If I understood your question correctly, I believe that the dN/dS family of methods (which compare codons of aligned sequences) would be a possibility in your case. Check out Ziheng Yang and others' publications for details on that. He developed the PAML package, which implements many models of codon evolution to detect positive, neutral, or negative selection -- some look in the whole gene, others look codon by codon, etc.. I hope this helps.

Yaah, Ka/Ks (dN/dS) is a good measure for selection. If ks/ks>1, it is positive selection, if ka/ks < 1, it is balancing selection and neutral if Ka/Ks-=1. In case you want to model the distributions, you can use mixture models to identify the number of distributions (each distribution corresponds to one whole genome duplication). But there are other methods like Zhp, Pi ratios, Fst etc based on the comparisons you want to make (Ex: all paralogs of the genome).

In addition to Joao Alves answer, if you had the sequences from multiple individuals you can use polymorphism based tests such as the HKA test, McDonald-Kreitman test or Tajima's D (to name a few). These tests can be more sensitive to selection than dN:dS which requires a lot of non-synonymous changes to see a signal.

dN/dS (as implemented in PAML) but you will need a rooted tree to apply the branch AND site model. If you have within species data, you won't be able to use it but would rather use Ka/Ks, McDonald-Kreitman, Tajima's D, Fu&Li or HKA, etc... (which could still be interesting if you have several sequences for each pop). You can check this website:

http://wwwabi.snv.jussieu.fr/achaz/neutralitytest.html

You can also easily estimate a selection coefficient using this formula (From Hart and Clarke) :

-s = SQRT[(pt.q0)/(qt/p0)]-1

if you have access to allele frequencies across t generations (from 0 to t). This index is centered on 0 and a positive coefficient imply that p is favored over q.

Hope that helps