# Beta Diversity

## What is beta diversity?

Beta diversity is a comparison of samples to each other and answers the question “how different?”.

Beta diversity is the ratio between the regional and local species diversity. In other words, it measures the distance or dissimilarity between each sample pair.

A beta diversity distance matrix where the input metric is Relative Abundance to reflect the underlying microbiome composition of the community.

The aggregation level of the input data has been set to species level.

## What is the difference between alpha diversity and beta diversity?

Alpha diversity is how many different taxa are detected in each sample. Beta diversity is the difference in microbial composition between samples. Alpha diversity looks at each sample and asks how many. Beta diversity compares samples and asks what are the differences in microbial composition between the samples.

## PCoA

Principal Coordinate Analysis Plot (PCoA) is used for visualization of the data in the distance matrix in a 3D plot. The distance matrix is transformed into a new set of orthogonal axes where the first axis (PC1) can be used to explain the maximum amount of variation present in the dataset, followed by the second axis (PC2), third (PC3), etc.

## Options for viewing PCoA

Rotate graph - Click anywhere on the PCoA and hold down to rotate the graph.

Labels - You can click on a label to hide samples belonging to the corresponding cohort, click it again to show them.

Please note that selecting cohort labels in the Legend does not recompute the plot but only hides/reveals the corresponding samples while rescaling the axis. The axis label values for % variability explained by each principal coordinate (PCo) axis are not recalculated and correspond to a visualization including all cohorts and samples.

Export - Click "Export" in the top right corner to download the PCoA as a png or svg.

A range of different beta diversity metrics is available - see below:

## Jaccard

The Jaccard distance is based on the presence or absence of species (does not include abundance information). Values are from 0 to 1. A value of 0 means both samples share the exact same species and a value of 1 means both samples have no species in common.

## Bray-Curtis

Bray-Curtis - takes abundance into account; non-phylogeny based. Values are from 0 to 1. A value of 0 means that two samples share the same species at the exact same abundances. A value of 1 means two samples have completely different species abundances.

## PERMANOVA Analysis

How does PERMANOVA work and what do the results mean?

PERMANOVA stands for Permutational multivariate analysis of variance [1,2], and is a non-parametric multivariate statistical test. The test is based on the prior calculation of the distance between any two cohorts included to the Principal Coordinate Analysis of beta diversity. PERMANOVA measures the sum-of-squares within and between cohorts and makes use of the F test to compare within-cohort to between-cohort variance. PERMANOVA draws tests for significance by comparing the actual F test result to that gained from random permutations of the objects between the groups.

PERMANOVA is used to compare cohorts of samples and test the null hypothesis that the centroids and dispersion of the cohorts (as defined by the 3-dimensional Principal Coordinate space) are equivalent for all cohorts.

A rejection of the null hypothesis (p-values of 0.05 and below) means that either the centroid and/or the spread of the objects is different between the cohorts. This is a test on beta diversity this means that in this case the samples for two cohorts are drawn from distributions that are compositionally distinct.

A table lists for each cohort combination the number of included samples, the number of carries our permutations, the test statistic (returning the F statistic) and normalized p-value.

Viewing the test results

Above and to the right of the beta diversity Principal Coordinate Analysis (PCoA) chart you can find a Result Switcher and a Cohort Menu.

The Result Switcher allows you to hide the results (using the NONE setting, which is selected by default). Clicking on SIGNIFICANT will limit the results to only those cohort combinations for which the p-value is equal or lower than 0.05, i.e. which occupy a distinct space in the PCoA chart and for which therefore the microbiome composition differs with statistical significance. The ALL setting displays the PERMANOVA analysis results for all possible cohort combinations.

The Cohort Menu to the right of the Result Switcher offers another way to filter the displayed cohort combinations. A pulldown menu lists all possible cohort combinations. Selecting checkboxes for the cohort pairs of interest will reduce the rows with test statistics and p-values in the table accordingly. Please note that selections in the cohort switcher only affect the table, not the samples shown in the PCoA chart.

It is possible to export the PERMANOVA analysis results to TSV.

References

Anderson, M. (2001). A new method for non‐parametric multivariate analysis of variance. Austral Ecology 26(1), 32-46. https://dx.doi.org/10.1111/j.1442-9993.2001.01070.pp.x

Anderson, M. (2014). Permutational Multivariate Analysis of Variance (PERMANOVA). Wiley StatsRef: Statistics Reference Online. https://doi.org/10.1002/9781118445112.stat07841

Updated 10 months ago