Chao1 and Shannon negatively correlated

Hello everybody,

I am reporting Chao1 (species richness) and Shannon (eveness) to characterize alpha diversity in different microbiomes. Both indexes are negatively correlated in my data: as Chao1 increases, Shannon decreases. Is that possible? I am having a hard time to find a biological interpretation. Any suggestion? Thanks in advance!

Pablo

Hello Pablo,

Yes! Here's the key detail:

Shannon measures both richness and evenness using a natural logarithm.

Chao1 measures richness in a really clever way:

Chao1 looks at all the taxa in a sample with counts of 2 or 1 and uses that to estimates the number of taxa that are truly in the sample but were not observed and reported a count of zero.

This is super different from Shannon.

high Chao1, low Shannon low Chao 1, high Shannon
high richness (especially with rare taxa), but uneven Lower richness (especially with rare taxa), but more even

Edit: Here's an example:

id Baseline No singletons Less even
1 90 90 140
2 50 50 50
3 50 50 50
4 50 50 2
5 2 2 2
6 2 2 2
7 2 2 2
8 2 2 2
9 1 2 1
10 1 2 1
11 1 2 1
12 1 2 1

Here's their alpha diversity stats:

group Chao1 Shannon
Baseline 13.2 1.571764
No singletons 12.0 1.627690
Less even 13.0 1.246139

Note how Chao1 is more affected by losing 1s then by a large decrease in evenness! :scream_cat:

Note how Shannon can detect both, and is also much more sensitive to changes in evenness.

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