# Chao1 and Shannon negatively correlated

**URL:** https://forum.qiime2.org/t/chao1-and-shannon-negatively-correlated/23675
**Category:** General Discussion
**Tags:** best-of-the-forum
**Created:** [July 21, 2022, 4:05pm UTC](https://forum.qiime2.org/t/chao1-and-shannon-negatively-correlated/23675 "2022-07-21T16:05:28Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![provira](https://forum.qiime2.org/letter_avatar_proxy/v4/letter/p/ebca7d/32.png) [@provira](https://forum.qiime2.org/u/provira)
#### Post date: [July 21, 2022, 4:05pm UTC](https://forum.qiime2.org/t/chao1-and-shannon-negatively-correlated/23675/1 "2022-07-21T16:05:28Z")

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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

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### Author: ![colinbrislawn](https://forum.qiime2.org/user_avatar/forum.qiime2.org/colinbrislawn/32/6221_2.png) [@colinbrislawn](https://forum.qiime2.org/u/colinbrislawn)
#### Post date: [July 21, 2022, 9:10pm UTC](https://forum.qiime2.org/t/chao1-and-shannon-negatively-correlated/23675/2 "2022-07-21T21:10:57Z")

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Hello Pablo,

> [@provira](#):
>
> as Chao1 increases, Shannon decreases. Is that possible?

Yes! Here's the key detail:

> [@provira](#):
>
> Chao1 (species richness) and Shannon (eveness)

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.

> [@provira](#):
>
> I am having a hard time to find a biological interpretation.

| 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 |

 ![image](https://forum-qiime2-org.s3.dualstack.us-west-2.amazonaws.com/original/2X/4/410999818f88265e4a1d07f9417a86fd01926bc8.png)

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 |

 ![image](https://forum-qiime2-org.s3.dualstack.us-west-2.amazonaws.com/original/2X/1/196b9b165a6c41c4ed0d605db751483e22f355f9.png)

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

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