I may be oversimplifying this a little but could you compare the observed number of differences between seqA and seqB (dist(seqA, seqB)) to the expected number?

The expected number will be a function of the overall number of differences observed on the full sequences:

per-site probability of observing a difference = (dist(fullA, fullB) / length(fullA)) 

expected number of differences = per-site probability * length(seqA)

Using the per-site probability you could calculate the cumulative probability of observing the result (same or different) across all sites. This would represent the probability of observing the differences between seqA and seqB given the number of differences observed between fullA and fullB.

I am afraid I am not well versed and don't having any literature to support the above.

Hi Aminael

If you have sequences from several individuals, you could use coalescent simulation in  DnaSP (http://www.ub.edu/dnasp/). Then you could compare the expectations derived from the full sequence (by Joseph's method or another) to those derived from the coalescent using the small sequences.

Dear Joseph,

Thank you for your answer!!! Indeed, Modolo et al. 2014 (http://10.1093/gbe/evu026) apply an approach similar to the one you described in your answer. They report that: the number of different nucleotides between the two sequences follow a Binomial(Ln,pn) distribution with Ln being the length of the pair of sequences of and pn the probability of having a nucleotide dissimilarity. A binomial test could then be applied to calculate  for each pair of sequences n the probability of having a number of different nucleotides lower than expected, or unilateral P-value.

Dear Pablo,

I will look at DnaSP to derive the expected nucleotide dissimilarities on the small sequence.

Thank you so much for the replies. 

Best,

Aminael