Chao1 and Shannon negatively correlated

provira · July 21, 2022, 4:05pm

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

colinbrislawn · July 21, 2022, 9:10pm

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!

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

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

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

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