A rebuttal to the comments on the genome order index

Recently, Elhaik et al. [Elhaik, E., Graur, D., Josic, K., 2008. 'Genome order index' should not be used for defining compositional constraints in nucleotide sequences. Comp. Biol. Chem. 32, 147] commented on the genome order index, which is defined as S=a(2)+c(2)+g(2)+t(2) where a, c, g and t denote corresponding base frequencies. They claimed that (1) "S<1/3 is in fact a mathematical property that is always true", and (2) "S is strictly equivalent to and derivable from the Shannon H function". The first claim is apparently wrong: for instance, when a=c=0.5, g=t=0, S=0.5>1/3. The second claim is also incorrect because S and H are different special cases of the alpha-order entropy, having different functional forms that are neither strictly derivable from nor equivalent to each other. Therefore, the conclusions made in their comments are wrong.