Who is the Alpha…metric?

Consider this, I approach you on your morning walk and present you with 2 excel files. They represent microbial distribution (from a recent sequencing run) I say, and elaborate no further. Invariably, the first question you might ask is, what makes them different? Statisticians over the ages have come to express that exact question in two broad aspects:

1. what does the sample population look like within itself (alpha mindset)
2. how distant this sample is relative to any other, or more aptly put, who’s the beta?

Generally, diversity metrics for biological data describe how similar or different any number of samples are internally using simple calculations of:

1. presence/absence of species in each samples’ microbial communities (aka richness of species)
2. relative abundance of species within each sample (idea of evenness)
3. phylogenetic component (weight of the history of changes in evolution using sum of branch lengths; can depict how much of the shared evolution between the communities impacts the final differences)
4. how different they are as a whole against each other (beta diversity, more on this in the next article!), including what leads to the differences within communities

Alpha Diversity is about the diversity within a single ecosystem. It provides a single number representing the diversity of species in that location, aka how many species are present along with their relative abundance.

Use case: we can compare alpha diverity value across different samples and get a sense of which communities are more diverse as compared to others.

Some majorly used alpha diversity metrics:

1. Species richness: The total number of different species in a community
2. Shannon index: captures both the richness and evenness of species; common in information theory because it is less sensitive to outliers/rare species as it weighs everything by abundance. Rarefaction curves based on shanon index are more stable than comparing relative abundances directly. Higher index means better diversity in sample.
3. Simpson index: captures both the richness and evenness of species; calculates probablity of individual belonging to same species when randomly sampled from given community. Higher index value means lower diversity.
4. Pielou’s evenness index : focus only on the evenness or distribution of species in both samples, not on richness. Higher index means higher richness.
5. Faiths phylogentic diversity: phylogenetic richness (sum of branch length of all present species in that sample) branch lengths represent the number of evolutionary or genetic changes between the species, decided by algorithms like ERaBLE (Evolutionary Rates and Branch Length Estimation).), to estimate the relative evolutionary rates of the genes employed in the analysis. Higher value means greater richness in sample.
6. For samples that contain rare and low count species (< 3 occurances of species within the sample), we use metrics like Chao1 and ACE Index (abundance based coverage estimator). In many use cases, we tend to filter away low relative abundance species before comparison so using these metrics may not provide additional information.

Example of how to interpret these metrics

alpha doversity implementation in python

In above image, lets say the samples_rel_abundances.csv represents 2 samples, each with their peculiar distribution of microbial species. The simplest point of comparison is richness, or the species count, which is 5 for both (see 0% for some species). If we had more for either samples, we could say that sample richer than the other. It would be worthwhile to mention that chao1 is identical to richness in this example since we do not have any singletons or doubletons.

Then, we look at the relative abundance of each sample, or the evenness with which these species are spread over both sample. So we look at shanon index, which is a simple sum of log_(relative_abundance_for_species_n) which gives us 1.5 and 1.2 respectively. Now, a value higher than 3 generally is typical for high species richness and high evenness (think, rainforest) while anything close to 1.5 or below represents few species dominance (like a desert landscape or polluted environment).

Very closely linked to shanon index is the pielou’s evenness which is essentially a relative comparison between the samples and uses shanon index as a reference. I have seen 2 interpretations of this index but essentially, higher value in this index means a more even, healthier distribution of species diversity. One method uses simple division of shanon index for each sample by the maximum index and the other method divides the shanon index by log of species richness for each sample.

Then we come to simpson index, which also serves the same purpose as shanon index and is based on probablity of random sampling. Finally, the phylogenetic distance which is used to calculate evolutionary distance between species of a sample, indicates differences in diversity between the samples. Low value of this index can indicate more close relationships (less diverse) or dominance of certain species in the sample. This means that for some samples even if the richness is high, the phylogenetic distance could be lower and hence indicate that it is less diverse from the perspective of evolution.

As some closing remarks, it would be useful to mention the benefits that we get with alpha diversity:

univariate and continuous measurements (simple to measure and compare directly against samples as they can be used relatively against each other, at different time points) easy downstream analysis for eg they can be used directly in linear regression or as predictor in modeling quick visualisation potential as scatter plots or discrete box plots (see image below for example)

QIIME data comparison via boxplots

After this stage of analysis is complete, more interesting questions arise regarding how can we differentiate 2 samples quantitatively, especially in terms of how distant or dissimilar they are. This brings us to the topic of beta diversity, one with some pretty visualizations and comparisons. To be continued in my next article…