Why the Shanon divesity trend looks opposite to Faith's diversity ?

Hello! I was running alpha diversity for cervical samples microbiota. The samples were diveded across the cytology from control (NILM) to squamous cervical cancer (SCC). I observed an opposite trend beween Shannon diversity and Faith' diversity. Please can you help me to understand?
Thank you!

Hello and welcome to :qiime2:!

Metrics are just an attempt to quantify differences in the community, they are very different in the calculation with their pros and cons.

Faith PD and Shannon are different:

Faith PD: sum of the lengths of all those branches on the tree that span the members of the set.
So higher values mean that there are some phylogenetically distant bacteria in the sample.
Shannon: a measure of entropy, calculated by the following formula:
H' = - \sum_{i=1}^{S} (p_i \ln p_i)
Where pi is the proportion of bacteria in the community. It will give a higher value to samples, where there is many bacteria & the proportion of ALL bacteria is roughly equal.

I assume, that in your case higher Faith PD values show more distant phylogenetically bacteria occurring in samples. Together with decreasing Shannon index, it may mean that the abundance of these distinct bacteria is low. However, further inspection of the data is needed to prove it.

The trends are indeed opposite, but they don't contradict each other.



Thank you! It was helpful! I thought the same, but I want to be sure.

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