Hello,

The question I would like to ask is : Using edgeR's GLM methode nested interaction between two explaining variable, one continous variable (unlinked to genotype), the second genotype, is this interaction affected by the compositional biases ?

The logic of my reasoning is as follow : Any potential compositional biases (such as differing sequences, slightly different length and normalisation), should not be affected differently by the continuous variable.

Are these assumption correct ?

experimental design

row            Condition                     Species
1                       0                                   0
2                       0                                   1
3                       0                                   0                            
4                       0                                   1
... 
10                      1.5                                   1
11                       1.5                                  0
12                      1.5       1

I assume the technical biases you are asking about are differences in GC content or gene length for the same gene between the two species.

Yes the technical biases should, in principle, cancel out of any interaction term. That would be so whether the interaction is species x factor or species x covariate.

I am not sure what your question is.

If you are concerned about the composition biases between samples, then the edgeR scale normalization (eg. TMM) would take care of it. It has nothing to do with the interaction between your explanatory variables.

If your question is about how to incorporate a continuous variable into the design matrix, then it depends on the number of time points you have in your data. If your data only has two time points, as shown in your design, then you can simply treat it as a two-level factor and proceed with the standard edgeR DE analysis pipeline.