Should the least DE genes are the same as the ones with least tagwise dispersion in EdgeR ?

Question

[mohsamir2016]

Dear All, May be a naïve question, but buzzled me. I have a dataset where I created a DGElist object with TMM normalized count, and then estimated the tagwise dispersion from a design matrix.. code looks like :

dgeObj <- calcNormFactors(dgeObj)
design <- model.matrix(~Animal+Status)
y <- estimateDisp(dgeObj, design)
Tagwisedie<- y$tagwise.dispersion

From this code I obtained the 30 genes with the least Tagwise dispersion between two condition

I have also run DE analyses on the same dataset, and obtained the 30 genes that are the least DE between two condition

The question is : Should the 30 genes with least tagwise dispersion is the same as the 30 genes with least DE ?

In my hand it is not .. any comments ? or explanation

Thanks