Hello

Let aside the definition of "significant" which is very misleading and should probably banned in this context, I don't see why this would be impossible. It's also possible that something is messed up in your data :)

I would recommand you to plot an histogram of the pvalues under the null hypothesis, not only because it is a suspicious situation but also because it is always a good reflex to have with pvalues in general.

e.g : Plot the pvalues histogram from genes that you know for sure are not supposed to change in expression - even if in practice it can be a bit difficult to determine (I suppose your data are from a differential RNA-seq).

The pvalue histogram under the null hypothesis should be flat ! If not, there's a problem.

Then, independqntly of the H0 pvalues (which you might or might not be able to produce), plot all the pvalues histogram from all the genes together (you should be able to do so,

).

On this second histogram You should see a peak +/- around 0 (the alternative hypothesis, a.k.a differencially exprimated genes) and then a +/- sharp decrease until 1.

See http://varianceexplained.org/statistics/interpreting-pvalue-histogram/#:~:text=P%2Dvalues%20are%20specifically%20designed,that%20it%20doesn't%20fit.

Take attention to binning effects

If everything is right and you can exclude any bug in your code, then it seems possible for me that you have more ""significant"" qvalues than pvalues.

Especially I think this could happen when you are using an adaptative FDR control that depends on the true proportion of alternative hypothesis (e.g An "A la Storey" estimator) ...which seems to be the case if like I think your "qvalue" are defined by the paper of Storey and his related R bioconductor package.

You can have a better power (and therefore more ""significant"" results) with an adaptative FDR control t

over using only an arbitrary cutoff on the pvalues.

That's actually the whole point isnt it ?

So maybe I'm wrong but from my understanding it's not impossible at all... And you should keep this additonnal gene into account for your analysis at this chosen threshold.

Also keep in mind that if your FDR control is at 5% but you have 55 genes kept, the probability of having 0 false positive is (95%)^55 = 6%. So there is 94% of chances that at least one of your detections is a false positive one

If you're doing aprimary analysis that's fine. But if you're discussing each gene in details in a paper, you might want a simplified and more impactfull/straightforward interpretation at a FDR of 1% (where you might have really lots of chances that not any detection is a false positives). But you don't have to.

It's often insightfull to try many FDR control level and see what categories of genes stay when alpha decreases.

Be carefull also that all the assumptions described in Storey et al are met in your data (dependencies between pvalues, etc). Strictly speaking, all their theoretical assumptions will be broken on your real world data. The point is "how much" are they violated and "what does it change in my situation"