Allen - You are assuming that more data is always better. This is well known to be false within phylogenetics, although it is less well appreciated in most other disciplines. Statistical inconsistency can result in increasing the chance of inferring errors in the tree topology along with increasing estimates of confidence in those errors. This results in so-called long-branch-attraction in the 'Felsenstein zone'. Using AA sequences, or converting nucleotide sequences into AA sequences, even with the wrong reading frame or with non-coding sequences, can minimize this problem due to the greater number of character-states. Therefore, this is a distinct advantage for AA sequences. As you emphasize, this also involves throwing out lots of 'information', both useful and misleading, in the DNA sequences, which might be helpful in resolving short internodes in the tree.
AA sequences will provide information of elements that are more susceptible to micro/macro environmental selective pressure. If you use instead NT sequences you would expect more variability (of course this would depend if you use coding/non-coding regions). Of course a lot can be discussed here, but I think the question is the difference between NT or AA for the same homologous region, in which case, I believe the main topic would be if you do want to consider same-sense mutations on your analysis (NT) or not (AA).
Nucleotide sequence can be translate to protein sequence which complete the picture of phylogenetic analysis. My article: Genotyping and Phylogenetic Analysis of Cystic Echinococcosis Isolated from Camels and Humans in Egypt. American Journal of Epidemiology and Infectious Disease, 2014, Vol. 2, No. 3, 74-82
Available online at http://pubs.sciepub.com/ajeid/2/3/2
Due to the genetic code, most thrid-position mutations don't change the resulting aminoacid. Thus, two aminoacid sequences will be more conserved and similar between them than the related nucleotide sequences.
In some cases this increased conservation can increase the resolution of the phylogenetic relationships. For example, aminoacid translation is usaully used for phylogenomic studies.
for phylogeny, in this case you haven't an advantage in using the amino acid sequences compared to nucleotide sequences, as the latter generates much more information than the first (the amino acid sequence does not appear all mutations of the nucleotide sequence).
It depends on the degree of divergence between the sequences that you are studying. As Daniel pointed out, amino acid sequences end up being more conserved than the corresponding nucleotide sequences.
If you are interested in a recent radiation, nucleotide sequences might be more informative. On the other hand, if the divergence between groups is very old, nucleotide sequences will be less informative because they will saturate faster than ammoniated sequences (which means that a lot of the similarities in the sequences will be misleading and the result of multiple substitutions in the same position).
To answer your question directly, the biggest advantage to using AA sequences for phylogenetics, instead of DNA sequences, is they exhibit far less random homoplasy. This is because there are 20 different AA's, but only 4 different nucleotide bases. You didn't ask about the disadvantages, so I will leave it at this.
There is no advantage. This is illustrated by the fact that the DNA sequence can be converted into an AA sequence. When you do such a conversion, you are throwing out data. Even if much of that data is not phylogenetically informative, you can always decide to throw out some of that information later (i.e. throwing out third codon postions or throwing out transition substitutions). If you only have the AA sequences, you lose that option. Keeping all of the information will also increase the validity of NS substitution model selection.
Allen - You are assuming that more data is always better. This is well known to be false within phylogenetics, although it is less well appreciated in most other disciplines. Statistical inconsistency can result in increasing the chance of inferring errors in the tree topology along with increasing estimates of confidence in those errors. This results in so-called long-branch-attraction in the 'Felsenstein zone'. Using AA sequences, or converting nucleotide sequences into AA sequences, even with the wrong reading frame or with non-coding sequences, can minimize this problem due to the greater number of character-states. Therefore, this is a distinct advantage for AA sequences. As you emphasize, this also involves throwing out lots of 'information', both useful and misleading, in the DNA sequences, which might be helpful in resolving short internodes in the tree.
Guy - I don't disagree with any of that. I am just saying that if you have the DNA sequences, you have the option of looking at these things and deciding what to do. If you have only the AA sequences, you don't know if there was more useful information in the DNA sequences.
Allen - I agree. The original question was strictly about advantages, and I would still argue that more character states are better than fewer for phylogenetics independent of the other factors.
Guy - I see your point. I would love to have that argument sometime. I love to argue about this stuff! Given that Mahmoud has only AA sequences already, your answer is probably more useful to him.
Mahmoud - Good luck! I hope this was a little helpful.
Thanks to All who discussed my question and I saw all your points that were helpful for me. But I have a question if I have nucleotide sequences, Can I transform it to AA sequences and then construct a phylogenetic tree, will this lead to the same results with nucleotides-based phylogenetic tree?
As Guy has said, any variance in the data can result in differing tree topology. If you're after a quick and easy method of translating nucleotide data to an amino-acid alignment, MEGA is pretty good. You can easily shift reading frames/edit sequence data prior to anaylses too.