_manual(values = c(0, 1, 2, 5, 6, 8, 15, 16, 17, 18)) +
    scale_shape_manual(values = seq(0, n.community -1 ,1)) +
    scale_alpha_manual(values = seq(0.25, 1, 0.75/(length(resourceConcentration)-1))) +
    theme_bw()

In this part, different visualization of results demonstrate (in various facets) the gradual change of communities’ beta diversity. The first figure indicates that the initial community composition is more important than the combinations of initial available resources.

The first sub-figure in the second figure demonstrates that in an oligotrophic (less available nutrients) environment, communities won’t change much in a given time, whilst the last two sub-figures resemble each other, implying that the nutrient is no longer the limiting factor of the beta-diversity of the community. This pattern is further displayed in the following “curve plot”.

In the third figure, the second and the fourth community always stays more similar, despite their initial dissimilarity, indicating that they might belong to one community type. This can be validated by input 20 or even 50 as n.community in this case study: communities turns into clusters in each sub-figures.

print(umap_CRM_gradient_plot)

print(umap_CRM_gradient_plot + facet_grid(concentration ~ ., labeller = label_both))

print(umap_CRM_gradient_plot + facet_grid(medium ~ concentration, labeller = label_both))

print(umap_CRM_gradient_plot + facet_grid(community ~ concentration, labeller = label_both))

print(umap_CRM_gradient_plot + facet_grid(community ~ medium, labeller = label_both))

“Saturation curve” of average beta-diversity between communities with community 1

In this part, we’d like to demonstrate that the average distance from other communities to community 1 will reach to a threshold of nutrients, after which the average distance won’t increase along with the total concentration of nutrients.

To do so, we first define a function calculating the mean distance to the first community.

Construct a function taking umap_CRM_coor as df and return the mean distance

average_distance <- function(df, res_conc_type, com_type, method = "euclidean"){
    sub_df <- df[df$concentration == res_conc_type & df$community == com_type,]
    combines <- combn(sub_df$medium, 2)
    distances <- NULL
    for (i in seq_len(ncol(combines))) {
        distances[i] <- dist(sub_df[combines[,i], c(1, 2)])
    }
    # print(distances)
    return(mean(distances))
}
# average_distance(umap_CRM_coor, 1, 2)

Constructing dataframe to save results

distance_saturation_data <- data.frame(concentration = integer(),
                                       community = integer(),
                                       average_distance = numeric())

for (res_conc_type in unique(umap_CRM_coor$concentration)){
    for (com_type in unique(umap_CRM_coor$community)){
        ave_dist <- average_distance(umap_CRM_coor, res_conc_type, com_type)
        distance_saturation_data[nrow(distance_saturation_data)+1,] <-
            c(res_conc_type, com_type, ave_dist)
    }
}
# View(distance_saturation_data)
distance_saturation_data$average_distance <- as.numeric(distance_saturation_data$average_distance)
distance_saturation_data$concentration <- as.factor(distance_saturation_data$concentration)
distance_saturation_data$community <- as.factor(distance_saturation_data$community)
distance_saturation_data_plot <- ggplot(distance_saturation_data,
                                 aes(concentration, average_distance,
                                     color = community,
                                     group = community)) +
    geom_line() + geom_point() +
    scale_shape_manual(values = c(0, 1, 2, 5, 6, 8, 15, 16, 17, 18)) +
    labs(x = "resource concentration", y = "average distance between communities in UMAP") +
    theme_bw()

Visualize the distance plot

print(distance_saturation_data_plot)
# ggsave(paste0("CRMgradient_distance_curve_mod.pdf"), plot = distance_saturation_data_plot , dpi = 300, width = 12, height = 10, units = "cm", scale = 2)

miaSim package authors

2023-05-29

Introduction

Case study 2: Nutrient concentration threshold

Setup

test one run

Visualization