Both HMMER and BLAST report an e value for alignments. Is it calculated in the same way and - assuming that default settings are used - can they be compared directly (are the equivalent)? If not equivalent, what settings can be changed to make them equivalent?
They use very different algorithms so they should not have the same E-value. BLAST uses a position-independent substitution matrix (e.g. BLOSUM) while HMMER uses a position-dependent substitution matrix that is different for every profile. Check out the "Background and Brief History" section in the HMMER's user guide. It explains the conceptual differences at a very broad level.
Therefore, I don't think there's any way to make them equivalent.
E-value, in short, is a statistical measure of how likely it is that your sequence of interest could have arisen by pure chance. This definition is 'discipline-wide', so should be adhered to by any bioinformatics software that elects to provide it.
Thus, the longer and more complex your sequence is, the better (lower) E-value it will have when conducting sequence alignments.
As far as I am aware, they should be directly comparable. I don't see why they also wouldn't be calculated in exactly the same way.
HMMERs website does state that it utilises 2 different kinds of E-Value however:
The are then two E-values for the domain:
Conditional E-value - This is the E-value that the inclusion and reporting significant thresholds that are measured against (if defined as E-values). The conditional E-value is an attempt to measure the statistical significance of each domain, given that it has already been decided that the target sequence is a true homolog. It is the expected number of additional domains or hits that would be found with a domain/hit score this big in the set of sequences reported in the top hits list, if those sequences consisted only of random nonhomologous sequence outside the region that sufficed to define them as homologs.
Independent E-value - This is the significance of the sequence in the whole database search, if this were the only domain/hit that had been identified. If this E-value is not good, but the full sequence E-value is good, this is a potential red flag. Weak hits, none of which are good enough on their own, are summing up to lift the sequence up to a high score.
The calculation for E-Value via BLAST can be found here: