Permutational multivariate analysis of variance (PERMANOVA), also known as nonparametric multivariate analysis of variance, or ADONIS analysis. It uses the distance matrix (such as Euclidean distance, Bray-Curtis distance) to decompose the total variance, analyzes the explanation degree of different grouping factors or different environmental factors to the sample differences, and uses the "permutation test" to analyze the statistical significance of each variable explanation . Significant analysis.
one example
PCAFor example, after // dimensionality reduction visualization of species abundance data detected by metagenomics , there is some NMDSoverlap PCoAbetween samples in different groups, so how to judge whether there are significant differences in sample composition between these groups? This requires PERMANOVAa test to test whether the center points of samples in different groups overlap.
Taking the above PCoApicture as an example, the four groups of sample points circled by ellipses correspond to the four altitude groups. Are the community differences among these four groups of samples significant? The essence of testing community differences between groups is to test the differences between distance matrices, and ordinary ANOVA analysis is powerless. The analysis based on the distance matrix PerMANOVAshowed that the difference between these four groups was significant (p<0.05).
❝Rui J, Li J, Wang S, et al. Responses of Bacterial Communities to Simulated Climate Changes in Alpine Meadow Soil of the Qinghai-Tibet Plateau. Appl Environ Microbiol. 2015;81(17):6070-6077. doi:10.1128/AEM.00557-15
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Sample data and code collection
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PCoA
# Load package
library(vegan)
library(ggplot2)
library(ggthemes)
# Load data
otu <- read.table('otu.txt',row.names = 1,header = T)
group <- read.table('group.txt',header = T)
#pcoa
# vegdist函数，计算距离；method参数，选择距离类型
distance <- vegdist(otu, method = 'bray')
# 对加权距离进行PCoA分析
pcoa <- cmdscale(distance, k = (nrow(otu) - 1), eig = TRUE)
## plot data
# 提取样本点坐标
plot_data <- data.frame({pcoa$point})[1:2]
# 提取列名，便于后面操作。
plot_data$ID <- rownames(plot_data)
names(plot_data)[1:2] <- c('PCoA1', 'PCoA2')
# eig记录了PCoA排序结果中，主要排序轴的特征值（再除以特征值总和就是各轴的解释量）
eig = pcoa$eig
#为样本点坐标添加分组信息
plot_data <- merge(plot_data, group, by = 'ID', all.x = TRUE)
head(plot_data)
# 计算加权bray-curtis距离
dune_dist <- vegdist(otu, method="bray", binary=F)
dune_pcoa <- cmdscale(dune_dist, k=(nrow(otu) - 1), eig=T)
dune_pcoa_points <- as.data.frame(dune_pcoa$points)
sum_eig <- sum(dune_pcoa$eig)
eig_percent <- round(dune_pcoa$eig/sum_eig*100,1)
colnames(dune_pcoa_points) <- paste0("PCoA", 1:3)
dune_pcoa_result <- cbind(dune_pcoa_points, group)
head(dune_pcoa_result)
library(ggplot2)
ggplot(dune_pcoa_result, aes(x=PCoA1, y=PCoA2, fill=group)) +
geom_point(shape = 21,color = 'black',size=4) +
stat_ellipse(level=0.95)+
scale_fill_manual(values = c('#73bbaf','#d15b64','#592c93'))+
labs(x=paste("PCoA 1 (", eig_percent[1], "%)", sep=""),
y=paste("PCoA 2 (", eig_percent[2], "%)", sep="")) +
theme_classic()
PERMANOVA
# 基于bray-curtis距离进行计算
dune.div <- adonis2(otu ~ group, data = group, permutations = 999, method="bray")
dune.div
library(ggalt)
dune_adonis <- paste0("adonis R2: ",round(dune.div$R2,2), "; P-value: ", dune.div$`Pr(>F)`)
p <- ggplot(dune_pcoa_result, aes(x=PCoA1, y=PCoA2, fill=group)) +
geom_point(shape = 21,color = 'black',size=4) +
stat_ellipse(level=0.95)+
scale_fill_manual(values = c('#73bbaf','#d15b64','#592c93'))+
labs(x=paste("PCoA 1 (", eig_percent[1], "%)", sep=""),
y=paste("PCoA 2 (", eig_percent[2], "%)", sep=""),
title=dune_adonis) +
theme_classic()
p
Pair Adonis
# 配对Adonis确定两两分组之间对物种组成差异的影响
#devtools::install_github("pmartinezarbizu/pairwiseAdonis/pairwiseAdonis")
library(pairwiseAdonis)
dune.pairwise.adonis <- pairwise.adonis(x=otu, factors=group$group,
sim.function = "vegdist",
sim.method = "bray",
p.adjust.m = "BH",
reduce = NULL,
perm = 999)
library(ggpubr)
library(patchwork)
tab2 <- ggtexttable(dune.pairwise.adonis[,c("pairs","R2","p.value","p.adjusted")], rows = NULL,
theme = ttheme("blank")) %>%
tab_add_hline(at.row = 1:2, row.side = "top", linewidth = 1) %>%
tab_add_hline(at.row = nrow(dune.pairwise.adonis)+1, row.side = "bottom", linewidth = 1)
p + tab2 + plot_layout(design=c(area(1,1), area(2,1)))
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