clear case of expression upregulation is not detected by CAGEE

[MichaelHiller]

Dear Developers,
we are trying to use CAGEE to detect genes that are up/downregulated in a particular lineage of 2 sister species.
We have 7 species in total and this tree.

We are running
cagee -t tree.nh -i expression_matrix.tsv -o run_default/result
with expression_matrix.tsv containing 12334 genes.

Our top-ranked gene has expression levels of 0.64 to 3.8 in the background species and several hundred fold higher values (1660 and 2794) in the two focal species, as shown in this tree.

CAGEE reconstructs that their common ancestor (node 10) has a value of 2078, which makes sense.
Node 9, representing the next ancestor, also has the expected low expression of 2.18.
This clearly shows that a "credible" upregulation occurred on the branch between node 9 and 10.
However, comparing the credible intervals of the parent and child, the intervals DO overlap, because the node 9 interval is very large 1.32 to 5013.05.

Could you pls have a look and check if this is a bug? All the ancestral node values make perfect sense but this credible interval seems to be too large.
And if the clearest case of upregulation is not credible, we can likely not use CAGEE for our analysis.

Thx for having a look
Michael

[hahnlab-user]

Hi Michael,

As far as I can tell, this is not a bug, but rather an honest rendering of the uncertainty in the ancestral node state. While I don't know exactly what value of sigma^2 was inferred, it was clearly high enough--and the time long enough--that the ancestral states are inferred with large credible intervals. This is clear within each of the two main clades, as well.

Given then that there is only one outgroup species, with quite a long branch to it and to the root from the main two clades, this is just not enough to really move the credible intervals (though of course the ML estimate at this node is quite low, as you note).

All of this is to say: there is clearly a large and biologically significant change in gene expression! There is nothing wrong with using the MLEs at each internal node to make this point, either. It's just that there is some small probability that the shift happened on more than one branch of the tree.

Matt

[MichaelHiller]

Thx Matt, much appreciated.

We will see if we can "play around" a bit with the data to see what happens if we artificially shrink the longer branch or add more outgroups. If this works, we can see if we find more matched expression data to add to the analysis.

To increase power, instead checking whether the 95% Credible Intervals of the expression values of the start and end node of a focal branch do not overlap, would it make sense to compute the posterior of the difference and checking whether its 95% Credible Interval excludes 0?

[hahnlab-user]

I will have to think about your question on the posterior of the difference. But note that most ancestral state reconstruction offers no uncertainty: they simply take the MLE of the ancestral states as the value. So I'm not sure there's anything directly wrong with doing them same if you wish.

[MichaelHiller]

I should say that I am not an expert in Bayesian stats, though I know the basics.
Perplexity said "Checking whether the 95% credible intervals of A and B overlap is not equivalent to checking whether A−B credibly differs from 0. Two marginal intervals can overlap even when the difference is very likely nonzero, because the overlap ignores the covariance/correlation between A and B. " So maybe this is worth doing.

Thx for the help and thoughts.

[MichaelHiller]

Hi Matt,
here are three artificial, best case scenarios to explore whether adding data from additional outgroups would make a difference.
Unfortunately, they don't. Everything stays pretty much the same.

Somehow the credible interval of [1.32 - 5013] captures the remote possibility that the ancestral expression value of ~2 changed to 1000+ on the branch leading to node 9, then stayed high in the Desmodus and Diphylla and shrunk massively from 1000+ to 4.16 in the shorter branch leading to node 11 (the sister group).

We are exploring this gene, because if we can't claim a credible expression shift for the clearest case, all other expression shifts of 4-fold or 10-fold also won't be credible.

Thx for your thoughts.

[MichaelHiller]

Sorry, my node labels still refer to the initial scenario.
For scenario 3, where the ancestral branch is much shorter, the sentence should read
Somehow the credible interval of [1.32 - 5013] captures the remote possibility that the ancestral expression value of ~2 changed to 1000+ on the branch leading to node 16, then stayed high in the Desmodus and Diphylla group and shrunk massively from 1000+ to 4.16 (upper end of the interval) in the shorter branch leading to node 13 (the sister group).

[hahnlab-user]

Those are very cool examples. But just to say again: it's not that shifts aren't "credible" just because the credible intervals of ancestral states overlap. It's just uncertainty in the reconstruction of ancestral states.