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As the title says I would like to know which alignment method(global or local) should I use for sequences for which is assumed that they have common ancestry?
The sequences are 21 aa long peptide chains (proteins).
About the background of the sequences, it's only stated that it's ASSUMED that they are from the same ancestry.
The thing that we assume that they are from the same ancestry makes me confused. I know that on similar sequences with the same length usually, we use global.
My initial reaction is that 21 amino acids is too little information to demonstrate these proteins are homologues (which is the question behind your question). A homologous site means it shares a common ancestry and is distinguishable from random chance or convergent evolution. A common ancestor can be demonstrated using phylogeny (trees).
If a regular alignment program cannot align these sequences, such as clustalo or muscle, the assumption they are homologues cannot be easily tested using phylogeny. That would then become complicated at which point you would need to ask whether it is worth pursing the question.
My recommendation is to perform a simple protein-protein blast and assess the e-scores to get some feel about you data. Your question is achievable, but you would solve this in context to additional sequence data. Whether that sequence data is a denser sample or else contiguous sequence data needs further exploration.
If you are trying to figure out the proteins' evolutionary history (e.g. if they are homologous) then you want a global alignment. In fact, there are very few cases where a local alignment is better, local is usually done only because it is far more efficient and less computationally expensive than global. But with tiny sequences of just as few residues such as the ones you have, you would want global almost every time.
The only case I can think of where you might prefer local alignment is when you have sequences that share little overall sequence similarity but you suspect they carry some sort of shared motif. For example, in proteins, that could be a protein domain. In that case, you would want to do a local alignment (possibly using something like blast) to identify those sub-regions of higher similarity.
Note that simple sequence similarity isn't really enough for you to decide whether they are indeed homologous. A more sophisticated approach such as psi-blast or HMMER will give better results. Nevertheless, a simple alignment will help you at least discard some obviously non-homologous sequences.
