Beta Diversity Analysis
Welcome to this tutorial on Beta Diversity Analysis within Paired Samples. Our focus here is to understand the variations in microbial community structure and composition across different groups and within individual subjects over time. We aim to identify patterns and extract meaningful insights from microbiome data using various functions provided by MicrobiomeStat.
For those beta diversity-based functions, they all have a dist.obj parameter, which accepts a list of distance matrices. If the parameter is not specified, mStat_calculate_beta_diversity will be automatically called. MicrobiomeStats supports "BC" (Bray-Curtis), "Jaccard", "UniFrac" (unweighted), "GUniFrac" (generalized), "WUniFrac" (weighted), and "JS" (Jensen-Shannon divergence). The user can create his own list of distance matrices and pass it to dist.obj. We recommend the user to create a list of distance matrices once in the analysis and then use it repeatedly.
In beta diversity-based visualization functions as well as those testing functions based on changes, when covariates (adj.vars) are presented, the covariate effects will be removed using mStat_calculate_adjusted_distance function. The method used is referenced below. However, we recommend the user to perform covariate adjustment explicitly and store the adjusted beta diversity object for future repeated use.
Shi, Y., Zhang, L., Do, K. A., Peterson, C. B., & Jenq, R. R. (2020). aPCoA: covariate adjusted principal coordinates analysis. Bioinformatics, 36(13), 4099-4101. PMID: 32339223 PMCID: PMC7332564.
This process ensures the extracted microbial patterns are not confounded by the specified covariates, thus presenting a cleaner representation of the microbial community structure.
Based on the distance matrices, we can also extract the first several principal coordinates (PCs), which capture the main variation in the data. PCs can be calculated by calling mstat_calculate_PC function. While users are free to select between "mds" and "nmds" as their ordination method, in scenarios where pc.obj is not provided beforehand, the toolkit defaults to the "mds" method. Researchers favoring advanced ordination techniques like t-SNE or UMAP can employ external tools to compute results. For those PC-based functions, they all have a pc.obj parameter, which accepts a list of PC matrices based on a variety of beta diversity measures. If the parameter is not specified, mStat_calculate_PC will be called automatically. Or the users can create their own list of PC matrices and pass it to pc.obj. We recommend the user to create the list once in the analysis and use it repeatedly.
We begin our analysis by statistically testing beta diversity differences using the generate_beta_change_test_pair() function. This function fits linear models where the dependent variable is the distance between two time points from the same subject in a paired samples design, relating these beta diversity measures to the grouping variable and covariates.
The function returns coefficient tables with p-values for assessing associations with each beta diversity measure. These tables enable rigorous hypothesis testing complementing visualization for paired samples designs.
| Distance | Term | Estimate | Std.Error | Statistic | P.Value |
|---|---|---|---|---|---|
BC | (Intercept) | 0.175 | 0.0186 | 9.42 | 8.24e-12 |
BC | sexmale | 0.0671 | 0.0217 | 3.09 | 3.58e-3 |
BC | groupPlacebo | -0.0157 | 0.0210 | -0.746 | 4.60e-1 |
| Distance | Term | Estimate | Std.Error | Statistic | P.Value |
|---|---|---|---|---|---|
Jaccard | (Intercept) | 0.294 | 0.0246 | 12.0 | 6.04e-15 |
Jaccard | sexmale | 0.0853 | 0.0288 | 2.96 | 5.06e-3 |
Jaccard | groupPlacebo | -0.0207 | 0.0279 | -0.744 | 4.61e-1 |
Next, we explore the generate_beta_ordination_pair() function. This function generates ordination plots based on the microbial community structures of samples.
The generate_beta_change_boxplot_pair() function is another tool that aids in beta diversity-based visualization. This function quantifies the beta diversity changes within individual subjects over time.
The generate_beta_pc_change_boxplot_pair() function provides the functionality to explore the differences in specific ordination Axes between different groups. The pc.ind parameter is used to specify which Principal Coordinates (PCs) or axes to analyze after conducting a Multidimensional Scaling (MDS) or Nonmetric Multidimensional Scaling (NMDS).
Lastly, the generate_beta_pc_boxplot_long() function traces the trajectory of each subject's beta diversity across two time points on specific ordination axes. However, when the number of subjects is large, the individual connection lines can become too cluttered, making the plot difficult to interpret. To address this, we have set a threshold: when the number of subjects (n_subjects) exceeds 25, the individual connection lines are replaced with overall connection lines, improving the clarity and readability of the plot.
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